International Journal of Mathematics in Operational Research (111 papers in press)

Regular Issues

• New Weibull-Pareto Poisson Distribution: Properties, Actuarial measures, and Applications  
  by Fastel Chipepa, Mavis Pararai, Wilbert Nkomo 
  Abstract: A new power series distribution called the new Weibull-Pareto Poisson distribution is developed. The proposed model is very flexible in modelling heavy-tailed data. Some of the statistical properties are also derived and these include moments, moment generating function, and R
  Keywords: Weibull-Pareto distribution; power series distribution; maximum likelihood estimation; risk measures; poisson distribution.
  DOI: 10.1504/IJMOR.2023.10059698
   
  
• Joining Strategy for Double Orbit Retrial Queue with Imperfect Service and Vacation under N-policy  
  by Palak Mehta, Madhu Jain 
  Abstract: Optimal joining policy for Markovian retrial queueing system operating under N-policy and having ordinary and premium orbits, has been investigated. There is provision of additional service to the unsatisfactory ordinary orbit customers whereas unsatisfactory executive orbit customers may re-join the queue as a feedback customer. The proposed queueing system is investigated by implementing probability generating function (PGF) approach and evaluating various performance measures. Numerical experiments are performed to validate the analytical metrics obtained. The adaptive neuro fuzzy inference system (ANFIS) approach has also been implemented to authenticate the feasibility of intelligence computing for various metrics. The optimal joining probability is obtained by maximising the profit function value using particle swarm optimisation (PSO). The sensitivity of the queueing indices along with cost function has also examined by conducting the numerical simulation.
  Keywords: double orbit retrial queue; N-policy; imperfect service; feedback; joining strategy; particle swarm optimisation; PSO.
  DOI: 10.1504/IJMOR.2023.10059879
   
  
• Integrated Management and Optimization of Vaccination and Treatment Processes in a Batching System with Observation and Limited Space  
  by Ayyappan G, Sankeetha S 
  Abstract: This study examines a single-server system that incorporates multiple vacations. Customer arrivals adhere to a Markovian arrival process (MAP), and two types of service are applied, both following a phase-type distribution. Upon arrival, customers are grouped into batches of size L. Following service, customers enter an observation room, waiting for a predetermined duration. Subsequently, customers either leave the system if comfortable, or they join queue 2 for further service if not. Queue 2 follows a non-preemptive policy guided by the server. In the absence of customers, the server experiences multiple vacations following an exponential distribution. The server remains idle if customers are in the observation hall or if the number of customers in queue 1 is below L. This intricate system is represented as a quasi-birth-and-death (QBD) process, which we analyse using matrix-based methods. Also analysing the busy period, invariant probability, and performance metrics through graphical and numerical approaches.
  Keywords: Markovian arrival process; MAP; phase type service; multiple vacation; bulk service; non-preemptive priority.
  DOI: 10.1504/IJMOR.2023.10059922
   
  
• A New Heavy-Tailed Generalized Exponentiated Half Logistic-G Distribution with Actuarial Measures and Applications  
  by Thatayaoner Moakofi, Agolame Puoetsile, Broderick Oluyede 
  Abstract: This work introduce and investigate the new heavy-tailed generalised exponentiated half logistic-G (HT-GEN-EHL-G) family of distributions. The study involves the derivation and analysis of statistical properties associated with HT-GEN-EHL-G distribution. Employing the maximum likelihood estimation technique, we estimate model parameters and evaluate the consistency of these estimators through simulation studies. Additionally, we develop actuarial metrics (risk measures) tailored to this distribution. The practical utility of the HT-GEN-EHL-G family of distributions is demonstrated through the analysis of four real-life datasets from diverse fields. These applications emphasise the significance and versatility of the newly introduced HT-GEN-EHL-G family of distributions.
  Keywords: heavy-tailed distribution; exponentiated half-logistic-G distribution; estimation; applicability.
  DOI: 10.1504/IJMOR.2023.10059923
   
  
• Optimized Variable Step-Size Algorithm for the Solution of Dynamical Systems  
  by Joshua Sunday, Richard Olatokunbo Akinola, Joshua Amawa Kwanamu, Dominic Raymond 
  Abstract: This study focuses on the formulation of optimised variable step-size algorithm (OVSSA) for the solution of dynamical systems. In order to minimise the number of iterations and number of steps taken as well as improve the accuracy of the proposed algorithm, an embedded strategy was deployed in formulating the method using variable stepsize mode. One of the major advantages of the proposed OVSSA is that the algorithm automatically fine-tunes (or adjusts) the stepsize to suit the problem under consideration according to the variable stepsize strategy defined by the authors. Convergence properties of the OVSSA were also analysed theoretically in order to validate its stability and computational reliability. The OVSSA was employed in solving dynamical systems like the Van der Pol, Genesio-Tesi, Kepler and Lorenz systems. The results generated as a result of the application of the OVSSA on dynamical systems clearly showed that the method is convergent and computationally reliable.
  Keywords: algorithm; chaos; convergence; dynamical system; fixed stepsize; initial value problem; optimise; stability; stiffness; variable stepsize.
  DOI: 10.1504/IJMOR.2023.10060082
   
  
• A Queueing Model with Balking, Server Vacation and Working Breakdown  
  by Kamlesh Kumar, Dr. Madhu Jain 
  Abstract: This paper focuses on a single server queueing model that includes customer's balking, server vacation, and working breakdown. When there is no customer in the system or the system becomes empty, the server goes on a vacation and returns back when one or more customer available in the system. The server resumes service to the customers accumulated during its vacation period. There is always the possibility of a server breakdown while providing services to the customers, which may result in slower service rate. Slower service rate is considered as working breakdown state of the server or a defective mode of service. If the server is providing normal or defective service, customers may balk. For the system states, some practicable performance measures such as average number of customers in the system, average total cost function, and system throughput have been established for the various system states.
  Keywords: Markovian queue; balking; server vacation; working breakdown; probability generating function; PGF; cost function.
  DOI: 10.1504/IJMOR.2023.10060110
   
  
• A multi-machine bicriteria flow shop scheduling with sequence dependent setup time  
  by Meenakshi Sharma, Sameer Sharma, Nidhi Joshi 
  Abstract: Bicriteria flow shop scheduling problem with sequence dependent setup time (BPFSSP/SDST) is addressed in this paper. The objective of scheduling problem is to minimise weighted sum of makespan and system utilisation time, when both criteria are equal weighted. To solve the referred scheduling problem in small size machine-job environment, a mixed-integer programming model is developed and implemented. Since permutation flow shop scheduling problem with SDST is NP-complete in nature, therefore, the heuristic approach based on Nawaz, Enscore, Ham (NEH) neighbourhood structure and metaheuristic approach of hybrid iterated greedy algorithm with delay time, are proposed and implemented to optimise aforementioned scheduling bicriteria. The computation experiment is carried out to evaluate the performance of all developed heuristics and metaheuristics on varying size job-machine environment. The comparative analysis reported with response variable average relative percentage deviation (ARPD) verifies the effectiveness of proposed computation techniques over existing ones in solving the referred scheduling problem.
  Keywords: Scheduling; bicriteria; sequence dependent setup time; iterated greedy algorithms; local search.
  DOI: 10.1504/IJMOR.2023.10060188
   
  
• Recital facts of MX/G/1 Queues with Setup Time, Phases of Service, and Vacation  
  by S. Maragathasundari, K. Karthikeyan 
  Abstract: Researching group queueing systems that combine setup time and vacation work stages into a single server service is the aim of this MX/G/1 queueing study. In this queueing system, arrival time follows the Poisson distribution and service time follows a general distribution. The model is well equipped with setup time phases to do both a key maintenance task during the break and the necessary server pre-processing job. Additionally, the system is unavailable during the disruption because service disruptions are inevitable. The aforementioned mathematical queueing problem is solved using the supplemental variable technique, and the system’s performance metrics are obtained. From the calculated probability generation function of queue size at a random time for the different system states, we extract performance measures such as the server’s probability of idle time, the utilisation factor, the average queue length, and the average wait time. It is backed by methods for numerical portrayal, graphic representation, and real-world applications. This paradigm is entirely legal due to its practical use and algebraic demarcation mechanism. The graph provides precise readings of the implemented limitations.
  Keywords: non-Markovian queueing problem; batch arrival; supplementary variable technique; setup time stages; vacation; service interruption.
  DOI: 10.1504/IJMOR.2023.10060301
   
  
• Strong Perturbation Bounds for the Stationary Distribution of the Main Multiserver Retrial Queue Model  
  by Nabil Ait Yala, Badredine Issaadi, Karim Abbas 
  Abstract: Many queuing models are represented by Markov chains with infinite countable state space and we will often want to know their stationary distributions in order to deduce their characteristics, but the calculation of these distributions is generally difficult, if not impossible, and do not have closed form solutions because of the infinite number of equations to solve. This is why researchers try to obtain approximations that converge quickly to these distributions. Perturbation theory for Markov chains addresses the question of what impact can occur on a stationary distribution of a Markov chain if its transition matrix is slightly disturbed. In this paper, we use the strong stability approach based on the drift condition to establish analytic error bounds for the generalised truncation of a main multi-server retrial queue model. At the end of this article, we give numerical examples in order to show the quality of the error bounds obtained.
  Keywords: Markov chains; perturbation theory; truncation; strong stability; Lyapunov function; drift condition; retrial queueing systems.
  DOI: 10.1504/IJMOR.2023.10060302
   
  
• Solving the Vehicle Routing Problem with Search Algorithms: A Comparative Analysis  
  by Oladimeji Samuel Sowole  
  Abstract: The vehicle routing problem (VRP) is a well-known optimisation problem in operations research, with applications in logistics, transportation, and supply chain management. This paper offers a comparative analysis of search algorithms used to solve the VRP, focusing on their strengths and weaknesses. It introduces the VRP and its variants, highlighting the challenges and constraints involved. Various search algorithms, such as genetic algorithms, simulated annealing, and ant colony optimisation, are examined, discussing their principles, advantages, and limitations. Real-world case studies in package delivery, waste collection, and emergency response demonstrate the application of these algorithms. Factors influencing algorithm performance, including problem size, complexity, and parameters, are discussed. Recommendations for selecting appropriate search algorithms for different VRP instances are provided. The paper aims to provide readers with a comprehensive understanding of using search algorithms to solve the VRP, aiding decision-making in similar optimisation problems.
  Keywords: vehicle routing problem; VRP; search algorithms; metaheuristics; ant colony optimisation; ACO; particle swarm optimisation; PSO; genetic algorithms.
  DOI: 10.1504/IJMOR.2023.10060409
   
  
• Optimal joint dynamic pricing and inventory replenishment policy for perishable products with freshness-sensitive demand  
  by Mahmoud Dehghan Nayeri, Roghaye Haddad 
  Abstract: This paper aims to propose a mathematical model for joint pricing and inventory replenishment decisions of a retailer who faces a freshness-sensitive demand. The retailer has the option to submit fast replenishment orders with lower profit margins to other peer retailers within the short lifecycle of the perishable products in addition to the regular replenishment orders that take place at the start of the lifecycle. Also, the retailer can sell the end-of-season perished product at lower prices. The proposed model is capable of handling different types of demand and freshness functions. To show the applicability of the proposed model, it is used to optimise pricing, discounting, inventory, and replenishment decisions of two product categories of a major retailer in Iran using real-world data. Results indicate that the retailer should pursue a specific joint pricing and replenishment strategy in each product category. A sensitivity analysis is also performed for initial inventory and initial price for each of the categories. Results revealed that each of the factors contributes differently to the total profit in each category. The total profit showed a different level of sensitivity to changes in the two aforementioned tweaked parameters.
  Keywords: dynamic pricing; inventory management; perishable products; inventory replenishment.
  DOI: 10.1504/IJMOR.2023.10060510
   
  
• Analysis of Non-Markovian batch arrival retrial queue with priority services, Vacation and Vacation Interruption Under Random Environment, Negative Arrival, Immediate Feedback, Differentiate Breakdown, Repair  
  by Ayyappan G, NITHYA S 
  Abstract: In this study, we construct a single server retrial queueing system with two classes of customers, vacation and vacation interruption under random environment, negative arrival, immediate feedback, differentiate breakdown and repair. Customers can be divided into two distinct categories, such as priority and ordinary. This concept emphasises non-preemptive priority discipline. Customers arrive according to Poisson processes for priority and ordinary. The server constantly offers a single service for both priority and ordinary customers, and the service is distributed arbitrarily. In this study, we compute the Laplace transforms of the time-dependent probabilities of system states using the probability generating function and supplementary variable technique. Numerical results are obtained which are also examined to facilitate the sensitivity analysis of system descriptions.
  Keywords: Batch Arrivals; Priority Queues; Vacation and Vacation Interruption Under Random Environment; Negative Arrival; Immediate Feedback; Differentiate Breakdown; Repair.
  DOI: 10.1504/IJMOR.2023.10060515
   
  
• A Transient M[x]/M(k,k)/1 Queue with Reneging and Setup Time for Service  
  by Aliakbar Montazer Haghighi, Dimitar Mishev 
  Abstract: In this paper, we analyse a transient queuing model, in which tasks arrival in bulks of varying sizes with compound Poisson process, there is a single server serving batches of tasks with limited sizes with a minimum and a maximum, according with exponential distribution, with setup times for service with also exponential distribution, and impatient tasks that may renege while the server is busy with also exponential distribution. The transient probability generating function for the number in the system, special cases to verify it and some performance measures have been found.
  Keywords: transient queue; Markov process; Poisson; reneging; exponential service; setup time; probability generating function; moments.
  DOI: 10.1504/IJMOR.2023.10060539
   
  
• IOT-Botnet Attack Detection and Mitigation using Ensembled-Deep-Learning-Model  
  by Swapna Thota, D. Menaka 
  Abstract: In this study, we propose an ensembled deep learning model for robust IoT-botnet attack detection. The model comprises six phases: data preprocessing, data augmentation using SMOTE, feature extraction (central tendency, dispersion, and information gain), feature selection using the clan updated grasshopper optimisation algorithm (CUGOA), and attack detection. The detection model integrates DCNN, attention-based bi-LSTM, and optimised RNN, with fine-tuning using CUGOA. When an attack is detected, our new botnet traffic filter (BTF) mitigates it, enhancing network reliability. Our model outperforms existing approaches in terms of accuracy, sensitivity, specificity, and precision.
  Keywords: botnet; internet of things; deep learning cyber security; intrusion detection.
  DOI: 10.1504/IJMOR.2023.10060717
   
  
• An Inventory model with hybrid time-stock dependent demand for Seasonal products with trade credit policy  
  by Prokash Mondal, Sudhansu Khanra, Pritha Das 
  Abstract: This study examines an EOQ model with a hybrid time- and stock-dependent demand function for a seasonal product context of shortages. In several marketing strategies that have a strong connection to stock time and stock both play a crucial role in customer decision-making vendors always entice customers to buy more by displaying many products. This investigation aims to present the best inventory management technique for perishable products with hybrid demand that is time- and stock-dependent under partial backlog with a trade credit policy. The provided EOQ model is validated using a numerical illustration. Finally, sensitivity analysis has been employed to examine the effects of changes in the values of system factors using MATLAB software (Version 2014a).
  Keywords: inventory; time-stock dependent demand; partial backlogging; deterioration; trade credit policy.
  DOI: 10.1504/IJMOR.2023.10060978
   
  
• A study of transient solution of fractional M/M/2 queue with homogeneous and heterogeneous servers  
  by Nanduri Sujatha, GVSR Deekshitulu 
  Abstract: In queuing models with multiple servers, all the servers may not be completely active and may not work with same efficiency. Keeping this in view, a multiserver fractional queue with heterogeneous servers has been analysed in the present paper. Transient state probablities and also performance measures of the model such as average number of customers in the system, average number of customers in the queue, etc. have been computed. Variations in these performance measures have been observed both numerically and graphically with respect to partial activity of the server. Further, efficiency of transient M/M/2 fractional queueing model consisting of heterogeneous servers is compared with efficiency of transient M/M/2 fractional queuing model with homogeneous servers.
  Keywords: transient solution; fractional queue; Mittag-Leffler function; heterogeneous servers.
  DOI: 10.1504/IJMOR.2023.10061079
   
  
• Job Shop Scheduling in Wafer Fab with Random Job Arrivals using Hybrid Tabu Search  
  by Rosshairy Abdul Rahman, Kean Heong Lee, Syariza Abdul-Rahman, Azhar Mahdi Ibadi 
  Abstract: Job shop scheduling (JSS) plays an important role in the manufacturing sector to minimise makespan and avoid bottleneck situations. Wafer fabrication (Wafer Fab) is a costly and complex manufacturing system that demands several billion dollars investment with many repeated processes. Scheduling of Wafer Fab is vital to produce wafers and to achieve on-time delivery to customers. As such, this study proposes a hybrid tabu search model to solve JSS problem by minimising makespan while concurrently maximising the average machine utilisation. Initially, the concept of bin packing was deployed to obtain the initial solution using random greedy algorithm. Tabu search algorithm (TSA) was then employed to enhance solutions around the neighbourhood area. The findings successfully improved the schedule of jobs in Wafer Fab manufacturing, where the enhancement of 6.2% in makespan minimisation was achieved. Thus, it shows the ability to utilise the machines equally and avoid bottlenecks in Wafer Fab manufacturing.
  Keywords: job shop scheduling; JSS; random greedy bin packing; Wafer Fab; tabu search algorithm; TSA; makespan; manufacturing; tabu tenure size; metaheuristics.
  DOI: 10.1504/IJMOR.2023.10061422
   
  
• Optimizing inventory in business environments: Combining matrix analytic methods with a working vacation, cancellation policy, and working breakdown  
  by Ayyappan G, N. Arulmozhi 
  Abstract: The inventory system of the single-server Markovian arrival process with working vacations, working breakdowns under a Bernoulli schedule, and cancellation policy are discussed. The server begins to go on a working vacation when there is no customer in the system even if the inventory level is positive. If any customers arrive while he is end of his working vacation time, a normal busy period begins. If not, he will simply remain idle in regular mode. When a system breaks down, it either offers slowservice to the current customers with probability p or immediately undergoes a repair phase with probability q. We derive the invariant vector, busy period, waiting time distribution, total cost, and computation of performance measures using the matrix analytic technique.
  Keywords: Markovian Arrival Process; Phase-type service; (s,Q) policy; Working vacation; Working breakdown; Cancellation policy.
  DOI: 10.1504/IJMOR.2023.10061482
   
  
• Analysis of MAP/PH/1 Retrial Inventory Queueing System with Phase type Vacation and Unreliable Server  
  by Ayyappan G, MEENA S 
  Abstract: In this study, a retrial queueing inventory system with a fixed retrial rate, single vacation, breakdown, and repair is investigated. We have made the assumption that customers arrive through a Markovian arrival process and that the server will offer phase-type services to them. The (s, S) policy is used to replenish the inventory, and it is anticipated that the replenishing time will follow an exponential distribution. The server goes on vacation if there are no consumers in the orbit, or zero inventory, or both. When a server breaks down, it quickly starts the repair process, and the customer enters the infinite size of the orbit. In the steady state, it is possible to determine the number of customers in the orbit, the inventory level, and the status of the servers. The cost analysis is derived, and several significant performance measurements are established. Furthermore, a few numerical demonstrations are given to clarify our mathematical model.
  Keywords: Queueing-inventory; Markovian Arrival Process; Phase-type distribution;(s; S)-type policy; Retrial; Single Vacation; Breakdown and Repair; Matrix Analytic Method.
  DOI: 10.1504/IJMOR.2023.10061611
   
  
• On Efficient Solutions to Bi-objective Max-Linear Programming Problems  
  by Abdulhadi Aminu, Sunday Olowo, Salusi Usaini 
  Abstract: A number of methods for determining solutions to max-linear programming problem with one objective function have been developed. In this work, we introduce the concept of bi-objective max-linear programming problem subject to two sided constraints (BOMLP) for both minimisation and maximisation cases, then we proposed two methods for determining efficient solutions to the problem and developed improved algorithms based an alternating and bisecting method of solving two sided max-linear system. Performance of the methods were compared based on effectiveness, user friendly and task time, in fact the second method is found to be faster than the first method, some numerical examples were considered to test the problems and using MATLAB software .
  Keywords: bi-objective max-linear programming; two-sided system; optimal solution; efficient solution; pseudo-polynomial algorithms.
  DOI: 10.1504/IJMOR.2023.10061663
   
  
• An Enhancing IOT Security with a Trinary Deep Learning Paradigm and Squirrel Reptilian Optimisation  
  by K. Navaz, Muthuvairavan Pillai.N, G. Shanmugasundaram, T.Rajesh Kumar, C. Jehan 
  Abstract: This research work proposes a novel approach for IoT intrusion detection using a trinary deep learning paradigm. The proposed model aims to address the challenges of large data requirements and false positives commonly encountered in IoT network security. The model consists of four phases: pre-processing, multi-modal feature extraction, optimal feature selection, and intrusion detection. Initially, the collected raw data is pre-processed using data cleaning techniques and Z-score normalisation, which helps to standardise the data for further analysis. Following pre-processing, multi-modal feature extraction techniques are applied, including measures of central tendency, database features, statistical dispersion, and information entropy-based features. To select the most relevant features from the extracted set, the squirrel reptilian optimisation algorithm is employed. SRO combines the squirrel search algorithm and reptile search algorithm to optimise feature selection, ensuring that only the most informative features are utilised for intrusion detection.
  Keywords: IoT; intrusion detection; multi-modal feature extraction; squirrel reptilian optimisation algorithm; SRO; trinary-deep-learning-paradigm; CNN; RBFN; RBM.
  DOI: 10.1504/IJMOR.2023.10061665
   
  
• A Markovian two server queue with state dependent hybrid service discipline  
  by Kalyanaraman R, B. Anurathi 
  Abstract: A Markovian two server model is constructed by assuming a new concept. The concept is that upto the service of N customers, the two servers acts as homogeneous servers after which the servers acts like heterogeneous servers. In practice, in particular, if the servers are human beings, they cannot serve in the same spirit till the end of the busy period.~These practical situations leads to study of queues with heterogeneous servers.~This model is analyzed in steady state by deriving the difference equations and applying the recrussive concept for solution.~For this model the waiting time distribution and some system performance measures are obtained, particular cases are derived.~The practical applicability of the model is tested by presenting some numerical illustrations. A cost model is developed by defining the total expected cost function and also sensitivity analysis is carried out to investigate the effect of system parameters on the expected cost function.
  Keywords: two server queue; homogeneous server; heterogeneous server; performance measures.
  DOI: 10.1504/IJMOR.2023.10061666
   
  
• A Healthcare Divisions Inventory Model for Deteriorating Items with a Variable Deterioration Rate Under Permissible Delay in Payments  
  by Mukesh Kumar, Manoj Kumar Sharma, Ajay Sharma, Shalu Chaudhary 
  Abstract: The deterioration of medicines is an extensive trend in the healthcare sector. There are a lot of medicines and pharmaceutical products, such as generic injectables, caplets, ophthalmic liquids, ointments, tablets, etc., that have short expirations; therefore, there is a requirement to develop methods to use them within their expiration time. Most of the public health system encounters this problem frequently occurs. To solve this problem, the authors developed an inventory model based on four features of the healthcare sector: time-dependent demand rate, holding cost, deterioration rate, partially backlogged shortages in demand, and credit period offered by pharmaceuticals. We also considered the time duration, which is free from interest on credit, and the rate of interest. However, the hospitals have the reserve money to make the payments at the beginning, but they decide to take advantage of the credit period. We validated this model by using a numerical example and explaining the sensitivity analysis.
  Keywords: inventory; demand; pharmaceutical products; deterioration and permissible delay payments.
  DOI: 10.1504/IJMOR.2023.10062077
   
  
• A Genetic algorithm combined with mathematical programming to solve Generalised Quadratic Multiple Knapsack Problem  
  by Yassine Adouani 
  Abstract: In this paper, the generalised quadratic multiple knapsack problem (GQMKP) is tackled with an efficient hybrid approach, called GA&IP, which combines a binary genetic algorithm (GA) with integer programming (IP) to solve the GQMKP problem. In the GA&IP approach, a linearisation technique is used to transform the GQMKP into a linear problem called LGQMKP. After that, the LGQMKP is transformed into several dependent classical knapsack problems using a GA. Finally, an IP algorithm is applied to optimally solve each knapsack problem. The effectiveness of the GA&IP approach is demonstrated through experimentation on 96 diverse benchmark instances that are commonly used in the field. Experimental results show the effectiveness of the proposed GA&IP in solving the GQMKP problem and the hybridisation with integer programming can enhance the genetic algorithm.
  Keywords: generalised quadratic knapsack problem; genetic algorithm; integer programming.
  DOI: 10.1504/IJMOR.2023.10062398
   
  
• Analysis of Markovian Queuing Model with Two Phase of Services, Single and Multiple Working Vacations and Customer Balking  
  by K. Baby Saroja, V. Suvitha 
  Abstract: We analyse a single server balking queueing model with featuring two phases of service in series. During the first phase, customers receive individual service, and in the second phase, they have the option to choose between two distinct services based on their specific needs and receive batch service. To optimise resource utilisation, the server enters a working vacation when there is no customer in the system. We apply the Probability Generating Method to comprehensively analsze the system, considering both single and multiple working vacations. This research underscores the application's adaptability in addressing intricate data processing challenges within the queuing framework. Furthermore, we provide numerical results to demonstrate how the model performs under various conditions.
  Keywords: Two Phases in Series; Working Vacation; Balking; Batch Service.
  DOI: 10.1504/IJMOR.2023.10062491
   
  
• Enhancing Reliability and Performance of Sequential Chiller System using Copula  
  by Ameer Hassan Abdullahi, Abdulhadi Aminu, Ibrahim Yusuf 
  Abstract: Chiller systems play a pivotal role across various industries, providing essential cooling solutions. Ensuring their efficiency and reliability necessitates precise performance evaluation. The Gumbel-Hougaard family copula, an efficient approach for modelling multivariate dependencies, is used in this paper to carry out an in-depth examination of chiller machine systems. Through this method, we can capture intricate correlations between chiller system characteristics and performance metrics such as reliability, availability, mean time to failure (MTTF), cost and MTTF sensitivity. We further conducted sensitivity analysis using our copula-based model to identify key factors influencing chiller system performance. The efficacy of the copula-based approach in capturing intricate relationships between several chiller system features and critical performance measures is exemplified by numerical findings that are displayed in tables and graphs. We can make conclusions about the results since they have been validated using quantitative data and can be seen in tables and graphs. This deeper understanding will assist us in optimising system operations for improved cost-effectiveness and energy efficiency. Additionally, our copula-based approach enhances performance evaluation compared to traditional methods by allowing us to assess the system's resilience under varying operational conditions.
  Keywords: availability; efficiency; chiller systems; series-parallel system; transition diagram.
  DOI: 10.1504/IJMOR.2023.10062578
   
  
• Balancing Sustainability and Profitability in Inventory Management: Insights into Carbon Emissions, Consumer Demands, Payment Strategies, and Green Investments  
  by Manoj Kumar Sharma, Neha Rani, Anshika Rajpal 
  Abstract: Optimising inventory management practices is paramount in a world increasingly concerned with environmental stewardship. The present study focuses on four main aspects: 1) reducing carbon emissions; 2) responsiveness to price and freshness-dependent consumer demands; 3) evaluation of payment schemes; 4) assessment of investments in preservation and green technologies. By addressing these fundamental components of inventory management, the article offers valuable insights and practical recommendations for businesses striving to align their operations with sustainability goals. Achieving sustainability in inventory management contributes to environmental conservation and enhances competitiveness and long-term profitability. Payment methods wield significant influence in inventory management, impacting cash flow, supplier relations, and sustainability efforts. They serve as tools for sustainability, highlighting the trade-off between cash flow and environmental stewardship. Finally, a few computational instances and sensitivity analyses demonstrate the suggested model's features. The results and sensitivity analysis show that controllable carbon emissions favourably impact overall inventory model profit.
  Keywords: inventory management; carbon emissions; price and freshness dependent demand; comparison of payment scheme; preservation technology investment; green technology investment.
  DOI: 10.1504/IJMOR.2023.10062609
   
  
• Enhanced non-dominated sorting genetic algorithms for fuzzy multi-objective multi-route shortest path problem  
  by Aniket Todkar, Jayesh Dhodiya 
  Abstract: This study examines a fuzzy multi-objective multi-route short path problem (FMOMRSPP) by transforming it into a crisp multi-objective multi-route shortest path problem (MOMRSPP) using possibility distribution. Using -level sets, fuzzy judgement is categorised for the decision maker (DM) to optimise fuzzy objective function scenarios. This paper proposes aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and AL-based NSGA-III to obtain a Pareto-optimal solution that meets DM AL for the FMOMRSPP. A numerical example has been provided to demonstrate the usage of the presented methodologies. A comparison is presented between the proposed and several other approaches. The sensitivity of objective functions is also investigated with ALs and shape parameters. The coverage is determined to evaluate the effectiveness of the proposed methods.
  Keywords: multi-objective multi-route shortest path problem; MOMRSPP; NSGA-II; NSGA-III; aspiration level.
  DOI: 10.1504/IJMOR.2023.10062616
   
  
• Manufacturing supply chain with considering carbon cap policy and revenue from deteriorated items  
  by Santosh Shekhawat, Kalpna Sharma 
  Abstract: In presenting paper, a deteriorating nature inventories manufacturing supply chain studied. It is assumed that deteriorated and rejected inventories, instead of throwing out can be utilised to generate revenues which helps to increase profit, reduce carbon emissions, and solve the problem of disposal of deteriorated inventories. Price is an important factor that plays a decisive role for deteriorating nature inventories supply chain. The objective of the work is to establish a optimise profit model with some certain conditions. To authenticate the mathematical model a numerical example is considered. This work focused on utilise deteriorated inventories and reduce carbon emission. The use of deteriorated inventories at initial level of decay increases revenues, promote the balance utilisation of resources and decrease emission. This work is beneficial for manufacturers dealing with deteriorating inventories by providing mathematical design for deteriorated inventories utilisation, emission reduction emission and increase revenue.
  Keywords: deteriorating inventory; carbon emission; selling price-dependent demand; carbon cap.
  DOI: 10.1504/IJMOR.2024.10062716
   
  
• An adaptive hybrid direction algorithm for convex box-QP problems with enhanced pre-solving  
  by Abdelhek Laouar, Mohand Ouamer Bibi 
  Abstract: In this paper, we propose a new algorithm for solving quadratic programming problem with box constraints. The principle of the algorithm is to apply a preprocessing procedure to reduce the original problem. Then the resulting reduced problem will be solved by applying the adaptive method with a hybrid direction. A post-processing step (post-solving) is necessary to deduce the optimal solution of the original problem. In order to test the algorithm of the proposed method and to make sure of its effectiveness, a comparative study of the proposed method is made with active-set quadprog algorithm, the interior-point-convex quadprog algorithm of the MATLAB optimisation toolbox and the modified proportioning with reduced gradient projections algorithm (MPRGP). The obtained results show that the proposed algorithm presents good performances, it always performs better than the active set method and appears to be very competitive with the interior point method and the MPRGP algorithm, mainly for the problems having 'bi' sufficiently large with many active variables at the optimal solution and for problems where A is generalised diagonally dominant. In these cases, the optimal solution is obtained only by the pre-solving procedure.
  Keywords: Quadratic programming; Box constraints; Pre-solving; Adaptive method; Hybrid direction.
  DOI: 10.1504/IJMOR.2023.10062725
   
  
• Graphical Neural Network-Based MCDM for Evaluating Sustainable City Logistics Measures  
  by K. Vasantha Lakshmi, Udaya Kumara K. N 
  Abstract: This paper presents a novel approach to evaluate sustainable city logistics measures using a multi-criteria decision-making (MCDM) framework based on qualitative data. The proposed approach combines different weighing methods such as fuzzy DEMATEL, fuzzy AHP, to determine the weights of the criteria. The criteria are based on economic, environmental, social, and technical aspects, such as operational costs, energy consumption, revenues, air pollution, noise, land use, congestion, accidents, mobility, accessibility, freeing of public space, logistical efficiency, trip effectiveness, loading factor of vehicles, service quality, and customer coverage. The study also proposes a graphical neural network (GNN) with weighted MCDM for artificial intelligence-based decision-making, which helps in achieving a better selection of city logistics measures for urban freight logistics. The approach is implemented in MATLAB and compared with other deep learning models such as CNN, ANN, and DNN, showing higher performance. Furthermore, the paper presents an extrapolation-enhanced approach for modelling travel decision-making based on MCDM with GNN and error calculation, which provides higher performance. The results demonstrate the effectiveness of the proposed approach in selecting sustainable city logistics measures, which can contribute to improving urban freight logistics.
  Keywords: sustainable city logistics; social factors; multiple stakeholders; fuzzy logic methodology; normalised matrix; Pairwise similarity matrix; multi-criteria decision-making; MCDM.
  DOI: 10.1504/IJMOR.2023.10062726
   
  
• A sustainable demand disruption recovery model considering non-zero lead time and advance payment policy during any emergency like COVID-19 pandemic  
  by Dolagobinda Das, Gauranga Samanta 
  Abstract: This study considers three time frames (i.e., before lock-down, during lock-down, and after lock-down) and takes three distinct time-dependent demands that are effective for three time frames. Before lock-down, we use a linear time-dependent demand function; during lock-down, we use a demand function that suddenly drops close to zero due to lock-down restrictions; after a period of time, demand slowly increases to meet customers basic needs, and after the government relaxes lock-down restrictions, demand abruptly increases due to customers panic buying and overstocking nature. Subsequently, non-instantaneous deterioration rate is considered. Due to a significant rise in demand after lock-down, this research permits a shortage that is partially backlogged along with a non-zero lead time and also considers the advance payment policy to reduce the order cancellation rate. Also, green technology is implemented to reduce carbon emissions. Finally, sensitivity experiments are conducted on a few examples to validate the model.
  Keywords: demand disruption; deterioration; advance payment; COVID-19 lock-down; green inventory model; carbon emission.
  DOI: 10.1504/IJMOR.2024.10062828
   
  
• Reliability Measures of Repairable k-out-of-n System using Weighted Exponential-Lindley Distribution  
  by Sunita Sharma, Vinod Kumar, S.B. Singh 
  Abstract: This study focuses on the analysis of a k-out-of-n: F repairable system employing a novel lifetime distribution termed the weighted exponential-Lindley distribution (WXLD). The system under investigation assumes constant failure rates, while repair times follow the newly proposed WXLD. The repair process involves two personnel: a trainee for minor repairs and an expert for major repairs. Leveraging the supplementary variable technique and Laplace transformation, we derive key reliability measures for the system, including reliability, availability, expected profit, and sensitivity. To exemplify and validate the generalised results, the research employs a communication system as a practical application.
  Keywords: k-out-of-n: F system; weighted exponential-Lindley distribution; WXLD; supplementary variable technique; SVT; reliability; availability; expected profit; sensitivity; Laplace transformation; LT.
  DOI: 10.1504/IJMOR.2023.10062924
   
  
• A new approach for counting patterns in language theory, matchings, and set partitions.  
  by Fatima Hessas, Mouloud Goubi, Noria Benkhemmou 
  Abstract: The notion of pattern is widely studied in the literature. We focus our attention on patterns appearing in language theory, matchings, and set partitions. We start with some main tools of algebraic generating functions of sequences of numbers. We explain how the Bell, Fibonacci and generalised Fibonacci numbers can be used in the theory of patterns. In particular, we are interested in words containing patterns that are related to arbitrary length so as to provide enumeration formulae, and extract satisfying recurrence relations. Moreover, we revisit the work of Bloom and Elizalde concerning pattern avoidance in matchings and partitions in order to fulfil it with some enumeration formulae.
  Keywords: Language theory; patterns; generating functions; matchings; set partitions.
  DOI: 10.1504/IJMOR.2024.10062970
   
  
• Construction of distance measure for fermatean fuzzy sets and its application in educational assessment and medical diagnosis  
  by Dibakar Dutta, Palash Dutta, Brindaban Gohain 
  Abstract: Fermatean fuzzy sets (FFSs), an updated, expanded version of intuitionistic fuzzy sets (IFSs), are effective tools for expressing uncertainty and ambiguity in complicated issues. The distance measure is a crucial tool for illustrating the differences between two FFSs while dealing with Fermatean fuzzy information. It is currently unclear how to precisely calculate the distinction between two FFSs. We provide a novel distance measurement method for FFSs in this study. Then, we show that the chosen distance measurement method satisfies the distance functions axiomatic requirements. The presented distance measure is then evidenced with numerical examples to show that it is more accurate and reasonable than the Mizumoto(I) distance measure, Robert(I) distance measure, Robert(II) distance measure, Mizumoto(II) distance measure, Hellinger distance, Euclidean distance (ED) measure and triangle divergence distance measure, which is capable of overcoming the counter-intuitive circumstance. In addition, we successfully use the proposed distance measure approach to handle pattern recognition difficulties, educational assessment issues, and medical diagnosis issues in a fuzzy Fermatean environment. The experimental findings show how effectively the suggested distance measure method can handle real-world applications in a fuzzy Fermatean environment.
  Keywords: Fermatean fuzzy set; FFS; distance measure; educational assessment; medical diagnosis.
  DOI: 10.1504/IJMOR.2023.10062972
   
  
• Lexicographic multi-objective geometric programming problems with pentagonal fuzzy parameters using robust method  
  by Sudipta Mishra, Rashmi Ranjan Ota 
  Abstract: Fuzzy logic is the most useful method for simulating complex real-world problems. In the process of creating models and coming up with solutions, it integrates ambivalent information. This paper outlines the process for resolving lexicographic multi-objective geometric programming problems with fuzzy parameters. Geometric programming has been utilized as a solution technique for a specific solution to difficult non-linear problems for over 60 years. After the introduction of the pentagonal fuzzy parameters as the coefficients, the study utilizes the robust method to defuzzify the programming problems. Finally, the solution is reached using the geometric programming technique. Two numerical examples have been given to illustrate our proposed methodology.
  Keywords: geometric programming; multi-objective; lexicographic method; pentagonal fuzzy parameters; robust method.
  DOI: 10.1504/IJMOR.2023.10062978
   
  
• Self-Adjusting Formulae for the Solution of Fuzzy Differential Equations with Triangular Fuzzy Numbers  
  by Joshua Sunday, Joel Nimyel Ndam, Anthony Chukwuemeka Onyekonwu 
  Abstract: It is a known fact that in modelling real world phenomena, differential equations are indispensable. Uncertainty, unfortunately intervene with such real world problems. The uncertainty may arise from measurement error, determining initial/boundary conditions or even deficient data. Modelling these problems in the form of fuzzy differential equations (FDEs) helps in addressing such setbacks. This research focuses on deriving self-adjusting formulae (SAF) through the variable stepsize strategy for the solution of FDEs with triangular fuzzy numbers. The SAF, which is in the form of implicit block backward differentiation formulae (BBDF) was derived in such a way that it automatically adjusts the stepsize to fit the FDE under consideration. The BBDFs have been known for their unbounded region of absolute stability, thus making them suitable for solving FDEs. The results obtained showed that the SAF is computationally efficient, robust and reliable.
  Keywords: backward differentiation formulae; convergence; fuzzy differential equation; FDE; H-difference; Hukuhara derivative; interval differential equations; mathematical models.
  DOI: 10.1504/IJMOR.2023.10063110
   
  
• Non-linear fuzzy programming - a case study  
  by Arpita Kabiraj, Swapan Raha, Prasun Kumar Nayak 
  Abstract: In this article, we would like to attempt finding a convergent near optimal solution of a fuzzy non-linear programming problem (FNLPP) in which the objective as well as the constraints defining the relationship between variables are so imprecisely stated that it is practically impossible to represent by any existing crisp model. The primary aim of this research is to provide more flexibility to the decision-maker. Accordingly, to solve such a FNLPP, we use approximate reasoning which involves three stages: fuzzification, aggregation and defuzzification. The process is repeated till a convergent near optimal solution is attained. An algorithm is designed for the implementation of the proposal. Artificial examples have been considered to illustrate our approach and existing results are used for comparison. Finally, a case study is undertaken to demonstrate the effectiveness of our proposal.
  Keywords: Fuzzy non-linear programming problem (FNLPP); fuzzification; aggregation; defuzzification.
  DOI: 10.1504/IJMOR.2024.10063164
   
  
• Dynamic service management and priority handling in dual server queuing systems with breakdowns  
  by Ayyappan G, Sankeetha S 
  Abstract: This paper examines a dual-server system comprising server 1 and server 2, each with its dedicated queue (queue 1 and queue 2). Queue 1, with lower priority, can handle an unlimited number of tasks, while queue 2, with higher priority, has a maximum capacity of N tasks. Task arrivals follow a Markovian process, and their service times adhere to a phase-type distribution. In the event of server's breakdown, server 1 seamlessly takes over, minimising service disruptions. To address customer dissatisfaction, server 1 provides prompt feedback during these transitions. The study employs the quasi-birth-death (QBD) process, utilising matrix analytic methods with finite-dimensional block matrices to analyse steady-state behaviour. Performance metrics like busy periods, costs, and other relevant measures are assessed, yielding insights into system efficiency. Numerical computations and graphical representations showcase the system's performance across various scenarios, providing a comprehensive understanding of its operation.
  Keywords: Markovian arrival process; phase type service; vacation; priority queues; breakdown; repair.
  DOI: 10.1504/IJMOR.2024.10063513
   
  
• Investigation on inventory replenishment policy for a queueing system with catastrophic failure, negative arrival and discouraged customers  
  by Ayyappan G, N. Arulmozhi 
  Abstract: The single queues of inventory systems (IS) with warehouse catastrophes and negative arrivals (NA) occur in the service area were examined in this work. Arriving positive customers (P C) can queue up infinitely to make purchases. Customers in the system are still waiting for stock replenishment after catastrophes even when all of the system's commodities are destroyed. The positive customer that is now getting service from the server is disrupted and removed as a result of the negative arrival. The server is instantly impacted by the breakdown as a result of the negative customer's arrival. After examining queueing inventory system's stability conditions, busy period, and the transition probability vector was calculated using the matrix-analytic method. The results of numerical assessments have been presented together with formulas for performance measures.
  Keywords: Markovian arrival process; MAP; phase-type service; negative arrival; catastrophic failure; (s; S) and (s; Q) policies; repair.
  DOI: 10.1504/IJMOR.2024.10063626
   
  
• An Inventory System for Imperfect Products with the Effect of Carbon Emissions and with Free Transportation on a Prepaid Basis  
  by Sandeep Kumar, Robin Singh, Manoj Kumar, Mukesh Kumar, Prachi Fartyal 
  Abstract: The EPQ model is a mathematical model used for inventory management in shop floor systems. However, it assumes manufacturers pay upfront costs and may have low-grade items. The classical inventory model assumes no imperfect items are manufactured, but the production process may shift from controlled to uncontrolled states due to various causes. To make the current study more realistic, we represent a model with imperfect production that accounts for random carbon emissions under continuous prepayment. We also assumed that the production process was imperfect, so we got some defective items, and out of these, some were reworked. Further, it is assumed that the producer provides free shipping to the retailers on a prepaid basis. The concept of carbon emissions is related to transportation and production decisions. Due to environment-saving rules, a tax on carbon emissions is required to be paid by the manufacturer. The model is validated using a numerical example and sensitivity analysis.
  Keywords: inventory; carbon emission; imperfect products; transportation cost; prepayment.
  DOI: 10.1504/IJMOR.2024.10063627
   
  
• Solving Mixed Integer Linear Programming Problems with bounded variables by the Adaptive Method  
  by Houria Boussouira, Mohand Ouamer Bibi 
  Abstract: Unlike linear programming problems, mixed integer programming problems are very difficult to solve. In this paper, we elaborate a new cut for Mixed Integer Linear Programming (MIP) with upper and lower bounded variables. The obtained problems are solved by the adaptive method developed by Gabasov (1980) for solving linear programming problems. This algorithm allows solving directly the considered problem, without modifying it and avoids the drawbacks of the increase in the number of the variables and the constraints. In order to compare our method with the intlinprog method of the Matlab optimisation toolbox, numerical experiments on randomly generated test problems are presented, that involve the CPU time.
  Keywords: Mixed Integer Linear Programming; Generating Valid Inequalities; Adaptive Method.
  DOI: 10.1504/IJMOR.2024.10063628
   
  
• Towards Sustainable Two Warehouse Inventory Management: Flexible Payments and Demand-Driven Optimisation with Preservation Technology and Carbon Emission Considerations  
  by Neha Rani, Manoj Kumar Sharma 
  Abstract: This study explores the transformative impact of conservation and eco-friendly technologies on two warehouse inventory, aiming to prevent product degradation and substantially reduce carbon emissions in greenhouse operations. The research underscores the urgent need for government-led carbon emission laws to address environmental and economic repercussions. With a focus on the proposed model, two key contributions emerge: 1) strategic investments in eco-friendly technologies and conservation methods for minimising carbon emissions and product degradation; 2) the application of preservation technology to curtail product deterioration. The comprehensive model integrates factors such as demand dynamics, pricing, stock, expiry dates, payment delays, and inflation, seeking optimal order quantities, cycle durations, and selling prices for profit maximisation. Validated and exemplified quantitatively, the model's efficacy is demonstrated, complemented by a thorough sensitivity analysis. This research not only advances inventory management practices but also advocates for environmentally sustainable strategies with direct financial implications.
  Keywords: two warehouses inventory; price-stock and lifetime dependent demand; inflation; preservation technology; carbon emission.
  DOI: 10.1504/IJMOR.2024.10063711
   
  
• A Two-Tier Sustainable Supply Chain Model with the Influence of Carbon Release under a Fuzzy Environment  
  by Varuna Bhardwaj, Sunil Kumar, Vipin Kumar Tyagi 
  Abstract: Environmental sustainability is a worldwide issue in the present-day business management environment, and scholars have been concentrating broadly on this subject. It is difficult to run an organisation efficiently while ensuring the environment, and lots of companies have understood that they have to prioritise production with minimum waste and carbon emissions. Government measures to promote sustainability have also led corporations to emphasise minimising their carbon footprints across the supply chain by utilising green supply chain strategies. Green inventories contribute significantly to system design by minimising unfavourable environmental effects while enhancing positive economic and social consequences. In the course of production, keeping inventory, depreciation, shipping, and scrap management, the investigation evaluates concerns related to carbon emissions in both developer and vendor channels. In order to reduce total average expenses, a crisp model has been developed. Using the signed distance approach, the total average expenditure is defuzzified and proven to be convex with a unique approach. Both crisp and fuzzy scenarios undergo numerical analysis. Sensitivity analysis and visual representations are used to demonstrate how innovative the suggested technique is.
  Keywords: sustainable; degradation; carbon emission; developer; vendor.
  DOI: 10.1504/IJMOR.2024.10063847
   
  
• A Sustainable Production Model for Industry 4.0 with Fuzzy Optimization Approach  
  by Manisha Pant, Neelanjana Rajput, Seema Sharma, Anand Chauhan 
  Abstract: A clean and sustainable environment has become a primary goal for any organisation. Industrial Revolution 4.0 and sustainable development are two new technological and organisational patterns that are impacted by improving efficiency and ensuring long-term sustainability. The aim of this work is to make a sustainable supply chain smarter for which an autonomation inspection policy has been considered to reduce human mistakes. The demand rate for the retailer depends on marketing parameters that have been considered here. This study also explores a production system that switches from an in-control to an out-of-control state at random. There are uncertainties in some parameters of the system, the triangular intuitionistic fuzzy number has been used and the signed distance defuzzification method is applied to get the final total inventory cost in fuzzy environment. The proposed model is validated by using numerical illustration and sensitivity analysis of the relevant parameters has been provided.
  Keywords: optimisation; supply chain management; Industry 4.0; autonomation inspection policy; imperfect production; intuitionistic fuzzy number; defuzzification.
  DOI: 10.1504/IJMOR.2024.10064014
   
  
• Exploring Sustainable Inventory Control Models from 2011 to 2023: A Comprehensive Review  
  by Manoj Kumar Sharma, Neha Rani, Kanika ., Khushi Saini 
  Abstract: In recent years, the growing focus on sustainability has prompted the incorporation of external logistics costs into the EOQ model. The increasing importance of sustainable inventory management is becoming more evident in the current business environment. Companies widely acknowledge that adopting sustainable practices is imperative to achieve multiple objectives, including cost reduction, waste minimisation, and long-term viability assurance. Reducing the carbon emissions caused by inventory processes is paramount in this field. Because lowering one's carbon footprint is just as crucial as lowering one's traditional inventory expenses, this research dives into how these two concepts might be integrated into sustainable inventory management. This review provides a current and comprehensive overview of sustainable inventory models while concurrently encompassing the critical themes in publications spanning from January 2011 to February 2023 within the realm of carbon emissions.
  Keywords: sustainability; sustainable inventory management; SIM; carbon emission; optimisation.
  DOI: 10.1504/IJMOR.2024.10064134
   
  
• An Attempt on Neutrosophic Multi Attribute Decision Making based on Generalised Signed Distance Method  
  by Manas Karak, Tuhin Bera, Mahendra Rong, N.K. Mahapatra 
  Abstract: Decision making in todays uncertain scenario is a most challenging task to the experts. To assist the decision makers, this study deals with a ranking of neutrosophic number based on generalised signed distance method. Some important definitions like level-1 neutrosophic points and level (, , )-neutrosophic intervals are drawn initially. Then a number of properties and theorems on ranking of neutrosophic numbers are developed here. Finally, to establish our theoretical idea on ranking, we consider a real life multi-attribute decision-making problem and find the desired result. After that we make some comparative study of our model with some existing decision-making models.
  Keywords: Neutrosophic number and its ranking; neutrosophic points; neutrosophic intervals; signed distance method.
  DOI: 10.1504/IJMOR.2023.10064900
   
  
• The Strategic Value of Seller's Option in Buyback Guarantee Financing  
  by Yang Huang, Wenxuan Wang, Qiangqiang Wang 
  Abstract: This paper extends traditional bank credit (BC) and buyback guarantee (BG) financing models by considering uncertain salvage value, and proposes a novel buyback guarantee financing with seller's option (SBG). We derive the optimal decisions for the bank, retailer, and manufacturer under each financing scheme. Additionally, we compare the optimal decisions for the retailer and manufacturer when the BC contract, BG contract, and SBG contract are feasible. The results reveal that the optimal financing schemes for the manufacturer and retailer are not always aligned. Both parties stand to increase profits with the SBG contract compared to other contracts when the salvage value is high. Furthermore, there is a significant range where the supply chain could generate greater profits with the SBG contract compared to other contracts.
  Keywords: seller’s option; buyback guarantee financing; bank credit financing; supply chain management.
  DOI: 10.1504/IJMOR.2024.10064996
   
  
• Analysis of MAP/PH1,PH2/1 Retrial Inventory Queueing System with Phase type Vacation, Working Breakdown, Repair, Essential and Optional Inventories  
  by Meena S, Ayyappan G 
  Abstract: This research analyses an inventory retrial queueing system with a constant retrial rate, working breakdown, repair, single vacation and inventory items that are essential and optional. We assume that an arrival follows the Markovian arrival process and that the server will provide them with phase-type services. The (s1, S1) and (s2, S2) policies are used to replenish the essential and optional inventory items, respectively, and there will be an exponential distribution in the replenishment time. The server takes a single vacation if there are no orbital customers, no essential inventory, or both. The server provides an optional item, if there exists a positive inventory level, otherwise the customer gets only the essential item and then leaves the system. When a server breaks down, the server provides the slow mode service for the current customer and then starts the repair process. The number of consumers in orbit, inventory level, and server status may all be determined in the steady state. Numerous key performance indicators are defined, and a cost analysis is obtained. In order to make our mathematical concept clearer, a few numerical examples are provided.
  Keywords: queueing-inventory; (s; S) policy; retrial; essential and optional item; single vacation; working breakdown; repair; Markovian arrival process; MAP; phase-type distribution.
  DOI: 10.1504/IJMOR.2024.10065048
   
  
• The Ristic-Balakrishnan-Exponentiated Half Logistic-G Family of Distributions with Applications  
  by Broderick Oluyede, Kethamile Rannona 
  Abstract: In this paper, we introduce a new family of distributions called the Ristic-Balakrishnan-Exponentiated Half Logistic-G (RB-EHL-G) family of distributions. Statistical properties of the new family including hazard function, quantile function, moments, distribution of the order statistics and Renyi entropy are derived. Some special cases of the new family are presented. The maximum likelihood estimation technique is used to estimate the model parameters. A Monte Carlo simulation study is conducted in order to examine the bias and mean square error of the maximum likelihood estimators. Finally, the new family is applied to real life datasets to illustrate the usefulness of the proposed distribution.
  Keywords: Ristic and Balakrishan-G Distribution; Exponentiated Half Logistic-G Distribution; Maximum Likelihood Estimation.
  DOI: 10.1504/IJMOR.2023.10065419
   
  
• Optimising inventory replenishment system a case in multi-product multi-retailer  
  by Le Duc Dao, Huynh Nhat Huy 
  Abstract: Inventory management and replenishment are considered as important process in supply chain, especially in the retail industry. The replenishment process requires businesses to consider a large amount of information to support the decisions related to the appropriate quantity and timing of replenishment. The goal is to minimize costs associated with inventory including purchasing, holding and shortage costs at retail stores and maintain a high customer service level. The problem of the paper is formulated with mixed integer linear programming and to be solved by genetic algorithm to achieve optimal distribution cost for Firm. The results of the paper will support businesses in providing product replenishment strategies while considering related constraints on demand, budget, thereby providing businesses with the lowest operating costs and increasing competitiveness in the future.
  Keywords: inventory replenishment model; genetic algorithm; mixed integer linear programming.
  DOI: 10.1504/IJMOR.2024.10065465
   
  
• Sustainable Supplier Selection and Order Allocation Using Hybrid Fuzzy Weighting Methods, Scenario-Based Programming, and Flexible Robust Optimisation  
  by Mahtab Saneei, Mehdi Seifbarghy, Mohsen Hamidi 
  Abstract: In this research, a sustainable supplier selection and order allocation problem under uncertainty is modelled and solved. To weigh supplier selection criteria, four fuzzy methods have been applied. To determine suppliers' scores, two approaches of fuzzy Taguchi loss function (F-TLF) and fuzzy technique for order preference by similarity to ideal solution (F-TOPSIS) are used. Suppliers' scores are then incorporated into an objective function of a multi-objective optimisation model to allocate orders to suppliers. Three models of scenario-based programming, flexible robust programming, and a new scenario-based and flexible robust hybrid programming are presented. The optimisation objectives are minimising purchasing cost, maximising supplier desirability, and maximising value of purchasing from best suppliers. To solve the models, a hybrid method of Lai and Hwang and Torabi-Hassini is proposed. The three models have been solved using real data from the electronics industry.
  Keywords: supplier selection and order allocation; SSOA; fuzzy Taguchi loss function; F-TLF; flexible robust optimisation.
  DOI: 10.1504/IJMOR.2024.10065534
   
  
• EOQ-Type Inventory Models Incorporating Discount Policies and Carbon Emission with Warehouse Capacity and Capital Constraints  
  by Tiara Alamanda, Dharma Lesmono, Jonathan Hoseana 
  Abstract: In 2019, Kristiyani and Daryanto proposed an EOQ-type inventory model which takes into account the company's total carbon emission, and assumes that the item's purchase obeys the all-unit-discount policy. In this paper, we construct a modication of the model, by replacing the all-unit-discount policy with the incremental-discount policy. Furthermore, we complement both models with warehouse capacity and capital constraints. Using both models, we compute numerically the optimal order quantity satisfying both constraints, in the scenario of a building materials company in Bandung, Indonesia. At the obtained optimal state, we analyse the sensitivity of both the company's total cost and total carbon emission with respect to some of the models' parameters. The results show that both quantities depend particularly significantly on the fuel consumption of the vehicle used to transport the purchased items from the supplier to the company's warehouse.
  Keywords: EOQ; carbon emission; all-unit discount; incremental discount; warehouse ca- pacity; capital.
  DOI: 10.1504/IJMOR.2024.10065578
   
  
• Kernel Estimation Analysis of the Finite Source M/G/1 Queue with Retrial and Vacation  
  by Lyes Ikhlef, Karim Labadi 
  Abstract: In this work, we study the finite source queueing system with retrial and vacation when the service distribution of customers is unknown. We compute the qualitative analysis of this queueing system by the use of the Markov regenerative process and the kernel method. The two main quantities, one step transition probability matrix P of the embedded Markov chain (EMC) defined at regenerative instants and the mean time matrix A, that the queue spends in any state between two successive regeneration instants, for the system considered are obtained. The matrix P (resp. A) depends on the probability density function (pdf) (resp. cumulative distribution function (cdf)) of the service time. These two functions (pdf and cdf) are unknown and are estimated by using the two asymmetric kernels gamma and Birnbaum-Saunders. Finally, we establish an algorithm which gives us the estimators of: the one step transition probability matrix P, the mean time matrix A, the probability distribution of the number of customers in the orbit and the state of the server and the characteristics of our queueing system considered.
  Keywords: Retrial Model; Markov Regenerative Process; Gamma Kernel; Estimation; Vacation Policy.
  DOI: 10.1504/IJMOR.2024.10065624
   
  
• A Note on an EOQ Inventory Model with Varying Time-Dependent Demand and Shortages under the Conditions of Delay in Payment  
  by Trailokyanath Singh, Itishree Rout, A.K. Nayak 
  Abstract: In most of the classical inventory models, only demand is considered as the main factor for formulating the model. However, demand and deterioration are two main competitive factors that are necessary to represent any inventory model for deteriorating items. In this paper, an EOQ model has been framed to study the items over a finite time horizon with the following characteristics: 1) delay in payment is permitted; 2) demand is time-dependent quadratic function of time; 3) grace period for settling the account is known; 4) shortages in the system are fully backlogged. The formulation of the model is derived under case 1 the grace period is less than shortage period and case 2 the grace period is greater than shortage period of the inventory system. Finally, a couple of numerical examples and sensitivity analysis of the optimal solution with respect to different parameters of the model are presented.
  Keywords: constant deterioration rate; deteriorating items; economic order quantity; permissible delay in payments; shortages; time-dependent quadratic demand.
  DOI: 10.1504/IJMOR.2024.10065820
   
  
• An Optimal Inventory System under Markdown Dependent Demand Environment  
  by Sonia Dua, Sandeep Kumar Mogha, Himani Dem 
  Abstract: Green supply chain management (GSCM) prioritises sustainability-focused approaches that strategically manage risk and environmental concerns while optimising operational efficiencies, reducing costs, and maximising profits as traditional supply chain management does. However, coordinating various individual participants of any supply chain working towards a common objective presents perennial challenges for executives in managing a supply chain, particularly considering various strategic aspects of environmental issues. Thus, this study employs a hybrid approach to selecting a GSCM strategy and aims to identify the most suitable one. For this purpose, a multi-criteria decision-making technique was applied to data collected from supply chain executives in the defence industry to fill the methodological gap. The findings of this research reveal that the legislative perspective holds the highest criterion weight, while risk-based strategies are identified as the most effective GSCM approach. Notably, this study contributes to advancing strategic management research by presenting a hybrid approach demonstrating a grey-based hybrid application of the PIPRECIA-G and OCRA methods to GSCM strategy selection.
  Keywords: inventory model; markdown dependent demand; discount policy; carbon emission.
  DOI: 10.1504/IJMOR.2024.10065897
   
  
• Benchmarking Decision-Making Units' Efficiency for the Case of Integer-Valued Data and Fixed Factors: a Super Efficiency Slacks-Based Measure Approach  
  by Mushtaq Taleb, Mamdooh AttAllah, Ruzelan Khalid, Rosshairy Abdul Rahman 
  Abstract: The purpose of this paper is to develop a mixed integer SE-SBM approach with fixed inputs and outputs. The proposed approach is developed by modelling the integer requirements and fixed inputs and outputs into the objective function and the input and output constraints of Tone's (2002) SE-SBM approach in envelopment analysis (DEA). The scalar measure of the proposed approach depends on the discretionary mixed integer input excesses and discretionary mixed integer output shortfalls, as well as discretionary mixed integer input savings and discretionary mixed integer output surpluses. The approach can also identify sources of super-efficient status of efficient banks by identifying their discretionary mixed integer inputs that can be increased and/or discretionary mixed integer outputs that can be decreased. The proposed approach guarantees the feasibility condition under the variable returns-to-scale and constant returns-to-scale technologies. A banking sector application of the proposed approach with four inputs and four outputs is run.
  Keywords: Integer-valued data envelopment analysis; fixed factors; Slack-based measure; Super efficiency; Banking sector.
  DOI: 10.1504/IJMOR.2024.10066066
   
  
• A Weighted Neutrosophic Fuzzy Goal Programming Approach to Optimise Multi-Objective Assignment Problem  
  by Debasmita Sarkar, Pankaj Kumar Srivastava 
  Abstract: Assignment problems (APs) hold significant in industrial organisation, resource allocation, developing service systems, etc. Assigning appropriate jobs to the right employees is crucial when aiming to achieve objectives like cost-saving, ensuring production quality, and estimating production time. Decision makers (DMs) face immense pressure to optimise all of the objectives simultaneously determined to thrive in todays rapidly evolving market. Therefore, here considers, multi-objective assignment problems (MOAPs) to optimise all the objectives comprehensively. Additionally, only a tiny portion of the literature concentrates on both the quality of the commodities and the consistency of the objective functions while solving MOAPs and the consistency of the objective functions. Thus, in the proposed study, each tasks quality undergoes evolution using a neutrosophic linguistic scale. Weights are determined employing the neutrosophic analytic hierarchy process (NAHP) to avoid comparisons and ensure the consistency in the objective functions. The weighted single valued neutrosophic fuzzy goal programming (WSVNFGP) method is proposed toresolve the deterministic MOAP and find Pareto-optimal solutions by combining weights. The study is strengthened by a fair contrast of the proposed algorithm with other widely-used approaches, leading to approval of the reasonability of the proposed algorithm over other schemes.
  Keywords: multi-objective assignment problem; single-valued neutrosophic triangular fuzzy numbers; weighted neutrosophic fuzzy goal programming; pareto-optimal solution.
  DOI: 10.1504/IJMOR.2024.10066170
   
  
• Solving an EOQ model for Stock, Selling Price and Customer's Income Dependent Demand under Dense Lock Fuzzy Environment  
  by Suman Maity, Sujit Kumar De, Madhumangal Pal, Sankar Prasad Mondal 
  Abstract: In this paper, we have developed an economic order quantity (EOQ) model for degrading items in which two decision-makers collaborate to make decision, one of them acting as the industrialist (developer) and the other as the accountable manager. Although, customers' income might create a vital impact on the demand rate of the products. But none of the researchers took it into account for their model. In this study, the demand rate is considered as a function of selling price, stock, and customers' income and later it has been fuzzified. The problem is solved by using dense lock fuzzy environment. The notion of a dense fuzzy set, which depends on number of turnovers made at industrial process. Additionally, we have covered the basic idea of dense lock fuzzy sets along with the relevant membership functions and defuzzification techniques via solution algorithm. Numerical outputs reveals that the joint decision-makers provide the objective function finer optimum. To support the new approach, a thoughtful analysis, a graphical representation, and a conclusion are provided.
  Keywords: EOQ model; deteriorating items; dense lock fuzzy set; defuzzification; optimisation.
  DOI: 10.1504/IJMOR.2024.10066259
   
  
• Short-term origin-destination demand forecasting in rail transit systems: parallel model architecture and gravity approach  
  by Tissawat Asavanant, Hiroshi Morita 
  Abstract: Short-term origin-destination (OD) forecasting in passenger rail transit is notoriously difficult due to the high magnitude of scale, dimension, noise, and skewness of the OD matrices. Additionally, unforeseen OD data remains an issue for the data-driven models. In this paper, we address the issue of unforeseen OD data in real-time forecasting case, by using the adjusted parallel model architecture (APMA), a forecasting improvement strategy, and the reconstruction of the problem into an origin-based vector sum projection gravity (OVG) model. The forecasting problem can be split into concatenation and chained forecasting scenarios. Variations of the APMA model are tested on real-time datasets from Bangkok Subway. The proposed APMA-OVG model performs satisfactorily when compared to recent benchmarks for the unforeseen data on the concatenation case. The performance deteriorates in the chained forecast case due to accumulated error of the step-wise forecasting process when forecasting steps are broken down.
  Keywords: parallel model architecture; PMA; origin-destination matrices; gravity model; hybrid model; public transportation network; short-term forecasting.
  DOI: 10.1504/IJMOR.2024.10066486
   
  
• Supplementary variable technique approach on retrial queue with feedback and backup server during Bernoulli's lengthy vacation and random repairs.  
  by R. Poornima , K. Kirupa  
  Abstract: This paper explores a steady-state retrial queueing system with a single server, coupled with a backup server. Client arrivals occur in batches following a compound Poisson process. If the server is idle, one of the clients from the batch receives service immediately, and the remaining clients enter the orbit. Otherwise, the entire incoming batch joins the orbit. Unsatisfied clients after receiving service may become feedback clients. After the completion of each service, the server may enter a vacation period of random length. The server has the option to extend its vacation with certain probability. Breakdowns of the main server can occur at any point during the busy state. Repairs of the server commence without delay. During vacation and repair time of the main server, clients receive service from a backup server. Performance metrics, such as the mean of the system size, mean of the orbit size, server availability and server failure frequency are computed. Cost analysis has been carried out with the cost parameters. The stochastic decomposition law is verified for the proposed model. Numerical results are also presented to validate the impact of parameters on the system.
  Keywords: batch arrival; Bernoulli extended vacation; backup server; random breakdown and feedback.
  DOI: 10.1504/IJMOR.2024.10066498
   
  
• Replenishment of Bhadla Solar Park using Interval Valued Neutrosophic Threshold Graph  
  by R. Keerthana, Venkatesh S, R.U. Gobithaasan 
  Abstract: In this article, an interval valued neutrosophic threshold graph (IVNTG) G, a novel perspective on interval valued neutrosophic graph has been newly introduced. The concept of interval valued intuitionistic fuzzy threshold graph (IVIFTG) G, a special case of IVNTG is also defined together with alternating four-cycle, threshold dimension and threshold partition number for IVNG and IVIFG. Further, the bounds (G) '(G)' and (G) '(G)' are found and the equality becomes true only when G and G are triangle free graph. To demonstrate a practical significance, the article uses IVNTG to solve the replenishment problem on Bhadla Solar Park, an application which contributes towards SDGs, 7, 8 and 13 and the proposed algorithm helps to determine the allocation, consumption and distribution of solar energy in Bhadla Solar Park.
  Keywords: Interval Valued Intuitionistic Fuzzy Threshold Graph; Interval Valued Neutrosophic Threshold Graph; SDG; Bhadla Solar Park.
  DOI: 10.1504/IJMOR.2024.10066814
   
  
• Bifurcation Analysis and Effective Approaches to Control for Measles using SEIR Mathematical Model  
  by H.A. Bhavithra, S. Sindu Devi 
  Abstract: The aim of this work is to create the SEIR model for measles in Indonesia. The model has four compartments built into its construction. The SEIR model analysis yields local stability at the basic reproductive number and the fuzzy disease-free equilibrium is calculated. Sensitivity analysis has been done as part of control strategies, and after that, a fuzzy reproduction number control approach has been put into practice. The bifurcation theorem deals with dynamical systems that have one or more external parameters and how the parameters might change and affect the way the solution set is structured. In essence, this type of behaviour is dictated by the stability of solutions and how they may alter when the parameters change. The Euler method is used to carry out the numerical stimulation.
  Keywords: fuzzy equilibrium points; fuzzy basic reproduction number; backward bifurcation analysis; Euler method.
  DOI: 10.1504/IJMOR.2024.10066815
   
  
• Designing of Single Acceptance Sampling Plan based on Time Truncated Life Test under New Weibull-Pareto Distribution  
  by S. Swathi Sundari, G. Kannan, S. Balamurali, K. Lakshmanan, G. Selvaraj 
  Abstract: This article focuses on designing a single acceptance sampling plan (SASP) that guarantees the percentile lifetime (lifespan) of a product follows a new Weibull-Pareto distribution (NWPD) on the basis of a time-truncated life test (TTL) with a known shape parameter. Considering both producers risk () and consumers risk (), a two-point technique to the operating characteristic (OC) curve is applied in this study to find the most appropriate suitable plan parameters like sample size (n) and acceptance number (c). Our aim is to simultaneously satisfy the expectations of both producers and consumers. To select the most appropriate plan parameters, we generate tables representing various percentile values of the NWPD.
  Keywords: new Weibull-Pareto distribution; NWPD; percentile life; single acceptance sampling plan; SASP; time truncated life test; TTL test.
  DOI: 10.1504/IJMOR.2024.10066816
   
  
• Performance Comparison of Random Forest and BILSTM for Intrusion Detection in Cyber Security Environment  
  by A. Prashanthi, R. Ravinder Reddy 
  Abstract: The widespread adoption of the internet has led to an increase in network attacks, making traditional signature-based detection methods less effective against zero-day attacks. This research examines the efficacy of anomaly-based detection techniques in identifying these threats, using two artificial intelligence models: CNN-BiLSTM and random forest classifier. Data for training and testing these models was sourced from the CICIDS2017 dataset. Results showed a high success rate, with CNN-BiLSTM achieving 95% and random forest classifier achieving 98%. These findings suggest that anomaly-based detection offers a robust strategy for detecting zero-day network attacks. The research also underscores the necessity of assessing detection systems through various performance metrics, including accuracy, precision, recall, and F1 score. Such metrics provide a comprehensive understanding of an algorithm's effectiveness in diverse scenarios, which is crucial for developing more advanced and secure network security systems capable of addressing emerging threats.
  Keywords: anomaly-based detection; zero-day attacks; machine learning; BiLSTM; random forest classifier; CICIDS2017.
  DOI: 10.1504/IJMOR.2024.10066924
   
  
• Numerical Investigation of Phase type Inventory Queueing System with (s,S) policy, Degrading Service, Single Vacation, Closedown, Breakdown, Repair and Impatient Customers  
  by Ayyappan G, Meena S 
  Abstract: This analyses an inventory queueing system with degrading service, single vacation, breakdown, repair, closedown, and impatient customers. We assume that an arrival follows the Markovian arrival process, and that the server will provide them with phase-type services. The (s, S) policy to replenish the items and the replenishing duration follow an exponential distribution. The arriving customer should get the service whenever the inventory item level is positive. Otherwise, they must wait in front of the service station. The rate of service will decrease until the degradation is resolved. The number of customers in the system, the inventory level, and server status may all be determined in a steady state. Numerous key performance indicators are defined, busy period analysis is obtained, and cost analysis is obtained. To make our mathematical concept clearer, a few numerical examples are provided.
  Keywords: queueing-inventory; (s,S) policy; degrading service; single vacation; breakdown; repair; closedown; Markovian arrival process; MAP.
  DOI: 10.1504/IJMOR.2024.10066932
   
  
• Analysis of a Finite Retrial Queuing System with Orbital Search using Generalised Inverses  
  by Kalyanaraman R, S.B. Pattabiraman 
  Abstract: A simple, efficient, numerically stable algorithm to the analysis of a M/M/1/3/3 retrial queue with orbital search is given in terms of group generalized inverses. The interarrival time and service time are two different exponential distributions. There are three sources, each source generate primary customers. The primary arrivals first check whether the server is idle. If the server is idle, he enters the service station. Otherwise, he enters the orbit and retries, the inter retrial times follows negative exponential distribution. After being serviced, the customer returns to the source. Also, after completing service no one competing for service, with probability p, the server carries search for customers in the orbit and instantly picks up a customer, if available, directly from the orbit.Such a queue is called retrial queue with orbital search. Using the algorithm developed in Kalyanaraman and Pattabiraman (2010), the stationary distribution andmean first passage time distributions are obtained. Some operating chracteristics are calculated. Some particular models are also given.
  Keywords: Retrial queue - Orbital search - Generalised inverses - Stationary distribution - Mean first passage time - Operating characteristics.
  DOI: 10.1504/IJMOR.2024.10066959
   
  
• M/G/1 Queue with Regular and Optional phases of Services and Vacations  
  by Kalyanaraman R, Vidya K 
  Abstract: This paper deals with a non-Markovian single server queue with phase type service and phase type vacation. The service time and vacation time of each phase is generally distributed. The probability generating function of number of customers in the system at an arbitrary time point and at departure point is obtained in steady state. Some important performance measures are derived. Some numerical illustrations are also provided.
  Keywords: Non-Markovian queue; Phase type service; Phase-type vacation; Probability generating function; Performance measures; Numerical example.
  DOI: 10.1504/IJMOR.2024.10066961
   
  
• Strategic Pricing: Examining the Impact of Showrooming Behaviour on Manufacturer-Retailer Dynamics in a Supply Chain  
  by Ping Su, Xiangling Hu, Jaideep Motwani 
  Abstract: We study a two-stage supply chain where a manufacturer sells through two competing retailers: a brick-and-mortar retailer and an online retailer. Using a Stackelberg game model, we examine the manufacturers wholesale price and the BM retailers sales effort decisions in the presence of customers showrooming behaviour. We analyse how the availability of price-matching guarantees affects two product categories: non-showrooming and showrooming. Our findings show that price-matching strategy enhances the BM retailers sales effort, the manufacturers profit, and overall supply chain profitability for non-showrooming products, but is ineffective for showrooming products. For non-showrooming products, price-matching guarantee complements sales effort, with the manufacturer lowering its wholesale price to encourage more sales effort. For showrooming products, price-matching guarantees substitutes for sales effort, with the manufacturers aggressive pricing discouraging sales efforts. Therefore, we recommend universally offering price-matching guarantees for non-showrooming products and restricting them to customer requests for showrooming products.
  Keywords: Showrooming; Sales Effort; Stackelberg Game; Strategic Pricing.
  DOI: 10.1504/IJMOR.2024.10067161
   
  
• A Fuzzy MS-TORO Approach for Aircraft Rerouting Problem  
  by Miriam Bongo 
  Abstract: Stakeholders of the commercial aviation industry seek to uphold their individual interests but are faced to generate a unified decision which does not only satisfy their own interests but also of others. In this paper, fuzzy multiple stakeholder-based target-oriented robust-optimisation (MS-TORO) approach is utilised to address a choice problem in the aircraft rerouting process. The proposed model is based on an optimisation model which primary goal is to balance the interests of stakeholders at a certain extent of deviation from the target metric. The key results of the model showed an aggregated solution to the apparent conflict of interests among stakeholders. Furthermore, the model also highlighted the risk profile of stakeholders via the deviation metric. Such a novel framework serves beneficial to balance the interests of stakeholders in the decision process not only in the air transportation domain but also to other similar areas.
  Keywords: aircraft rerouting; airline industry; airport management; air traffic management; fuzzy set theory; multiple stakeholder-based target-oriented robust-optimisation approach.
  DOI: 10.1504/IJMOR.2024.10067164
   
  
• A Discussion of Newton's Law of Cooling using Difference Equations in Fuzzy Frames as an Alternative to the Traditional Continuous Dynamical System  
  by Abdul Alamin, Mostafijur Rahaman, Soheil Salahshour, Sankar Prasad Mondal, Shariful Alam, Kamal Hossain Gazi, Md Jahangir Mian 
  Abstract: This study, a notable one in the field of heat transfer, adapts a discrete and continuous heat transfer model in a fuzzy environment using fuzzy assumptions. This model was developed using the idea of discrete actual observation data and explored using a fuzzy framework in an effort to thoroughly analyse the experiments on natural occurrences. Using the Hukuhara difference notion, fuzzy arithmetic and difference calculus approach, fuzzy solutions to the governing model are demonstrated. In order to visualise the graphical solution and for usefulness to the suggested approaches, experimental data (both in crisp and fuzzy) of heat transfer of a hot glass of 40 ml water is taken in Newton's law of cooling. In discrete fuzzy frame Newtons law of cooling gives stable solution for some a [0, 1] and significant outcomes are observed from graphical solutions.
  Keywords: Hukuhara difference; fuzzy difference equation; Newton’s law of cooling.
  DOI: 10.1504/IJMOR.2024.10067203
   
  
• An Inventory Model with Power Demand and Preservation Technology Investment under Advanced and Delayed Payment Policies  
  by Loganayaki S, Kirupa K 
  Abstract: This study focuses on an inventory model for non-instantaneous, time-varying deteriorating items with preservation technology investment. The customer demand follows a power pattern function over time. During stockout periods, customer demands are partially backlogged. Additionally, the retailer pre-pays a certain amount of the purchasing cost as an advance payment to the supplier, with the balance paid at a later credit period. Three possible cases are identified based on the available credit period. The retailer incurs a carbon tax for each unit of carbon gas emitted during the processes of ordering, holding, and disposing of deteriorated items. The objective of the study is to minimize the total cost by determining the optimal cycle time, preservation technology investment, and positive inventory time. An algorithm is presented for the numerical optimization of the proposed model. Sensitivity analysis is conducted to evaluate the impact of parameters on model outcomes, providing valuable managerial insights.
  Keywords: inventory; non-instantaneous deterioration; power demand pattern; partial backlogging; advance payment; delay in payment; preservation technology investment; carbon tax.
  DOI: 10.1504/IJMOR.2024.10067204
   
  
• Numerical Solutions of Initial Value Problem by using Modified Euler's Method and Taylor's Method  
  by Rashmi Kumari, V.K. Pandey 
  Abstract: The numerical solution of differential equations (DEs) holds paramount importance in mathematical modeling for applications in science and engineering. It is frequently challenging to find accurate solutions to differential equations that define real-life issues due to their complexity. Since analytical solutions are unavailable for most differential equations, the main way to gain meaningful insights into the solution is through numerical computations. This article describes the numerical solutions of Fractional Differential Equations (FDEs) with Initial Value Problem (IVP) using the Modified Euler's Method (MEM) and Taylor's Method (TM). In addition to calculating the precise analytical solution, we also found the solutions to a few numerical problems. Next, for validation, a list of the accuracy discrepancies between analytical and approximation answers is provided. We found that the accuracy of a solution increases with minimal step sizes. Numerical models and figures are shown and analyzed to illustrate the efficacy of the proposed methodology.
  Keywords: Initial value problem; Taylor's method; Modified Euler's method; Numerical solution.
  DOI: 10.1504/IJMOR.2024.10067271
   
  
• Gerber-Shiu Analysis of the MAP/PH Omega Risk Model with Level-Dependent Premium Rate  
  by Sreeshamim P. P., M.J. Jacob 
  Abstract: This paper investigates the Gerber-Shiu function (G-SF) of the MAP/PH omega insurance risk process with level-dependent premium arrival. The omega model differentiates between ruin and bankruptcy, providing a more realistic assessment of an insurance companys financial stability. By incorporating Markovian arrival processes (MAPs) for claim arrivals and phase-type (PH) distributions for claim sizes, the MAP/PH omega risk model offers a robust framework for analysing risk. The level-dependent premium rate adjusts based on the insurers reserve levels, making the model more flexible and applicable to real-world scenarios. We derive integro-differential equations for the G-SF, providing insights into the expected discounted penalty at bankruptcy. Numerical solutions demonstrate the models practical applications, revealing that higher initial surpluses correlate with lower expected penalties and bankruptcy probabilities.
  Keywords: MAP claim arrivals; phase-type (PH) claims; bankruptcy probability; level-dependent premium rate; dividend barrier; Gerber-Shiu function (G-SF).
  DOI: 10.1504/IJMOR.2024.10067523
   
  
• Optimal Order Policy based on Three-Item Inventory Models with Weibull Distribution Deterioration and Price-Dependent Demand  
  by Claudia Priscilla, Dharma Lesmono, Jonathan Hoseana 
  Abstract: We construct three one-item inventory models with Weibull distribution deterioration, corresponding to three different dependences of the item's demand rate on its selling price: linear, quadratic, and exponential. We combine the three models to obtain five different three-item inventory models, corresponding to the existing five different order policies: the individual order policy, the three semi-joint order policies, and the joint order policy. We carry out a computational analysis of these models, which reveals that the joint order policy - that of ordering the three items simultaneously - gives the highest total profit, and that under this policy, the total profit depends most sensitively on the constant coefficient of the quadratic demand-rate function, i.e., the second item's demand rate in the case of zero selling price.
  Keywords: inventory model; Weibull distribution; deterioration; price-dependent demand; order policy.
  DOI: 10.1504/IJMOR.2024.10067565
   
  
• Uncertainty Propagation in M/G/1/K Queue Modelled by Parametric p-box using Taylor Series Expansion Approach  
  by Zina Hamoudi, Sofiane Ouazine, Karim ABBAS, Kamel Haouam 
  Abstract: The main purpose of the current paper is to use the multivariate Taylor series expansion for analysing of the M/G/1/K queue, we give a new formula of the closed-form expressions for the higher-order sensitivity of discrete-time Markov chain stationary distribution with respect to multiple parameter using a fundamental matrix. We also include the probability boxes, we assume that all parameters have a uniform distribution. In addition, we use the Markov's inequality to estimate the risk incurred by working with uncertain performances of the M/G/1/K queue. Several numerical examples are also presented and the obtained results are compared to the corresponding Monte Carlo simulation.
  Keywords: M/G/1/K queue; Probability-boxes; epistemic uncertainty; multivariate Taylor-series expansions; Risk analysis; Monte Carlo simulation.
  DOI: 10.1504/IJMOR.2024.10067569
   
  
• A Study on Retrial Queueing Model with Additional Breakdown Services and Complete Vacation  
  by Madhumidha Ramachandran, S. Balaji 
  Abstract: In this research, we explore a retrial queuing model with additional breakdown service and complete vacation. If a customer accesses the system and discovers that the server is busy, they enter an orbit, a space with an unlimited capacity. From the orbit, they keep attempting to access the service. The main server crashes as a result of a disaster. In the event of a breakdown, the main server is sent for repair; in the meantime, it will operate more (working breakdown). The server will attempt a complete vacation if the orbit is empty as soon as the working breakdown is completed. By utilizing the supplementary variable technique (SVT), the performance metrics are acquired. Also, the mean busy period and mean busy cycle are discussed. Several specific cases of this model are provided. Further, some numerical results are demonstrated to explore the act of different variables on distinct system performance metrics.
  Keywords: retrial queues; working breakdown services; repair; complete vacation.
  DOI: 10.1504/IJMOR.2024.10067578
   
  
• The Refractory Emission during Inspection Waiting under Pentagonal Fuzzy Number in a Sustainable Inventory Model  
  by Saranyaa P, C. Sugapriya, Nagarajan Deivanayagam Pillai, Kavikumar Jacob 
  Abstract: Every item in traditional inventory control problems is of the highest quality and that the inspection procedure operates flawlessly. In this paper, it is extended for imperfect items, where mistakes of types I and II happen while the inspection is being done and also expands the economic production quantity model. When a batch of perfect items is finally replaced after a special inspection procedure, customers who receive and return imperfect items wait for it in the suggested inventory problem. In the inspection, the defective goods are under the rework plant through electrical vehicle to become the defective goods as finished goods. In addition, the lower-quality items are discounted and sold out quickly, a numerical example was given, and the impact of the primary parameters on the overall profit was examined through a sensitivity analysis.
  Keywords: Waiting Expenses; Defuzzification; Refractory; emission; kiln refractory.
  DOI: 10.1504/IJMOR.2024.10067845
   
  
• A Mathematical Approach to Solve Multi-Objective Pentagonal Fuzzy Linear Plus Linear Fractional Programming Problems  
  by Sujit Maharana, Suvasis Nayak 
  Abstract: Optimization algorithms efficiently deal with many real life problems. In numerous practical circumstances, the concept of fuzziness can be utilized for the problems with uncertainty. This paper deals with a computationally simple and efficient solution approach to solve a mathematical model of fuzzy multi-objective linear plus linear fractional programming problem which is designed in an environment of pentagonal fuzzy numbers. In this model, fuzzy cuts are used in the objective functions to transform the fuzzy valued functions into crisp interval-valued forms and the concept of ranking function is used in the constraints to convert the fuzzy valued inequalities into deterministic expressions. First order Taylor's series approximation is used as the linearization process. Furthermore, the weighting sum method with analytic hierarchy process is applied to tackle the multi-objective optimization. To justify and validate the feasibility, two existing numerical examples are solved and also the computational results are comparatively studied.
  Keywords: Linear plus linear fractional programming; Multi-objective optimization; Pentagonal fuzzy numbers; Interval valued functions.
  DOI: 10.1504/IJMOR.2024.10067850
   
  
• Bernoulli Vacation Bulk Queue with Essential, Optional Service, Unreliable Server and State Dependent Arrival Rates  
  by Kalyanaraman R, Sivasuprajha R.V 
  Abstract: This paper presents the steady state analysis of a single server, bulk arrival, fixed batch service, Bernoulli vacation queue. The arrival follows compound Poisson process with state dependent arrival rates. The service time follows general distribution and services are given in batches of fixed size. The server provides two types of services called, essential and optional service to each batch. At each service completion point, the server takes vacation of Bernoulli type. The vacation period is generally distributed. In addition, during server's busy state, the server may breakdown immediately, the server is send for repair. The number of breakdowns follows Poisson process where as the repair period follows general distribution. For this queueing system the steady state probabilities are derived in terms of probability generating function. The expected number of customers and mean waiting times at various server states are derived. Numerical illustrations are given.
  Keywords: Non-Markovian queue ; Bulk arrival queue ; Fixed batch size ; Bernoulli vacation ; Essential and Optional service ; Unreliable server ; State dependent rates.
  DOI: 10.1504/IJMOR.2024.10067988
   
  
• A Fuzzy Inventory Approach Involving Twin Storehouses with Price-Varying Consumption Considering Partial Delay and Ecological Sustainability  
  by Varuna Bhardwaj, Sunil Kumar, Vipin Kumar Tyagi 
  Abstract: As warming the planet becomes a contentious topic, different nations attempt to reduce greenhouse gas emissions by funding numerous initiatives and encouraging companies to go green. The techniques for supply administration include storing products as stocks are utilized to meet the needs of the consumer. The set-up for storing stuff has capabilities that improve ecological sustainability for extending the lifespan period of items. To reduce overall costs, which include the expense of greenhouse gas emissions, we designed a twin-storehouse stock simulation of degrading goods with a Price-varying demand pattern and permitted shortfalls under partially backlogged circumstances in both crisp and fuzzy ecosystems. A computational instance is used to demonstrate the applicability of the provided framework. To explain the scenario, an evaluation of sensitivity is included. The last section discusses the final words and possible potential expansions.
  Keywords: Partial Delay; Procurement; Requisition; Hired Storage; Owned Storage.
  DOI: 10.1504/IJMOR.2024.10068052
   
  
• Sustainable Supply Chain for Developing new Product with considering Political Aspect using Mathematical Programming and Fuzzy Multi-Criteria Decision Making  
  by Samaneh Mirzamohammadi, Meghdad Jahromi 
  Abstract: This paper describes a method in order to design an optimal configuration for a sustainable supply chain with respect to product architecture. Recent situations and some limitations of co-working with international suppliers caused many companies to try to retain and increase the sustainability rate of their supply chain. Given this concern, in this paper through reviewing the literature and using experts' viewpoints, the considered dimensions of sustainability have been developed. In fact, in addition to financial, environmental and social aspects of sustainability, the political aspect must be been taken into consideration for many supply chains. Political sustainability aspect is considered to reduce the risk of non-delivery of components and modules in different situations. The main focus of this paper is to consider platform sustainability and supply chain cost simultaneously. For this purpose, first, a Fuzzy Analytic Hierarchy Process (FAHP) is used to weight sustainability factors and then based on these weights, FTOPSIS method is used to determine the sustainable indexes for suppliers. In addition, a multi-objective mathematical programming has been developed to decide on the supply chain configuration.
  Keywords: Sustainable supply chain; Product architecture; Political sustainability.
  DOI: 10.1504/IJMOR.2024.10068476
   
  
• An Optimal Ordering Policy Model of Delayed Deteriorating Pharmaceutical Items with Price Sensitive Demand, Uniform Distribution Deterioration Rate and Customer Service Level in Healthcare Environment  
  by Yahaya Ahmed, Abubakar Musa 
  Abstract: In 2019, Rastogi and Singh explored an inventory system for varying deteriorating pharmaceutical items with price-sensitive demand and variable holding cost under partial backlogging in healthcare industries. However, the model formulation considers the items to deteriorate instantaneously. On the contrary, majority of pharmaceutical products (medicines or drugs) exhibit delayed deterioration, that is, deterioration starts after certain period in stock. In addition, customer service level is a crucial issue in the pharmaceutical inventory management. This research, therefore, reformulates Rastogi and Singh (2019) model incorporating more realistic assumptions such as: delayed deterioration, customer service level and mean uniform distribution deterioration rate. The objective of the research is to find the optimal replenishment policy that minimises the retailer's total average cost by computing the optimal ordering quantity and optimal cycle period. Solution algorithm is proposed. The model's application is validated with some numerical examples and sensitivity analysis.
  Keywords: Delayed Deterioration; Healthcare Environment; Ordering Policy; Service level; Uniform Distribution.
  DOI: 10.1504/IJMOR.2024.10068603
   
  
• Threshold Selection for Extreme Value Estimation based on Uncertainty Theory  
  by Justin Chirima, Frank Ranganai Matenda, Mabutho Sibanda 
  Abstract: This paper examines an inverse linear uncertainty distribution threshold selection approach for fitting the Generalised Pareto Distribution (GPD). The threshold is an unknown quantity which needs to be estimated. To estimate GPD parameters, the peaks-over-threshold method is applied. An algorithm based on the linear uncertainty distribution is developed and used in establishing the optimal threshold for fitting the GPD. Initially, the algorithm is tested on hypothetical data with known thresholds, Fort Collins precipitation data and Newlyn, Cornwall wave height data found in R. Finally, Nikkei 225 index data and Hang Seng index data found on Yahoo finance is analysed using the proposed method to establish if the algorithm can be applied to real life data from financial markets. We discovered that the developed procedure is capable of determining distinct thresholds using information from the mean residual life plot and the threshold stability plot.
  Keywords: uncertainty distribution; threshold; generalised Pareto distribution; mean residual life plot; threshold stability plot; peaks-over-threshold.
  DOI: 10.1504/IJMOR.2024.10068770
   
  
• Study of A Production Inventory Policy with Finite Products Life, Few Imperfect Products and Demand Reliant on Stock-Level  
  by Sandeep Kumar, Robin Singh, Mukesh Kumar, Birjesh Kumar, Deepak Kumar, Rahul Singh 
  Abstract: The current work is about an inventory policy that permits a few imperfect products for reproduction, and this permission results in some deterioration. The life of products is considered finite, and demand is taken as stock-level dependent. The model has additionally taken into consideration the consistent manufacturing rate, which ends after a favoured stage of stocks, and that is the top stage of it. Caused by demand for products, imperfect items, and decay in products, the inventory lowers to zero, at which point the manufacturing cycle begins once more. To verify and illustrate the study, some numerical examples are carried out and bound to delineate the use and appropriateness of the inventory policy. Also, a sensitivity analysis is presented. The present study finds the entire optimal inventory cost, the optimal ordering cost, and the ordering cycle that maximise the expected total profit per unit of time.
  Keywords: Production; imperfect products; stock-level; deterioration; optimal.
  DOI: 10.1504/IJMOR.2024.10068890
   
  
• Two Three-Layer Architectures for Stacking Ensemble Learning  
  by Safia Abdouche, Paul Honeine 
  Abstract: Stacking is an increasingly popular ensemble learning strategy, investigated in many fields to improve the performance of a prediction system due to its efficiency, flexibility, and versatility. In this paper, we propose two different stacking architectures, aiming to provide three-layer models. The first one operates in a recursiveway, integrating in a first level several stacking models, each defined on a subset of base models, and then their results are staked again to get the final prediction results. The second architecture is an iterative one that combines the base learners using different meta-learners, and then the results of the meta-learners are combined using a last stacking to provide the final prediction results. We studied the proposed architectures by considering a large set of heterogeneous base models and several types of the meta-models. By conducting extensive experiments, we demonstrate the relevance of the proposed methods, showing that they outperform conventional ML models as well as bagging and boosting models on several real-world datasets.
  Keywords: Ensemble Learning; Stacking Strategy; Base Learners Selection; Predictive Modeling.
  DOI: 10.1504/IJMOR.2024.10069012
   
  
• Investigation of Buy-Now-Pay-Later and Advance Payment Options in a Queueing-Inventory System with Hybrid Reordering Policy  
  by Abdul Reiyas M, Anzen Koffer Vishnukumaran, Venkatesan Thiyagarajan, Jeganathan Kathirvel 
  Abstract: This study explores the integration of buy-now-pay-later (BNPL) and advance payment (AP) schemes in the queueing-inventory system (QIS), analysing their impact on system performance, customer behaviour, and inventory management. BNPL method allows customers to defer payments while receiving goods immediately, while advance payment systems require customers to pay upfront, affecting order fulfilment and inventory dynamics. We examine how these payment methods influence customer arrivals, service times, and inventory replenishment policies in the QIS. By considering the interaction between payment schemes and emergency replenishment strategy, we provide insights into the optimal management of inventory levels and queueing processes. The stability condition and the steady-state distribution of the given system are derived under a strategy by truncating the size of the infinite pool using Neuts and Raos truncation method. The various numerical analysis has been computed.
  Keywords: Buy-Now-Pay-Later; Advance Payment; Hybrid Reordering Policy; Negative Customers; Queueing-Inventory System.
  DOI: 10.1504/IJMOR.2024.10069022
   
  
• Is your Bank Financially Stable? Inspection of financial Health of Banks using the Novel Approach RAAS  
  by Shanky Garg, Rashmi Bhardwaj 
  Abstract: A powerful financial system is required for a robust and vibrant economy. The performance of any countrys economy depends on the Banking institution. Analysis of the performance of banks is necessary for policymakers, companies, industries, and customers who put their hard-earned money into them. Through performance analysis, necessary steps can be taken to help financially weak banks. Failure of Banks is a dangerous situation for the customers and investors. Even though the government has made efforts to devise possible ways to rescue customers. It is the customers responsibility to keep an eye on these institutions. In this study, we propose a novel multicriteria decision-making (MCDM) approach i.e., ranking alternatives based on area similarity (RAAS) through which we can easily analyse the health of our banks using some basic metrics so that customers can get a fair idea about the health of their banks. A case study is done by taking seven banks financial statements. Among them, ICICI and HDFC top the list. A comparative analysis with other methods of MCDM is done to analyse the efficiency of the proposed model. When compared with RAPS (6%), MCRAT (5.56%), and TOPSIS (12%), RAAS has the highest accuracy with an error value of 4.86%.
  Keywords: Bank Failure; Financial Health; MCDM; Performance Analysis; RAAS.
  DOI: 10.1504/IJMOR.2024.10069124
   
  
• Analytics of Uncertain Advertisement Sharing in an Imperfect Production Inventory Model in Green Supply Chain System  
  by Madhusudan Dolai, Shyamal Kumar Mondal 
  Abstract: In today's competitive market, green production is gaining traction due to environmental concerns. This study examines the green degree of final products in production systems with imperfect quality, where production costs vary with the green degree. Advertising plays a crucial role in business, traditionally handled by manufacturers alone. This paper introduces a coordinated advertising policy between manufacturers and retailers, analyzed in both crisp and fuzzy environments. We also develop a new nonlinear fuzzy number, termed the sine fuzzy number, to address uncertainties in advertisement sharing. Our model optimally determines the frequency of advertisements, the product's green degree, and the number of business cycles. Results indicate that when manufacturing managers incorporate advertisement strategies alongside the product's green degree, they achieve greater economic profitability under certain conditions in both crisp and fuzzy models. Notably, equal advertising efforts from both the manufacturer and the retailer maximise profits for the integrated system.
  Keywords: Imperfect production; Green products; Advertisement coordination; Credit period; Sine fuzzy number; Signed distance method.
  DOI: 10.1504/IJMOR.2025.10069217
   
  
• Analysis of an M/G/1 queue in two-way communication under general retrial policy  
  by Sowmiya S, P. Rajadurai 
  Abstract: In this paper, we have analyzed the performance of inbound and outbound calls under the general retrial policy. The incoming calls follow the Poisson arrival process, whereas the outgoing calls follow an exponential distribution time. The server dials the outgoing call only when the server is idle. Once the customer arrives and finds the server is in the busy stage, then they will join the retrial queue called orbit. The proposed concept is used in telecommunication and call centers to optimize waiting times and satisfy customer needs. Using the supplementary variable technique and probability-generating function, we have derived the mean arrival (incoming call) time and mean service time. Some Numerical examples and graphical representations are illustrated using MATLAB.
  Keywords: Retrial queue; Inbound call; Outbound call; Supplementary variable technique; Coupled Switching.
  
  
• The Inventory Model for Optimal Replenishment Policy with Deterioration and Various Interest Rates: Two Levels Permissible Delay in Payment Strategy  
  by Jitendra Kaushik 
  Abstract: Here, I developed an 'EOQ' model for the deteriorating items considering the price and time-dependent ramp-type demand function. I considered two rates for interest charged and discussed four different possibilities according to the length of the time slots: 1) both the rates lie in the growing phase; 2) one lies in the growing, and another lies in the constant phase. Permissible delay in payment provides an opportunity for extra sales, which increases revenue for suppliers and retailers. Suitable numerical examples are provided to demonstrate the obtained results. The comparison of models is presented considering permissible delay and without permissible delay; our results highlight higher profit to retailers in case of permissible delay. Then, sensitivity analysis is performed, and its implication is discussed from a managerial perspective.
  Keywords: economic order quantity; nonlinear demand function; permissible delay in payment; PDP: deterioration; shortage; inventory model.
  DOI: 10.1504/IJMOR.2023.10069219
   
  
• A New Method for Solving Optimal Control Problem with Bounded Control Variable  
  by Daya Ouidja, Aidene Mohamed 
  Abstract: A new approach to solving the optimal control problem with bounded control variable is discussed. It is built on the fusion of the adaptive method with hybrid direction, and the indirect finishing procedure. By discretizing, we obtain an approximate solution to the initial problem, which will serve as the initial solution for the second step of our method. In the final step, the finishing procedure allows us to find the optimal solution to our problem by resolving a system of nonlinear equations through the Newton method to determine the switching times that allow us to form the optimal bang-bang control shape. This procedure is described in detail using a numerical example.
  Keywords: optimal control problem; optimality criterion; discretization; adaptive method; hybrid direction; finishing procedure; bang-bang control.
  DOI: 10.1504/IJMOR.2024.10069220
   
  
• Type II Half Logistic Unit Inverse Weibull Distribution: a Comprehensive Examination Of Statistical Inference And Comparative Performance  
  by Shameera T, Bindu P.P. 
  Abstract: This study uses the unit inverse Weibull distribution to create a novel lifespan distribution known as the type II half logistic unit inverse Weibull distribution (TIIHLUIWD). There has been discussion of a number of statistical features, including moments, probability weighted moments,cumulative hazard rate function, revised hazard rate function, and survival function. We have also investigated additional features such as the quantile function, mean deviation, order statistics, kurtosis, and skewness. There has been discussion of a number of estimate techniques, such as maximum likelihood, moments, Cramer-Von Mises, weighted and ordinary least square, and PC estimations. To evaluate the precision and accuracy of the parameters, simulation studies were carried out. Using two real-world applications, comparative assessments were carried out to demonstrate the usefulness and efficacy of the suggested model in relation to other models that are currently in use.
  Keywords: Type II half logistic unit inverse Weibull distribution; statistical properties; estimation; simulation study.
  DOI: 10.1504/IJMOR.2024.10069227
   
  
• A Steady State Analysis of an Optional Differentiated Working Vacation Queue with Working Breakdown  
  by Muthukumar S., Ebenesar Anna Bagyam J 
  Abstract: In this work, we study the steady state behaviour of the M/M/1 queue with working breakdown and optionally differentiated working vacations. After each busy time, the server takes either an optional working vacation I or II. If a server breaks down during busy periods, it will provide the minimum number of services until it is repaired. The probability-generating function is used to determine the model's steady-state solution. Moreover, various indicators of the performance of the specified model are discussed in explicit form. The PSO algorithm is also used for cost optimisation analysis. The effects of parameters are demonstrated with numerical examples.
  Keywords: Single server queue; multiple variants of working vacations; working breakdown; repair; stationary analysis; and optimization.
  DOI: 10.1504/IJMOR.2024.10069621
   
  
• An Application of Job-Shop Optimising Model for Solving Multiple Project Scheduling in Digital Marketing Company  
  by Le Dao, Huynh Nguyen Khang Thinh 
  Abstract: Business organisations nowadays must carry multiple different projects at the same time to deliver the final products to customers or improve the competency core of the organisation with limitation in human resources. Addressing these resource-constrained multi-project scheduling is essential because it schedules the tasks of multiple projects in case such that no employee suffers overallocated tasks situation while it still can minimise the makespan or completion date of each project. This study aims to develop a Job Shop Scheduling model combining with the weighted sum method to find the optimal makespan of each project according to its priority while making sure no overallocation of tasks does not happen to any worker. Overall, the result of the study will support business in minimising the completion dates of multiple projects. The model also eliminated 50 overallocated tasks, preventing workforce strain, potential negative impacts on labour costs and employee performance due to overtime working.
  Keywords: Multi-project scheduling Job Shop Scheduling model Makespan.
  DOI: 10.1504/IJMOR.2025.10069907
   
  
• A Fuzzy Multi-Objective Supplier Selection and Order Allocation Model with Time Value of Money  
  by Mohsen Hamidi, Mehdi Seifbarghy, Aychar Khajavipour 
  Abstract: In this research, a supplier selection and order allocation problem with the concept of time value of money is modelled and solved. The manufacturer/buyer obtains its required items from different suppliers and can pay suppliers in the future with different interest rates agreed upon between the buyer and suppliers. The optimisation model includes three objectives concerning purchasing cost, quality, and delivery time. Quality and delivery time have been converted into monetary values and have been integrated with purchasing cost in the objective function. The three-objective model minimises purchasing cost considering the time value of money, quality cost, and delivery time penalty. Demand of supplied items is deemed uncertain and delivery time is a fuzzy parameter. Scenario-based and robust optimisation approaches are applied to deal with demand uncertainty of the models. To assess the performance of the models, numerical examples are solved and sensitivity analysis has been performed on key parameters.
  Keywords: Supplier Selection and Order Allocation; Time Value of Money; Scenario-based Programming; Robust Optimization.
  DOI: 10.1504/IJMOR.2025.10069983
   
  
• Analysis and Empirical Investigation of Queueing Inventory System: Two Classes of Customer under Non-Pre-Emptive Priority, Single Vacation, and (s, S) Replenishment Policy  
  by Ayyappan G, N. Arulmozhi 
  Abstract: The arrival of priority and regular customers is governed by the Markovian arrival process, with two distinct categories of customers being observed. The duration of their service times is determined by the phase-type distribution. The system consists of an infinite capacity for ordinary customers and priority customers having finite buffer capacity of N size. Maximum S items in the inventory. Arriving priority customer which find the inventory zero is lost (lost sales). If a ordinary customer discovers the inventory to be empty, they may be waiting to line. The utilisation of the (s, S) policy is also implemented within the system. The number of priority and regular customers in the system is analysed using the matrix analytic method. Furthermore, a thorough examination of steady-state analysis, busy period, cost analysis, and numerical exemplifications are all carried out.
  Keywords: Markovian Arrival Process; Phase-Type service; Non-preemptive priority; (s; S) policy; Single vacation; Breakdown,.
  DOI: 10.1504/IJMOR.2025.10069989
   
  
• Flexible Production System for Green Products with Warm-up Period, Reworking, and Automated Screening Process Considering Preservation Technology and Multi-Variate Demand  
  by Sunit Kumar, Rachna Kumari, Dharmendra Yadav 
  Abstract: For green products, an economic production quantity (EPQ) inventory model is developed in the current study considering warm-up period, volume flexibility, automated screening process, and reworking. Here, imperfect production rate and warm-up period are linked with each other. Impact of greenness-and-selling price reliant demand on the inventory policy for green production is investigated. Effect of PT and GT also incorporated in the model. Developed model is explored for the perspective of economic and environment sustainability. The proposed model aims to determine the values of production period, production rate, investment in preservation and green technology, and selling price, with the goal of maximizing the total profit of the green manufacturing system while accounting for inflation. To validate the developed model, we also conduct sensitivity analysis and numerical analysis.
  Keywords: Green Technology; EPQ; Warmup Period; Preservation Technology; Carbon Tax; Multi-Variate Demand.
  DOI: 10.1504/IJMOR.2025.10070280
   
  
• A Novel Approach to Optimise Fuzzy Association Rule by using Evolutionary Genetics Algorithm  
  by Bijayini Mohanty, Santilata Champati, Swadhin Kumar Barisal 
  Abstract: In data mining, extracting useful information from complicated and ambiguous datasets has remained a significant issue. To address such problems, the fuzzy logic approach is becoming increasingly very popular. The traditional association rule mining and clustering are two highly efficient approaches for finding underlying information in this discipline. This approach integrates the fuzzy logic theory to improve the efficiency of these two approaches. The integrated approach is more adaptive to dealing with real-world data. So, this study proposes a hybrid framework that effectively explores and optimises the number of generated rules. This work provides a unique cluster fuzzy association rules (CFARs) technique by combining fuzzy association rule mining and fuzzy C-means clustering. The proposed model generates three clusters for the fuzzy association rules for the considered online retail dataset. This approach processes the primary set of CFAR to filter-out optimal number of rules. The optimisation process is carried out under the guidance of evolutionary genetics algorithm. This mining methods 5,000 fuzzy association rules from the consider data, which is later reduced to 2,005 number of cluster fuzzy association rules through the optimisation process.
  Keywords: Data mining; Fuzzy Logic; Association Rule Mining; C-means Clustering; Evolutionary Genetics Algorithm; Apriori Algorithm.
  DOI: 10.1504/IJMOR.2025.10070282
   
  
• Optimal Replenishment Policy for a Deteriorating Multi-Item Inventory Model with Stock-Dependent Demand and Backorder  
  by Dharma Lesmono, Taufik Limansyah, Ignatius A. Sandy 
  Abstract: This paper presents a mathematical model for multi-item deteriorated items, considering stock-dependent demands. The models primary objective is to minimise the total cost under various replenishment policies, such as individual, joint, or combined, by determining the optimal time between replenishments and when the stock reaches zero. We illustrate the models application with a numerical example involving three items and determine the optimal replenishment policy. Then, sensitivity analysis is performed for the joint ordering cost for two and three items to establish the bound for either the joint replenishment policy or the combined order policy is favourable, giving the minimum total cost.
  Keywords: multi-item; replenishment policy; time- and stock-dependent demand; deterioration.
  DOI: 10.1504/IJMOR.2025.10070289
   
  
• Flexible Group Service Queueing Model with Starting Failure, Essential Repair, Optional Repair and Impatient Customer  
  by Ayyappan G, S. Kalaiarasi Sundaram 
  Abstract: In this paper we examine a particular queueing model wherein the services are provided in groups ranging from 1 to a pre defined constant, say K, and the arrival follows a Markovian arrival process. The service time of each individual customer follows phase type distribution. The maximum of each customers individual service time within a group is defined as the group's service time. At the service completion moment if there are fewer customers than K, the server won't begin the subsequent service until the system's customer size reaches K or a randomly assigned admission period expires, whichever happens first. The phase type representation of the service times depends on the group's size. Upon starting the service, starting failure may happen, which would lead to essential repair and optional repair and when the server is in essential repair the customer in the pool may renege.
  Keywords: Markovian Arrival Process; Flexible group service; Phase type Distributions; Starting Failure; Essential Repair; Optional Repair; Impatient Customer.
  DOI: 10.1504/IJMOR.2025.10070292
   
  
• Necessary Optimality Conditions for Fractional Control Problems  
  by A. Pattnaik, S. Padhan 
  Abstract: A control problem is a mathematical model of a dynamic system, where one needs to extremise the performance of the system which satisfies some physical constraints and determine a suitable control law. In this paper, a control problem is constructed using Caputo fractional derivatives. We have derived involved Hamiltonian functional using Caputo fractional derivatives and integrals. We have used it to prove Pontryagins minimum principle. Then we obtain the necessary optimality conditions for the fractional unconstrained and constrained control problems to attain the extremum using the Hamiltonian functional and Pontryagins minimum principle, respectively. In addition, we have also studied the consequences of these results. A counterexample is given to justify the importance of the new findings with the help of suitable Mathematica codes. It is also observed that some of the results previously reported in the literature are the particular case of the present investigations.
  Keywords: Caputo fractional derivative; Hamiltonian functional; Pontryagin's minimum principle; Fractional optimal control problem.
  DOI: 10.1504/IJMOR.2025.10070293
   
  
• An MS-TORO Approach for Allocating Scarce Intangible Resources  
  by Eunice Cristyl Del Pilar, Miriam Bongo 
  Abstract: Scarce intangible resources have always been challenging to allocate, given their distinct nature compared to tangible resources. As a means of allocation, the literature by far focused on less objective approaches, which discount the significant role that multiple stakeholders with diverse, conflicting interests play in the decision-making process. To advance this limitation, this paper employs a multiple-stakeholder-based target-oriented robust-optimization (MS-TORO) approach to allocate scarce intangible resources. As a case study, scarce intangible resources are represented by skilled medical staff intended to be assigned to victims of extreme scarcity-inducing situations such as natural disasters, economic downturns, and epidemics. The results revealed that the allocation of intangible resources significantly varies according to the individual interests of stakeholders; as such, these individual interests have been satisfactorily balanced through the MS-TORO approach.
  Keywords: intangible resources; allocation problem; MS-TORO approach.
  DOI: 10.1504/IJMOR.2025.10070340
   
  
• Impact of Efficient Targets by DEA Models - Insights from Time-Series Data of Japanese Retail Companies  
  by Xu Wang, Hiroki Iwamoto, Takashi Hasuike 
  Abstract: Data envelopment analysis(DEA) is a widely used approach for assessing the relative efficiency of decision making units (DMUs) with multiple inputs and outputs. Different DEA models may provide diverse efficient targets; it is crucial to investigate the efficiency-enhancing impact of these targets. This study compares the impact of the efficient targets provided by conventional and nearest-distance DEA models. To accomplish this, we employ several novel analytical methods leveraging time-series data spanning 2018-2020, encompassing 72 retail companies in Japan. This study is conducted under the assumption that DMUs can achieve efficient targets provided by DEA models. Then, utilising time-series data enables us to evaluate the long-term impact of efficient targets on enhancing the efficiency of inefficient DMUs. The results of experiments clarify that the efficiency-enhancing capability and characteristics of efficient targets provided by the two types of DEA models, which are expected to serve as a preliminary reference for DEA users.
  Keywords: Data Envelopment Analysis; Conventional Model; Nearest-distance Model; Efficient target; Efficiency enhancement; Time-series data.
  DOI: 10.1504/IJMOR.2025.10070342
   
  
• Improving Medical Diagnosis with Innovative Pythagorean Fuzzy Correlation in Clustering and Pattern Recognition  
  by Jishu Jana, Jyoti Bajaj, Satish Kumar 
  Abstract: Pythagorean fuzzy set is a very potent and practical generalization of intuitionistic fuzzy sets. Compared to intuitionistic fuzzy sets, it has a diverse working areas. Nowadays, the correlation coefficient is an emerging tool for handling a various types of decision-making problems. This study presents a novel correlation coefficient methodology that readily addresses the drawbacks of the existing methodologies. Comparison with existing methods in numerous counter-intuitive circumstances demonstrates its superiority. It is successfully and effectively used to resolve problems with pattern recognition, medical diagnosis, and clustering of any type of data into Pythagorean fuzzy sets. In illustrated cases, its outputs are also compared with the outputs of existing approaches. This approach turned out to be the most dependable, effective, reliable, practical, and valid among all the existing methods.
  Keywords: Pythagorean Fuzzy Set; Correlation Coefficient; Pattern Detection; Medical diagnosis; Clustering.
  DOI: 10.1504/IJMOR.2025.10070387
   
  
• A Multi-Commodity Vehicle Routing Problem for Vermicomposting Supply Chain  
  by Sukhpal ., Kaushal Kumar 
  Abstract: The vermicomposting supply chain is a type of two-echelon supply chain that is made up of suppliers of organic waste, suppliers of earthworms, etc. for raw material, a vermicomposting manufacturing unit to produce vermicompost, and customers of the vermicompost. This article is primarily concentrated on second-echelon transportation from manufacturing unit to customers. Moreover, customer demand for vermicompost comes in different packet sizes that makes the multi-commodity vehicle routing problem most appropriate to handle the second echelon of vermicomposting supply chain. An integer programming formulation is provided for the proposed vermicomposting problem. The proposed routing problem is computationally complex as it involves multiple interrelated sub-problems such as vehicle assignment, commodity allocation, and route optimisation. Therefore, an efficient solution algorithm based on a greedy-based approach has also been provided. To evaluate the proposed methods, extensive computational experiments have been conducted on benchmark scenarios drawn from an actual problem of vermicomposting supply chain.
  Keywords: Multi-Commodity; vehicle routing problem; vermicompost; greedy search algorithm; integer programming.
  DOI: 10.1504/IJMOR.2025.10070485
   
  
• On Asymptotic Behaviour of Random Walk Process with Two Barriers arising in Buffer Stock Problem  
  by Tahir Khaniyev, Zulfiye Hanalioglu, Hilala Jafarova 
  Abstract: This study investigates a random walk process with two barriers, incorporating triangularly distributed interference of chance, as it arises in the buffer stock problem. Under certain conditions, the process is shown to be ergodic, and an exact formula is derived for the characteristic function of its ergodic distribution. The characteristic function of the ergodic distribution is then expressed by the characteristics of the boundary functionals. Moreover, using the obtained results, the limiting form of the characteristic function for the ergodic distribution of standardized process is determined. Finally, asymptotic results are established for all moments of the ergodic distributions of both considered processes.
  Keywords: Random walk with two barriers; Characteristic function; Moments of Ergodic distribution; Asymptotic behaviour; Triangular distribution.
  DOI: 10.1504/IJMOR.2025.10070488
   
  
• A fuzzy nonlinear economic production model with production capacity constraints and shortage penalties  
  by Anuradha Sahoo, Minakshi Panda 
  Abstract: A novel multi-objective nonlinear economic production quantity model is developed under the production capacity constraint and shortage constraint in a finite time horizon. This model aims to optimise two objectives: minimising total cost and maximising customer satisfaction level within a finite time horizon. This model specifies that demand is constant and shortages occur only at a particular time period. Also penalty cost is included due to shortages. Various parameters involved in the model such as production rate, production cost, holding cost, penalty cost, and demand are fuzzy in nature. Signed distance method and graded mean integration method are used to defuzzify the fuzzy model. Objective function’s graphs are included. Pareto fronts for different objective functions are provided to show the validity of the model.
  Keywords: economic production quantity model; penalty cost; fuzzy number; inventory model; shortages; Pareto front; defuzzification.
  DOI: 10.1504/IJMOR.2024.10070568
   
  
• A three-player cooperative advertising Stackelberg differential game-theoretic model with leader and follower subsidy schemes  
  by Peter Emeke Ezimadu, Jacob Chinedum Ehiwario, Sophia Oghenevwaire Ezimadu 
  Abstract: Cooperative advertising models studies usually major on two parties. This work considers a cooperative advertising model in which all three members of a supply channel directly engage in advertising, with the manufacturer and distributor subsidising the distributor and retailer’s advertising efforts respectively. It considers a Stackelberg differential game in which the manufacturer is the channel leader, and the distributor and retailer are the first and second followers respectively. The study determines the players’ advertising efforts, subsidy rates and payoffs through backward induction, and the awareness share through differential equation. The paper considers a situation where: neither the manufacturer nor the distributor provides subsidy; the manufacturer’s provided subsidy is not given to the retailer; the distributor provides intervention subsidy in the absence of subsidy from the manufacturer; and both the manufacturer and the distributor provide subsidy. Using illustrations, it discusses the effect of the decision variables and awareness on the payoffs.
  Keywords: cooperative advertising; coop ad; Stackelberg differential game; supply channel; infinite horizon game; subsidy; backward induction.
  DOI: 10.1504/IJMOR.2025.10070581
   
  
• On the number of nonnegative solutions for Diophantine equation and application for Frobenius problem and integer programming.  
  by Noria Benkhemmou, Mouloud Goubi, Fatima Hessas 
  Abstract: Diophantine equations have been the subject of much research in the literature. In this work we focus our attention on the study of the number of nonnegative solutions of a linear Diophantine equation. Using algebraic short generating functions and the concept of complete Bell polynomials, we present an explicit formula and establish recurrence relations. These are useful to propose a new approach for the construction of efficient algorithms for the computation of the Frobenius number of any order, and for the solution of some linear integer problems, such as the subset integer programming problem and the 0-1 knapsack problem. We demonstrate that these problems can be solved efficiently.
  Keywords: Diophantine equation; Frobenius number; short generating functions; integer programming; knapsack problem.
  DOI: 10.1504/IJMOR.2025.10070582
   
  
• Optimal Replenishment Policy under Finite Planning Horizon with Fuzzy Parameters  
  by Janani R, Geetha Krithivasan 
  Abstract: This article deals with fuzzy EOQ inventory model with a finite planning horizon for deteriorating items. In this research, we develop two models. In model I, we examine two distinct scenarios. In the first scenario, we assume that product demand is fuzzy in nature, while in the second scenario, we consider the cost components to be fuzzy. In Model II, we address carbon emission and green investment. Here we treat the carbon emission to be fuzzy in nature. Triangular fuzzy numbers and trapezoidal fuzzy numbers are used to fuzzify the parameters of the inventory system. The signed distance method is used for defuzzification. The optimal values for cycle time and order quantity are determined. The related optimal inventory cost for the two models is also determined. Numerical illustrations are given to demonstrate the solution procedure. The managerial insights obtained from our work is also highlighted.
  Keywords: Deterioration; Finite planning horizon; Signed-distance method; Triangular fuzzy number; Trapezoidal fuzzy number; Carbon emission; Green technology.
  DOI: 10.1504/IJMOR.2025.10070852