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International Journal of Mathematics in Operational Research

International Journal of Mathematics in Operational Research (IJMOR)

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International Journal of Mathematics in Operational Research (106 papers in press)

Regular Issues

  • Dependability Prediction of a Hybrid Multi Client Computer Networking System Using Gumbel-Hougaard Family Copula   Order a copy of this article
    by Abdul Kareem Lado, Abubakar Bawa Zarogi, Nura Jibrin Fagge 
    Abstract: This paper presents a Markov model of a computer networking system. It consists of four subsystems: z client, router, load balancer, and two distributed data based servers. They are arranged in a series-parallel configuration and integrated with a switch. The paper research objectives include evaluating the system for various dependability metrics and to see the effect of the repairs. Unit failure is presumed to be continuous and follows exponential distribution, and two repairs are available: general repair addresses partially failed states while copula repair addresses the system failure. The derived equations are studied utilising supplementary variables techniques and Laplace conversion procedures in order to obtain dependability metrics expressions such as reliability, availability, MTTF, sensitivity, and costs. The results were justified using numerical examples and presented in Tables and Figures. It was observed that copula repair produces better outcomes than general repair and therefore recommended for optimal performance of the system.
    Keywords: availability; reliability; cost implication; computer networking; system.
    DOI: 10.1504/IJMOR.2023.10055103
  • A hybrid modified cuckoo search algorithm for the uncapacitated examination timetabling   Order a copy of this article
    by Cheraitia Meryem, Rewayda Razaq Abo Alsabeh 
    Abstract: In this study, we investigate the effectiveness of cuckoo search algorithm (CSA) for solving the uncapacitated examination timetabling problem (UETTP). CSA is a popular metaheuristic optimisation algorithm that mimics the behaviour of cuckoos. Compared with other nature-inspired algorithms, it is more generic and robust for many optimisation problems. The CSA is easy to understand and implement. Furthermore, it represents a powerful search method with few controllable parameters and can be combined with additional strategies to increase effectiveness. We proposed a modified version of CSA. Moreover, a local search strategy is utilised to reinforce the CSA and improve the exploitation phase to develop and provide high-quality solutions. Extensive experiments were conducted using Carter benchmark datasets consisting of 12 instances selected from several real-world universities. The obtained results confirm that the hybrid modified CSA outperforms the basic CSA and it has comparable performance in comparison with other algorithms proposed in the literature.
    Keywords: examination timetabling; metaheuristic; cuckoo search algorithm; CSA; simulated annealing.
    DOI: 10.1504/IJMOR.2023.10055140
  • Preservation Technology Investment: A Catalyst for Sustainable Two-Warehouse Inventory Model and SDG Achievement   Order a copy of this article
    by Manoj Kumar Sharma, Divya Mandal 
    Abstract: Preservation technology investment in a two-warehouse inventory model can have a significant impact on the achievement of several United Nations Sustainability Development Goals (SDGs), including SDGs 2, 8, 12, and 13. In this article, we developed the two-warehouse inventory model and took the investment in preservation technology into account. An own warehouse of finite size and a rented warehouse for storing excess items that exceed the capacity of the own warehouse in practice. The holding cost of a rented warehouse is greater than and distinct from that of an owned warehouse. The shortage is not permitted. The purpose of this study is to design a policy for deteriorating inventory when a store invests in preservation technology to slow the rate of product degradation. The model’s utility and sensitivity examination of the appropriate resolution for a combination of features are illustrated mathematically.
    Keywords: sustainability development goals; two warehouses; preservation technology; price dependent demand.
    DOI: 10.1504/IJMOR.2023.10055545
  • “Analysis of MAP/PH/1 Queue with Differentiated Vacation, Vacation Interruption under N-Policy, Optional Service, Breakdown, Repair, Setup and Discouragement of customers ”   Order a copy of this article
    by AYYAPPAN Govindan, Archana Gurulakshmi 
    Abstract: This study looks at a single server queueing system with differentiated vacations, vacation interruption under N-policy, optional services, setup, discouragement, breakdown, and repair. For customers arrival, the Markovian arrival process (MAP) is applied, while phase type distributions (PH) are used for service and repair times. The server offers essential services to customers who are logged into the system on a first-come, first-served basis. The customer has the option to request another service (an additional service), if necessary, from the server after the essential service is complete. Here, we consider two types of vacation such as single and multiple vacations with distinct durations. Customers’ arrivals may be discouraged due to impatience during both vacation periods. The matrix analytical technique is used to determine the steady-state probability vector for this model. The stability condition, busy period analysis, cost analysis and system effectiveness are all found in this model. The outcome of numerical values and graphical representations are represented in the view of two dimensional and three dimensional graphs.
    Keywords: Markovian arrival process; MAP; phase type distribution; vacation interruption under N-policy; optional service; setup; discouragement; breakdown; phase type repair.
    DOI: 10.1504/IJMOR.2023.10055553
  • Ekeland Variational Principle on Intuitionistic Fuzzy Quasi Metric Spaces   Order a copy of this article
    by Riya Dutta, Prasun Kumar Nayak 
    Abstract: Utilizing Br
    Keywords: Intuitionistic fuzzy quasi metric space; Ekeland variational principle; Banach contraction principle; Caristi-Kirk fixed point theorem; Takahashi’s minimization theorem; Equlibrium point.
    DOI: 10.1504/IJMOR.2023.10055666
  • A Belief-degree Based Two Stage Multi-objective Solid Transportation Problem in a Green Supply Chain   Order a copy of this article
    by Vandana Kakran, Jayesh Dhodiya 
    Abstract: In recent years, transport networks have been a significant source of greenhouse gas emissions that have provoked rapid growth in global warming and contamination of air. As a result, the proposed research has captivated our interest which focuses on a two-stage green supply multi-objective solid transportation problem (2-GrSMOSTP) under an uncertain environment where all the parameters are regarded as uncertain variables. Two mathematical models for the uncertain model of 2-GrSMOSTP are formulated using expected and optimistic value criteria for deterministic conversion of the uncertain model. After deterministic conversion, these models are solved directly in the Lingo 18.0 software using the minimising distance method and the fuzzy programming technique. Finally, a numerical illustration is provided to demonstrate the application and algorithm of the models. The sensitivity of the optimistic-criterion-based model is also examined using confidence levels in order to investigate variation in the objective functions.
    Keywords: multi-objective; green supply chain network; GrSCN; solid transportation problem; STP; uncertain programming; fuzzy programming technique.
    DOI: 10.1504/IJMOR.2023.10055819
  • Optimal Inventory Economic Order Quantity Model for Inventory System with Imperfect Inspection Processes   Order a copy of this article
    by Julia T. Thomas, MAHESH KUMAR 
    Abstract: Inventory management is the core of supply and demand chain management. The economic order quantity (EOQ) model is the fundamental inventory management model that is assumed to bring only perfect items out of the ordered lot. A lot undergoes a single acceptance sampling plan with an imperfect inspection process before being placed in the inventory. The traditional inventory management process fails to address real-world sitations where each type of product is handled in a unique way by manufacturers. This paper formulates an EOQ model in a fuzzy environment while considering: 1) shortages and backorders; 2) the chance of misclassification; 3) fuzziness in the model parameters. An optimisation problem is developed to maximise the total profit. The existence and uniqueness of the optimal solutions are proved with the help of a theorem established for concavity conditions of the total expected profit function. A sensitivity analysis study is also conducted to examine the effect of inspection error on order quantity, backorder level, and total profit. Finally, several numerical examples are presented to illustrate the model derived.
    Keywords: economic order quantity; EOQ; imperfect quality; shortages; backorders; acceptable inspection level; acceptance sampling plan.
    DOI: 10.1504/IJMOR.2023.10056037
  • Economic Order Quantity Model for Pareto distributed decaying products with Quadratic Demand and Salvage Value   Order a copy of this article
    by Uttam Kumar Sharma, Varun Mohan, Sindhuja. S, Pervaiz Iqbal 
    Abstract: At present time, estimating demand and deterioration for some products become difficult. Because these key components of any economic order quantity (EOQ) model become dependable on price, freshness level and many other factors. On the other hand, rising competition does not allow managers to dispose of deteriorated items. In this paper, we incorporated salvage value parameter in EOQ model with quadratic time dependent demand and Pareto distributed deterioration. Also, the stock out condition is allowed and completely backlogged. With these axioms expressions for total inventory cost, inventory cycle time and lot size value are derived and optimised. Proposed model findings are described with the help of numerical example. Sensitivity analysis supports the relevance of salvage value parameter, i.e., rise in salvage value reduces the total inventory cost.
    Keywords: deterioration; variable demand; salvage value; variable holding cost.
    DOI: 10.1504/IJMOR.2023.10056088
  • Solving an EPQ model with Lagrange Interpolating Polynomial function via Game theory Approach   Order a copy of this article
    by Anup Khan, Sujit Kumar De, Prasun Kumar Nayak 
    Abstract: This article briefly discusses about classical economic production quantity (EPQ) model using game theoretic approach via Lagrange multiplier. It involves two stages of computations, in first stage, we develop a Mond-Weir dual of the EPQ cost minimisation problem with the help of weak and strong duality theory. Secondly, we have formulated an equivalent matrix game problem using Preda’s framework. The problem has been solved under convex optimisation, the game theoretic approach and Lagrange interpolating polynomial optimisation respectively with the help of a novel solution algorithm. The numerical illustration shows that a saddle point exists locally but for global optimality some duality gaps have been found. However, this study explains the role of Lagrange multiplier towards optimising the objective function and its corresponding range of variations also. Finally, we have done sensitivity analysis and graphical illustration to justify the novelty of this new approach.
    Keywords: EPQ model; matrix game; Lagrange interpolating polynomial; optimisation.
    DOI: 10.1504/IJMOR.2023.10056207
  • Survey on Queuing Models with Discouragement, Policies and Vacation   Order a copy of this article
    by C.K. Anjali, Sreekanth Kolledath 
    Abstract: Queuing models with discouragement, policies, and vacation have been extensively investigated due to its wide range of applications in real-life scenarios. The effectiveness of a queuing system is questioned when customers balk or renege. However, the loss of customers can be prevented up to some extent by using customer retention strategies. Also, implementing vacation and threshold policies appropriately in the system improves the servers' capacity for providing service effectively. Based on these concepts many surveys have been made on finite and infinite population queuing models. But we have observed from the queuing theory literature that surveys have not been done by combining both the finite and infinite population models. The main objective of this survey is to provide an overview of the relevant research works done on finite and infinite population models with impatience, policies and vacation. By taking into account the models and methodologies used in various research articles, we also attempt to provide an outline of the works discussed in tabular format.
    Keywords: machine repair problem; discouragement; balking; reneging; N-policy; F-policy; vacation; working vacation.
    DOI: 10.1504/IJMOR.2023.10056227
  • Decaying Inventory Model with Different Rates and Varying Costs under Preservation Technology Investment   Order a copy of this article
    by Abhinav Goel, Anshika Singh 
    Abstract: Decay, damage, or spoilage of any item is referred to as deterioration. Maintaining the product in excellent shape is a big problem for many retailers because the product loses value with increasing deterioration. Many papers have considered constant deterioration but in real life, the deterioration rate varies depending on the type of stock. This paper assumes that the item stored in the warehouse initially depletes due to demand and then, it decays at a constant and exponential rate, which is evident in the food and textile industries. With the utilisation of preservation technologies, the pace of degradation can be reduced. A mathematical framework with eventually decaying products is formed where demand depends on products and has variable carrying costs as the inventory's expense rises over time. A sample as a numerical analysis is presented to verify the outcome of the suggested model. An optimal solution for the cost function is calculated. Evaluation of sensitivity is done to determine how a modification of parameter affects the optimum solution, including and excluding preservation technology investment. Furthermore, the study's findings are used to generate several insightful managerial observations.
    Keywords: inventory; constant deterioration; exponential deterioration; stock-dependent demand; variable carrying cost; preservation technology; optimisation; non-instantaneous deterioration; EOQ.
    DOI: 10.1504/IJMOR.2023.10056265
  • Analysis of M[X1], M[X2] /G1, G2/1 Retrial queue with Priority services, Differentiate breakdown, Delayed repair, Bernoulli feedback, Balking and Working Vacation   Order a copy of this article
    by Ayyappan G, NITHYA S 
    Abstract: In this study, we construct a single server retrial queueing system with two types of breakdowns, delayed repair, Bernoulli feedback, balking and working vacation. Two different categories of customers like priority and ordinary are to be considered. This model proposes non-pre-emptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. For both ordinary and priority customers, the server consistently affords a single service that follows to general distribution. During certain periods, an arriving ordinary customer may balk the system. When the orbit and priority queue are empty after the service is ended, the server takes a single working vacation. In this study, we used probability generating function and supplementary variable technique to solve the Laplace transforms of time-dependent probabilities of system states. In order to accelerate the sensitivity analysis of system descriptions, numerical data are obtained and also examined.
    Keywords: retrial queues; batch arrivals; priority queues; working vacation; balking; differentiate breakdown; Bernoulli feedback; delayed repair.
    DOI: 10.1504/IJMOR.2023.10056402
  • Early Prediction of Chronic Kidney Disease via Ensemble-Deep-Learning Approach and Improved Dimensionality Reduction Approach   Order a copy of this article
    by R. Sengothai, R. Sivaraman 
    Abstract: This research proposes an ensemble-deep-learning approach and an enhanced dimensionality reduction method to predict chronic kidney disease (CKD) in its early stages. The proposed model has four major phases: pre-processing, feature extraction, feature selection, and CKD prediction. The pre-processed data is subjected to data cleaning and standardisation. Features are then extracted using PCA, statistical and higher-order statistical approaches, and the Spearman's rank correlation coefficient. Optimal features are selected using the hybrid optimisation model, which combines lemurs optimisation and harmony search algorithm. The CKD prediction phase uses an ensemble-deep-learning approach, including a transformer network, autoencoder, and feedforward neural network. The proposed model’s accuracy, precision, F1 score, recall, FNR, FPR, and FDR are compared with existing models, showing its superiority. The proposed model aims to predict CKD in its early stages, potentially reducing its growth rate and associated issues.
    Keywords: chronic kidney disease; CKD; hybrid optimisation model; ensemble-deep-learning approach; transformer network; autoencoder; feedforward neural network.
    DOI: 10.1504/IJMOR.2023.10056403
  • Study of a Birth-Death Process with Population Independent Death Rate.   Order a copy of this article
    by Mathew P. Sindu, Narayanan Viswanath 
    Abstract: Birth-death processes are extensively used in modelling several real-world phenomena. For example, the widely used exponential growth model is a pure birth model. This paper presents a birth-death process with time-inhomogeneous birth and death rates, where the death rate is independent of the population size. Transient analysis of the process is conducted using the generating function method. Mean, variance, and extinction probability are obtained by solving Volterra integral equations using numerical methods. A comparison, in terms of average, with the deterministic counterpart of the birth-death model, shows that it is the influence of the initial population size that separates the averages. A numerical study reveals that the new model outperforms the exponential growth model and could therefore be its substitute in several real-world applications including tumour growth modelling.
    Keywords: Birth-death process; Transient analysis; Volterra integral equation; Deterministic model; Exponential growth model.
    DOI: 10.1504/IJMOR.2023.10056408
  • Efficient Clustering-Based Constructive Heuristics for Capacitated Vehicle Routing   Order a copy of this article
    by Ankan Bose, Dipak Laha 
    Abstract: In this paper, we address the capacitated vehicle routing problem, a generalised variant of vehicle routing problems, in which the routes are assigned to a fleet of vehicles to serve customers meeting their demands in order to optimise certain criterion. Here, we aim to minimise total length of the routes. Although a plethora of research on vehicle routing appeared in the literature over many decades, a few good construction heuristics exist, namely, the heuristics of Clark and Wright (1964), Segerstedt (2014, 2018), which are used for minimising the total length of routes in the capacitated vehicle routing problem. In this paper, we have modified the heuristics of Segerstedt (2014, 2018) using K-means++ clustering in conjunction with a route merging procedure to enhance the solution quality for this problem. The computational results reveal that the modified approaches significantly improve their performance while not affecting their time-complexity.
    Keywords: Vehicle routing; K-Means clustering; K-means++ clustering; heuristics; optimization.
    DOI: 10.1504/IJMOR.2023.10056523
  • A neutrosophic application to the transportation problem with Mixed Constraints using single-valued trapezoidal neutrosophic numbers   Order a copy of this article
    by Kalaivani Kaspar, PALANIVEL K 
    Abstract: Fuzzy transportation problems have been developed to address the uncertainty in real-world problems Neutropsohic set plays a vital role in solving uncertainty which is the extension of fuzzy and the intuitionistic set The defuzzification approach using a proposed ranking function has been considered to convert the fuzzy and neutrosophic data into crisp data Moreover, this research is proposed a single-valued neutrosophic transportation problem with mixed constraints The work aims to deal with the transportation problem in terms of neutrosophic nature to obtain optimal results by using a proposed ranking function The problem explains mixed constraints by employing a conventional approach through numerical illustrations and the obtained results are compared with other ranking approaches Lastly, it shows the justification of the results and efficiency of the ranking function which gives the optimal transportation cost Lastly, MATLAB software has been used to show higher accuracy results for various ranking functions, and the proposed ranking function yields the most efficient optimal solution.
    Keywords: Transportation problem (TP); Neutrosophic set (NS); Single-valued Trapezoidal neutrosophic number (SVTNNs); Mixed constraint transportation problem.
    DOI: 10.1504/IJMOR.2023.10056633
  • A new three-term conjugate gradient method for unconstrained optimization and its applications in image restoration   Order a copy of this article
    by Hisham Mohammed, Hind H. Mohammed 
    Abstract: Conjugate gradient methods (CGM) are generally used to solve unconstrained optimisation problems. In this research, the three-term CGM was developed depending on the conjugate coefficient of the Fletcher and Reeves (FR) conjugate descent method and the second condition of the Wolfe's strong search line, and the strong Wolfe condition was used to obtain the step length. According to some assumptions, the properties of descent and global convergence have been achieved for the new proposed method. Finally, we used the proposed method to solve the unconstrained optimisation functions to show its efficiency, and it was actually superior to the FR and three-term Fletcher and Reeves (TTFR) methods. Hence, we used the proposed new conjugate gradient algorithm in image restoration and image denoising. According to the numerical results, the recently proposed algorithm outperforms both FR and Fletcher and Reeves (TTFR) algorithms.
    Keywords: algorithms; CG; optimisation; FR and TTFR; restoration; three-term Fletcher and Reeves; TTFR.
    DOI: 10.1504/IJMOR.2023.10056636
  • An inventory model and supply chain coordination for ameliorating items allowing for shortages under non-instantaneous replenishment   Order a copy of this article
    by Yunfeng Zhang, Ying Qin 
    Abstract: This study constructs an ameliorating item supply chain consisted of a single supplier and a single retailer. The replenishment from the supplier to the retailer takes a while to complete. The retailer is allowed to run out of stock. We analyse the order cycle, the profit of the supply chain system and the profit for each member under the cooperative and the non-cooperative decision-making conditions respectively. The results show that the profit of the supply chain system per unit time is higher under the cooperative decision making than under the non-cooperative decision making. However, compared with the latter, the former will lead to a decrease in the supplier's profit per unit time. To make up for the supplier's loss, a revenue-sharing contract is designed to coordinate the ameliorating item supply chain. The equilibrium solution is given by using the Nash bargaining theory. A numerical example is used to verify the main conclusions.
    Keywords: ameliorating items; supply chain coordination; inventory; revenue-sharing contract.
    DOI: 10.1504/IJMOR.2023.10056639
  • A Marketing-Oriented Production Inventory Model under Hybrid Carbon Policy with Carbon Emission Origin-Based Green Investments   Order a copy of this article
    by Srabani Shee, Tripti Chakrabarti 
    Abstract: This article studies an EPQ system for deteriorating products where demand rate is assumed to be a function of advertisement parameter and selling price under hybrid carbon regulation with green investment (GI). Here we consider latest type of market demand which is a combination of sales-price and the rate of advertisement of the product in the news and electronic media. The proposed hybrid carbon strategy is a mix of carbon cap-trade and carbon tax (CT) regulations. Here, the carbon emission (CE) arises from 3 origins setup, manufacturing and stock carrying process. The production-house can spend money on green equipments in all CEs origin independently to decrease CE. This article helps retailers to maximise the total profit through determination of optimal production time, advertising variables and amount of GI in the three origins. The numerical illustration helps to compare the objective value under different environment. Lastly, sensitivity analysis is calculated to learn the effect of the various parameters.
    Keywords: inventory; green investment; GI; advertisement and price sensitive demand; carbon tax policy; carbon cap and trade policy; hybrid carbon policy.
    DOI: 10.1504/IJMOR.2023.10056750
  • Impact of Carbon Emission Policies on a Production Inventory Model with Stock and Demand Dependent Production Rate and Preservation Technology Related Deterioration   Order a copy of this article
    by Srabani Shee, TRIPTI CHAKRABARTI 
    Abstract: This article considers an EPQ model for deteriorating items assuming price dependent demand with different carbon emission regulations. Most of the researchers have taken production rate as constant or independent of demand. However, in this model production rate has been taken to be linear combination of on-hand inventory and demand. Also, we consider that the producing and holding items in storage can generate CO2 emission. Moreover, we all know preservation machinery be able to change the rate of deterioration of produced item. So it is important to study the preservation strategy under carbon policies. For minimising the total cost in a production cycle, inventory systems are developed in carbon tax and cap-trade policies. Also, we make a comparison between the optimum results of the proposed inventory articles without carbon constraint and with two carbon strategies. At last, numerical example has been calculated to conclude the theoretical property of these articles and the effects of different parameters have been illustrated through sensitivity analysis.
    Keywords: inventory; EPQ model; preservation technology; carbon emission; carbon tax policy; carbon cap-trade policy.
    DOI: 10.1504/IJMOR.2023.10056751
  • A Hybrid transformer-based BERT and LSTM approach for vulnerability classification problems   Order a copy of this article
    by Mounesh Marali, R. Dhanalakshmi, Narendran Rajagopalan 
    Abstract: Industrial control systems (ICSs) are vulnerable to cyberattacks due to the growing corporate network and internet connectivity. Ensuring proper security and response to cyberattacks is critical as they can impact ICS performance, reliability, safety, and availability, leading to catastrophic losses. Cyber threat intelligence (CTI) helps companies avoid cyberattacks by relying on vulnerability databases such as CVEs from national vulnerability databases (NVDs). However, these databases may include flaws that compromise security solutions and hinder attack mitigation. To address this issue, automated categorisation of vulnerability data using deep learning (DL) is proposed. The study found that LSTM-tuned BERT designs outperform standard models in precision, F1 score, accuracy, and recall. Implementing DL vulnerability categorisation can enhance ICS security and decrease the threat environment.
    Keywords: vulnerability; classification; LSTM; BERT; Cyber threat intelligence.
    DOI: 10.1504/IJMOR.2023.10056753
  • Cost Benefit Analysis for Non-Markovian Bulk Queue with Server Failure   Order a copy of this article
    by Palaniamal S, Pradeep S 
    Abstract: The queueing system is significantly impacted by a breakdown, which also has complex consequences. The queueing system's functioning and dysfunction as a consequence of on-going server failure are discussed in this paper. This study investigates the server's uninterruptible failure in the presence of numerous breaks and state-dependent arrivals. The distinctive qualities and distinguishing characteristics of the queueing system are given, along with a cost model and an application example that demonstrates how the model has developed theoretically. Along with a thorough study of performance measures, the lowest overall average cost is also provided by figuring out the ideal batch size for the service.
    Keywords: cost benefit; bulk queue; server breakdown; supplementary variable technique; total average cost.
    DOI: 10.1504/IJMOR.2023.10056838
  • Development of a Block Method for Solving Multiple Order Odes   Order a copy of this article
    by Emmanuel O. Adeyefa, Adewale James, A.S. Olagunju, F.L. Joseph 
    Abstract: In this work, a convergent hybrid block method (CHBM) with two off-grid points for direct integration of first, second, and third-order initial value problems (IVPs) is proposed. The development of a block method for the solution of IVPs has been considered overwhelmingly in the literature. However, using a block method to directly solve multi-order IVPs has not been so common. Thus, the formulation of a single numerical algorithm for the direct numerical integration of first, second and third-order IVPs is our focus. The method is formulated from a continuous scheme derived using collocation and interpolation techniques and implemented in a block-by-block manner as a numerical integrator for IVPs. To assess the method’s applicability, efficiency, and accuracy, the convergence analysis has been investigated, and six test problems are considered.
    Keywords: block method; collocation; convergence; interpolation; multiple order ODEs.

  • Solving Triangular Fully Fuzzy Linear Fractional Programming Problem via Parametric Approach   Order a copy of this article
    by Rebaz Mustafa, Nejmaddin Sulaiman 
    Abstract: In this paper, the fully fuzzy linear fractional programming (FFLFP) problem is considered. The important point of this study is to illustrate an adapted method of parametric optimisation, which is a repeat operation technique that can be used to find an optimal solution for any linear fractional optimisation problem of any coefficient, such as an ordinary interval, rough interval, or fuzzy number. Here, the coefficients of the objective function, constraints, and decision variables are triangular fuzzy numbers (TrFNs), and the FFLFP problem is converted into a comparable deterministic three-linear fractional programming (LFP) problem under some assumptions. However, it can be utilised for the trapezoidal fuzzy number linear fractional programming problem. Finally, the suggested method produces the best or optimum solutions. A test numerical example of a triangular fuzzy linear fractional programming problem is given to present the performance of the procedure.
    Keywords: fully fuzzy linear fractional programming; FFLFP; linear fractional programming; LFP; parametric approach; triangular fuzzy number; TrFN.
    DOI: 10.1504/IJMOR.2023.10057017
  • Assignment Model for Employing Skilled IT Professionals for Appropriate Job Roles under Uncertainty with Different Ranking Approaches using Membership Functions   Order a copy of this article
    by Jency Leona Edward, Palanivel K 
    Abstract: Assignment problems (AP) have a wide range of practical applications because they are widely used in business, management science, and other professions. Due to the inapplicability of traditional and classical APs, particularly complicated real-world issues can be addressed using fuzzy APs which are more effective. Selecting the best candidate for the job can be challenging due to uncertainty and limited data, especially in the IT sector. The AP is one of the most important factors in decision-making for any kind of allocation or assignment. In this article, the assignment model has been employed in order to deal with the job assignment for skilled IT professionals by means of conventional approaches using fuzzy membership functions (FMF) with different ranking methods. Additionally, the model explains Moreover, the considered problem is converted into a crisp AP using the different ranking indexes and also the problem has been resolved using the existing traditional assignment methods which enhances the model efficiency. Lastly, the model concludes that the best candidate for the job was recruited and results were compared that the effective application of placement for the right candidate for the right job. the mathematical formulation, outlines, and methodology with numerical illustrations.
    Keywords: Fuzzy Assignment Problem; Ranking Methods; Robust Ranking Technique; Magnitude Ranking Method; Centroid Ranking Method; Ranking Function; Hungarian Method; MOA Method; Direct Methods.
    DOI: 10.1504/IJMOR.2023.10057021
  • Sensitivity Analysis of the Optimum Solution to Perturbations of the Profit of an Item in the Multiple-Choice Knapsack Problem   Order a copy of this article
    by Luay ALJASIM, Ferhan Al-Maliky 
    Abstract: Sensitivity analysis is the task of studying the behavior of the optimal solution of a problem due to changes in the parameter's data. In this paper, we study the sensitivity analysis for the optimum to the Multiple-Choice Knapsack Problem (MCKP), according to the perturbation of the pro fit of an arbitrary item. In turn, we study how much the pro fit of an arbitrary item in the original problem can vary without changing the optimal solution structure, the so-called sensitivity intervals that consist of lower and upper values (called limits). The obtained results are explained through a simple example, Furthermore, the performance of the proposed methods is evaluated on a set of larger problem instances. The obtained results are explained through a simple example. Furthermore, the performance of the proposed methods is evaluated on a set of larger problem instances.
    Keywords: Knapsack; Multiple Choice; Optimality; Optimization; Perturbation; Sensitivity Analysis.
    DOI: 10.1504/IJMOR.2023.10057123
  • Review the concepts of queues and inventory models   Order a copy of this article
    by Indumathi P, K. KARTHIKEYAN 
    Abstract: A queueing inventory system has been widely analysed due to its ubiquitous applications in the modern environment and ability to enhance accuracy in this field. The current investigation provides adequate knowledge about the queueing inventory systems. The main intend of the analysis is to reduce the waiting time and total optimal cost of inventory. The queueing systems, along with the inventory models, such as production inventory, stochastic, perishable products, an assorted variety of demands with diverse service times, and deteriorating inventory systems, are discussed. Based on the existing literature, this article offers some suggestions for using queueing inventory models in a wide variety of contexts. Examples of this include medical systems, traffic flow, scheduling, networking, and facility designs.
    Keywords: queueing inventory models; perishable inventory; production inventory; stochastic inventory; deteriorating inventory; demands.
    DOI: 10.1504/IJMOR.2023.10057148
  • Solving fuzzy shortest path problem with vertex transfer penalties under type-2 fuzzy environment   Order a copy of this article
    by Babita Chaini, Narmada Ranarahu 
    Abstract: Shortest path problems have many applications in the field of graph theory. However, the traditional shortest path algorithms only work in a situation where an edge penalty is a real number. In real-world situations like the shipping and transportation industry, the edge weight from a source node to the destination node often could not be defined through a real number due to incompleteness or inexactness, this can be challenging in some cases and can be defined through a fuzzy number. In this scenario, finding the shortest path between two nodes has already been solved in the past. In this paper, we are trying to find the shortest path between two nodes where the graph has transfer penalties at the node and the transfer penalties are defined by a type-2 trapezoidal fuzzy number. This problem has a go-to solution, i.e., to use a Kirby-Potts expansion to add parallel edges and then use the standard Dijkstra algorithm to find the shortest path. In this paper, we have not used any graph extension technique, but we have used a modified Dijkstra algorithm to manage the vertex penalty and find the shortest path in between the nodes. A numerical example is provided to explain the usefulness of the approach.
    Keywords: fuzzy shortest path problems; IT2TrFN; modified Dijkstra algorithm; transfer penalties.
    DOI: 10.1504/IJMOR.2023.10057214
  • Tetracontatetragonal fuzzy number with application of fuzzy transportation problem   Order a copy of this article
    by Sudha Rana, Deepak Kumar, Anita Kumari 
    Abstract: The objective of this paper is to introduce a new fuzzy number with forty four points called as tetracontatetragonal fuzzy number. Here, we derived a new ranking method for tetracontatetragonal fuzzy numbers. In this research work, we have investigated the results by implementing tetracontatetragonal fuzzy number to an unbalanced fuzzy transportation problem and we used four methods like Vogel’s approximation method (VAM), Russel’s approximation method (RAM), least cost’s approximation method and Modi’s approximation method to investigate the minimum cost transportation problem using tetracontatetragonal fuzzy numbers. We also calculated the minimum cost from a set of origins to a set of destinations in fuzzy transportation problem.
    Keywords: fuzzy number; tetracontatetragonal fuzzy number; crisp values; ranking function; fuzzy transportation problem; Russel’s approximation method; RAM; Vogel’s approximation method; VAM.
    DOI: 10.1504/IJMOR.2023.10057414
  • Workforce Skill-Enhancement Policies in Manpower Systems: Modelling, Analysis, and Structural Control   Order a copy of this article
    by Kannan Nilakantan 
    Abstract: This paper takes up the mathematical modelling of some recent skill-enhancement policies adopted in organisations for enhancing the skill levels of their employees using Markov modelling techniques. Three such policies or scenarios that organisations encounter or adopt are examined, viz.: 1) regular training of employees; 2) institution of 'time-bound promotions' in their lowermost echelons with a view to attract the best talent from the market; 3) adoption of 'periodic' policies to better adapt to seasonality and cyclic variations in their business requirements. These policies are mathematically modelled and their long-term behaviour and effect on the system structure are derived. A control analysis of the system structure under the influence of these policies is also presented. And concomitantly, it is found that 'proportionality-based recruitment control' policies show promise as a tool for structural control when such policies are in force.
    Keywords: skill-enhancement policies; time-bound promotions; regular training policies; periodic policies; proportionality-based recruitment control; Markov manpower systems.
    DOI: 10.1504/IJMOR.2023.10057428
  • Forecasting the Stock Direction using Ensemble Random Forest   Order a copy of this article
    by K. Senthamarai Kannan, PARIMYNDHAN V 
    Abstract: Predicting stock prices is a challenging task due to market fluctuations and the nonlinear nature of stock markets. Forecasting errors can increase investment risk, so reducing them is essential. In this study, financial data including high, low, open, and close prices of stocks were used to generate new variables. Here TCS stock data is employed to construct a Random forest model. This model predicts whether a stock will close positively or negatively based on past values of technical indicators. The findings in this work demonstrate that, using random forest for stock forecasting is beneficial for both institutional and retail stock investors. The unique contribution of our work is the utilised of technical indicators as high-accuracy features for predicting the direction of stock prices. The performance accuracy rate of 74% for the model is obtained by increasing the number of training cycles for the algorithm.
    Keywords: forecasting; random forest; RF; technical indicators; indicators; machine learning; ML; stock.
    DOI: 10.1504/IJMOR.2023.10057460
  • Finite Population and Finite Capacity Single Server Batch Service Queues With Compulsory Working Vacation   Order a copy of this article
    by Kalyanaraman R, Janani G 
    Abstract: A finite population Poisson queue with fixed batch service rule has been considered. After completion of each service the server takes vacation independent of the number of customers in the queue. During vacation, the server serves the customers in a slower rate. For this model, the system size probabilities are computed. Some system performance measures are derived. Also instead of finite population, infinite population model with finite waiting room capacity has been considered as a second model. The steady state results are obtained for this model. The two models are compared. Cost and profit structure are defined. Some numerical examples are given.
    Keywords: finite population queue; batch service; steady state probability; performance measures; compulsory vacation.
    DOI: 10.1504/IJMOR.2023.10057466
  • An EOQ Model for Deteriorating Item with backorder and time dependent exponential Demand   Order a copy of this article
    by Prokash Mondal, Sriparna Chowdhury, Pritha Das, Sanat Kumar Mazumder, Kajal De 
    Abstract: In this article, we have developed an economic order quantity (EOQ) model over a finite time horizon for an item with time dependent demand rate with a constant rate of deterioration in consideration of shortages (SFI policy) in inventory under permissible delay in payments and partial backlogging. The demand rate considers hare exponential to address the increment of demand, which greatly impacts the introduction of a new product in the market. Also, the backlogging rate is considered dependent on the hanging time duration of the customers instead of waiting in line of the customers. The model is solved analytically to obtain the optimal solution to the problem. It is then illustrated with the help of numerical examples. A sensitivity analysis of the optimal solution concerning the parameters of the inventory system is given.
    Keywords: inventory; economic order quantity; EOQ; deterioration; delay in payment; trade credit; backorder dependent.
    DOI: 10.1504/IJMOR.2023.10057584
  • Achieving optimal resource utilization in industrial environments: Combining polling methods and an exhaustive service discipline with an unreliable service   Order a copy of this article
    by Ayyappan G, SANKEETHA S 
    Abstract: Two types of queues, type I queue with infinite capacity and type II queue with a finite capacity, are both taken into account. While the service time distribution adheres to phase type, each queue's input process operates in line with the Markov arrival process (MAP). The server cycles through the line, starting with the type I queue, and provides standard service to everyone while also offering optional service based on the demands of the client. During the visiting period of each queue, a strict service discipline is observed. Working breakdown and repair are distributed exponentially, whereas many vacations are distributed according to a phase type. The entire number of consumers in the system are investigated using matrix analysis under the steady state probability vector. We analyse busy period analysis, an invariant probability vector, and few performance indicators in our model. The proposed model's numerical and graphical findings are also examined.
    Keywords: Markovian Arrival Process; Phase type service; Vacation; Exhaustive discipline; Optional service.
    DOI: 10.1504/IJMOR.2023.10057797
  • Recent trends of Economic Production Quantity Models (2000-2022)   Order a copy of this article
    by Suvetha Rajalingam, K. Rangarajan, P. Rajadurai 
    Abstract: This article presents a literature review of recent trends in economic production quantity models from 2000 to 2022. It examines several recent studies on EPQM focused on a production level, production cost, carbon emissions, product recycling, and imperfect production system. Also, it identified prospective research gaps and investigates the existing research trend of the justifiable economic production quantity models. Established on the potential exploration, it offers a direction for future research that could lead to the creation of a realistic and long-term economic production quantity system. We also surveyed the literature on optimising production through the use of integrated inventory models, multi-level production, and additive manufacturing.
    Keywords: economic production quantity; demand; carbon emission; additive manufacturing; fuzzy EPQ models.
    DOI: 10.1504/IJMOR.2023.10058010
  • On Independent Domination Topological Indices of Graphs   Order a copy of this article
    by Anjaneyulu Mekala, Vijaya Chandra Kumar U, R. Murali 
    Abstract: A dominating set (ds) D of a graph G = (V, E) is an independent dominating set (Ids), if the induces subgraph D has no edges. The independent domination number i(G) of graph G is the minimal cardinality of an Ids. In this paper we define a new independent degree domination (Idd) of each vertex k V(G), called an Idd of k and denoted by did(k) are introduced, as well as certain domination indices based on this Idd and also fundamental properties are investigated. We establish exact value for the Idd Zagreb indices of book graph, windmill graph, middle graph of cycle.
    Keywords: independent domination number; independent minimal dominating number; independent domination degree Zagreb indices.
    DOI: 10.1504/IJMOR.2023.10058151
  • Analysis of MAP/P H/1 queueing system with discarding customers having imperfect service, single vacation, feedback and impatient customers   Order a copy of this article
    by Ayyappan G, Archana Gurulakshmi 
    Abstract: In this paper, we analyse a single server queueing model where the service time follows a phase type distribution and the arrival process follows a Markovian arrival process with corresponding representations (D0, D1) of order m and (, T) of order n. When a customer enters for the service, a generalised Erlang clock with r stages is started concurrently. Due to the impatient, the customers may balk the system if server is in vacation period. By using matrix analytic method we find the steady state analysis in this model. Also we derive the expected waiting time, system performance measures, cost function and busy period. By using some performance measures we provide the numerical results and graphical representations.
    Keywords: Markovian arrival process; phase type service; imperfect service; Erlang clock; single vacation; Bernoulli feedback; balking.
    DOI: 10.1504/IJMOR.2023.10058201
  • Analysis of MAP/PH/1 Retrial queueing system with Two-stage vacations with imperfect service, N-policy service, Delayed feedback, Unreliable server and Discouragement customer   Order a copy of this article
    by Ayyappan G, N. ARULMOZHI 
    Abstract: In the present study, we investigate a continuous-time single server constant retrial queueing with a limitless system of capacity, two-stage vacations that include single working vacation and multiple vacations with imperfect service, N-policy service, delayed feedback, unreliable server, and discouragement customer. Once the operating environment is empty during a normal busy period, it initially takes a working vacation, during which the server can still provide service but at a slower rate. If the system is empty after this working vacation, the server will take a vacation and stop serving entirely. Otherwise, the server resumes its normal service rate. If there are fewer than N customers in orbit after the vacation period ends, the server resumes normal operation. If not, the server starts another vacation. When approaching the system using the matrix-analytic method, steady-state vector, busy period, and cost analysis are generated for this model. Analytical performance indices are assessed numerically.
    Keywords: multiple vacation; working vacation; unreliable server; imperfect service; delayed feedback.
    DOI: 10.1504/IJMOR.2023.10058270
  • Pricing and Return Strategies in a Dual-Channel Closed Loop Supply Chain considering Complementary Products and Sales Effort   Order a copy of this article
    by Subir Guin, Amit Sarkar, Brojeswar Pal 
    Abstract: Waste materials are polluting the environment as they are being stored. Additionally, with a shortage of raw materials and energy sources, remanufacturing would be beneficial. In this paper, we discuss a dual-channel closed-loop supply chain of a pair of complementary products involving two manufacturers and one retailer.The manufacturer of main products distributes the products through both online and traditional retail channels, while the manufacturer of complementary products does so only through the online channel. For remanufacturing, two manufacturers collect their end-of-used products through only the online channels. Then the pricing and remanufacturing decision problem is modelled based on four-game (centralised, vertical Nash, manufacturer Stackelberg, retailer Stackelberg) models, which differ in power structures. After that, the optimal results of the manufacturers and the retailer are analysed. Finally, a numerical result is proposed to analyse the analytical results and sensitivity to the respective parameters. Based on our research, we determined that channel and retailer profit along with return rate is highest for the centralised model, whether channel and retailer profit and sales effort are maximum for the manufacturer Stackelberg model under decentralised environment.
    Keywords: dual-channel; closed loop supply chain; complementary products; sales effort; vertical Nash; Stackelberg.
    DOI: 10.1504/IJMOR.2023.10058493
  • A sustainable inventory system under the impact of partial trade credit   Order a copy of this article
    by SONIA DUA, Sandeep Kumar Mogha, Himani Dem 
    Abstract: In present scenario, countries are required to focus more on reduction of carbon emission as it is one of the key factors of global warming. This article considers the approaches to decrease emissions arising from production, storage and transportation. Suppliers offers ample opportunity to overcome the burden of holding costs from retailers by adopting the permissible delay method. We have developed a mathematical model for sustainable inventory system involving deteriorating items with a partial trade credit policy. The long-term best ordering tactics are for retailers that maximise total annual profit while reducing carbon emissions is provided. An efficient algorithm is also proposed to obtain the solution with numerical example. Sensitivity analysis is also performed to study how the model behaves against the changes in some key parameters.
    Keywords: inventory model; partial trade credit; carbon emission cost; volume flexibility.
    DOI: 10.1504/IJMOR.2023.10058545
  • Solving an Exploitation based Marxian fuzzy EOQ Model   Order a copy of this article
    by Biswajit Roy, Kousik Bhattacharya, Sujit Kumar De 
    Abstract: This article deals with the clinical study of Marxian economic order quantity (M-EOQ) model under fuzzy environment. Initially the model has been viewed as multi-objective cost minimisation and profit maximisation problem under optimum rate of exploitation. Then we transform the multi-objective optimisation problem into single objective optimisation problem under suitable constraints. For optimising this objective function, we need to solve analytically a biquadratic equation where order quantity assumes as one of the decision variables. According to the nature of the roots of this biquadratic equation, we split the model into various sub models where the exploitation varies differently with the change of demand function. Incorporating the negative root of the biquadratic equation, we have formulated three different backlogging EOQ models. Considering a case study, we perform the numerical experimentation with the help of a solution algorithm. Moreover, to capture the non-random uncertainty of the model parameters, we construct an equivalent fuzzy shortage model. Our findings reveal that, shortage model is more beneficial than other sub-models for the decision maker all the time. Finally, numerical illustrations, sensitivity analysis, graphical illustrations and comparative study are done for justify the model followed by managerial insight, conclusion and scope of future work.
    Keywords: EOQ model; Marx’s theory; exploitation; fuzzy set; algorithm; optimisation.
    DOI: 10.1504/IJMOR.2023.10058781
  • Optimal Greening Efforts, Pricing and Inventory Strategies for Non Instantaneous Deteriorating Perishable Products under Price, Freshness and Green Efforts Dependent Demand with Price Discount   Order a copy of this article
    by DHARMESH KATARIYA, Kunal Shukla 
    Abstract: Nowadays, consumers who are concerned about their health prefer and expect nutritional and fresh sustainable products. Due to their freshness, healthfulness, and environmental friendliness, people are now using sustainable fresh perishable products. The price of products plays an important role in consumers purchasing behaviours. This article considers an inventory model for non-instantaneously deteriorating perishable fresh products with selling price, age of product (freshness), and greening efforts dependent demand. The quality of products reduces due to physical deterioration and degradation of the product's freshness, and hence, retailers offer a discount in the selling price to the buyer during a deteriorating period to boost demand. The objectives of the study are to determine the optimal selling price, an optimal period for replenishment cycle time, and an optimal value of greening efforts cost simultaneously while taking into account retailers total profit maximisation. A mathematical model is developed and validated using numerical results to reflect actual situations. To examine the reliability of the model, sensitivity analysis with regard to parameters is undertaken. Some keys managerial insights are presented, and the article concludes with a discussion of the future scope of related research.
    Keywords: inventory; freshness index; greening efforts; non-instantaneous deterioration; price discount; perishable products.
    DOI: 10.1504/IJMOR.2023.10058782
  • The Harris-G Power Series Class of Distributions with Applications   Order a copy of this article
    by Wellington F. Charumbira, Broderick Oluyede, Fastel Chipepa, Lesego Gabaitiri 
    Abstract: This study introduces a novel class of distributions (CoD) called the Harris-G power series (H-GPS) CoD. The model is obtained by compounding the Harris-G distribution with the power series distribution (PSD). Some statistical properties including quantile function, linear representation, distribution of order statistics, moments, probability weighted moments and R
    Keywords: Harris-G; power series; generalised distribution; maximum likelihood estimation; MLE; moments; order statistics; entropy.
    DOI: 10.1504/IJMOR.2023.10058927
  • Supplier - Retailer - Customer Trade credit policy for Perishables   Order a copy of this article
    by Jayashri P, Umamaheswari S 
    Abstract: Perishable items have a relatively short shelf life and degrade naturally. In particular, managing perishable inventory can be challenging, since shortages and wastage are closely associated. Preservation techniques are incorporated to maintain the shelf life of perishable items. The objective of this paper is to optimise the total inventory costs by minimising the deterioration rate and free up working capital for entrepreneurs. Genetic algorithm with one-point crossover, swap mutation and random selection is used to determine the optimal credit period and cycle time by varying different upstream credit periods. An economic order quantity is derived to determine an optimal ordering quantity for a trade credit inventory model. The total profit corresponding to various credit periods and time intervals is illustrated numerically. The effect of changes in key parameters of the optimal solution is investigated using sensitivity analysis. The model is applicable for perishable items like fruits, vegetables, meat, dairy products, and so on which need preservation to increase shelf life.
    Keywords: deteriorating; inventory; perishable; preservation technique; trade credit.
    DOI: 10.1504/IJMOR.2023.10058929
  • Fractional Black - Scholes Equation described by the Conformable Fractional Derivative with Three Different Methods   Order a copy of this article
    by Vijayan C, Manimaran R, Racshitha N 
    Abstract: This study deals with the conformable fractional derivative (CFD) operator and three different methods for solving the fractional Black-Scholes equation (FBSE) and the generalised fractional Black-Scholes equation (GFBSE). They are the variation iteration method (VIM), reduced differential transform method (RDTM) and homotopy analysis method (HAM). The redefined proposed methods are the conformable variation iteration method (CVIM), conformable fractional reduced differential transform method (CRDTM), and conformable homotopy analysis method (CHAM). Finally, images and tables are used to display the results of FBSE and GFBSE. These methods can be used to accurately solve both the fractional Black-Scholes equation and the generalised fractional Black-Scholes equation.
    Keywords: Black-Scholes equation; BSE; conformable fractional derivative; CFD; variational iteration method; VIM; reduced differential transform method; RDTM; homotopy analysis methods; HAM.
    DOI: 10.1504/IJMOR.2023.10058977
  • A two server tandem queueing model with Markovian arrival process, phase type service, working vacation, feedback, re-service, unreliable server, interrupted closedown and customers intolerance.   Order a copy of this article
    by Ayyappan G, Archana Gurulakshmi 
    Abstract: This paper intends to focus on two-server tandem queue with working vacation, feedback, re-service, unreliable server, interrupted closedown and impatient customers. Input flow of customers arrival is modelled using a Markovian arrival process (MAP) and the service time is considered to follow a phase type distribution. Customers impatience has been studied under phenomena of reneging and balking of this model. The essential and sufficient conditions for system stability is found. By using the matrix analytical method, the queueing model's steady-state probability distribution was derived. Additionally, we derived some performance indicators for the model. Finally, certain numerical examples were used to evaluate the impact of system parameters both numerically and graphically.
    Keywords: Markovian arrival process; MAP; phase type service; working vacation; re-service; interrupted closedown; reneging; balking; breakdown; repair.
    DOI: 10.1504/IJMOR.2023.10059085
  • The Marshall-Olkin Exponentiated Half Logistic-Type II Topp-Leone-G Family of Distributions with Applications   Order a copy of this article
    by Broderick Oluyede, Neo Dingalo, Fastel Chipepa 
    Abstract: In this work, we develop and present a new family of probability distributions called Marshall-Olkin Exponentiated Half Logistic-Type II Topp-Leone-G (MO-EHL-TII-TL-G) distribution. Statistical properties and the maximum likelihood estimates of the parameters of the proposed family of distributions were derived. Some special cases of the new family of distributions are presented. The performance of the maximum likelihood estimates is assessed by carrying out a simulation study. Two real-life data sets from different areas are applied on one special model namely, the Marshall-Olkin Exponentiated Half Logistic-Type II Topp-Leone-Weibull (MO-EHL-TII-TL-W) distribution to demonstrate the usefulness and applicability of the new family of distributions
    Keywords: Marshall-Olkin Distribution; Type II Topp-Leone-G Distribution; Exponentiated Half Logistic Distribution; Goodness-of-fit Statistics.
    DOI: 10.1504/IJMOR.2023.10059091
  • Copula Approach to Predict Reliability Factors of a Wide Range Communication System   Order a copy of this article
    by Abdul Kareem Lado, Abdulhadi Aminu, Ibrahim Yusuf 
    Abstract: Information can be passed between people, groups, gadgets, organisations, continents, and the rest of the globe through communication. Focusing on the aforementioned, this study takes into account a communication system made up of five subsystems: three servers, two switches, a router, and three clients, which are all grouped together in a series-parallel categorisation. Given that this system is operational, failure is inevitable. As a result, the failure of these subsystems appears to be constant and in accordance with the exponential function, general and copula repairs are offered to fix both partial and whole system failures. The mathematical transition figure of the system is used to construct partial differential equations, which are then solved with the use of a supplementary variable and the Laplace transformation method. The expressions for availability, reliability, mean time to failure (MTTF), sensitivity, and costs are realised using a mathematical tool. The study's findings are supported by specific examples.
    Keywords: availability; reliability; mean time to failure; MTTF; sensitivity; cost; communication; computer.
    DOI: 10.1504/IJMOR.2023.10059094
  • The Topp-Leone-Marshall-Olkin-G Power Series Class of Distributions: Properties and Applications   Order a copy of this article
    by Peter T. Chinofunga, Broderick Oluyede, Fastel Chipepa 
    Abstract: This study introduces a new class of distributions known as the Topp Leone Marshall-Olkin-G Power Series (TLMO-GPS). TLMO-G fanily of distributions is compounded with the Power Series distribution to get TLMO-GPS. Some statistical properties including quantile function, linear representation, order statistics, R
    Keywords: Topp Leone; Marshall Olkin; Generalised Distributions; Power Series; Moments; Maximum Likelihood Estimation; Goodness-of-fit Statistics.
    DOI: 10.1504/IJMOR.2023.10059095
  • The synthesis of the AHP as a well-posed mathematical problem and matrix norms appropriate for sensitivity analysis via condition number   Order a copy of this article
    by Gustavo Benitez Alvarez, Rafael G. De Almeida, Cecilia T. Hernández, Patrícia Alves Pereira De Sousa 
    Abstract: The analytic hierarchy process (AHP) is a decision making method, which has as its greatest criticism the rank reversal effect. This paper formulates the fourth step of the AHP (synthesis) as a well-posed mathematical problem. A theorem guarantees the existence of the square condensed original formulation for the AHP. This means that any decision problem modelled by AHP with a different number of alternatives and criteria can be condensed into a model with an equal number of alternatives and criteria without loss of condensed information. This condensed formulation can be better conditioned than the original rectangular formulation of the AHP. The square condensed equivalent formulation is also a well-posed mathematical problem. The concepts are applied to two practical cases from the literature, and sensitivity analysis is performed. Four classical matrix norms are reformulated to obtain theoretical bounds for the error estimate closer to actual error.
    Keywords: multiple criteria analysis; rank reversal; linear systems of equations; sensitivity analysis.
    DOI: 10.1504/IJMOR.2023.10059096
  • Fuzzy Weak Autocatalytic Set for Decision Making and Its Application to the Project Manager Selection   Order a copy of this article
    by Siti Salwana Mamat, Siti Rahmah Awang, Tahir Ahmad 
    Abstract: In decision making procedures, the comparison of alternatives is often necessary to determine the most suitable option among a set of choices. One commonly used approach is pairwise comparison, where each alternative is compared to every other alternative based on certain criteria. FWACS method offers a way to represent the pairwise comparisons of alternatives as a directed graph with fuzzy edges. The FWACS is a technique used to address problems involving multiple criteria. In this study, a new ranking approach using FWACS is implemented on a previously published MCDM problem. The purpose of this implementation is to showcase the effectiveness of the FWACS method in addressing decision problems that involve multiple criteria.
    Keywords: fuzzy weak autocatalytic set; FWACS; decision-making; project manager selection; ranking; graph theory.
    DOI: 10.1504/IJMOR.2023.10059280
  • Introduction of an arc rank order statistic for analysis of optimal solutions in traveling salesman problems   Order a copy of this article
    by Jerry Shaw, Donovan Fuqua, Hansuk Sohn, Manuel Ivan Rodriguez Borbon 
    Abstract: This research provides an empirically derived and previously unreported insight into the actual composition and common features of optimal solutions in travelling salesman problems (TSPs). One unreported characteristic of these solutions is the frequency with which a vertex is connected to another relatively near or distant vertex. Based on a mathematical question on optimal solution arc lengths, we introduce an arc rank statistic and use it to analyse optimal solutions for a range of standard TSPs. The resulting analysis shows, with few exceptions, that the frequency with which low-ranked arcs appear is a decreasing function. Further, the frequency distributions of arc ranks generally have fat tails. Log/log transforms of the frequency distributions were analysed to show linear relations; suggesting that the distribution of arc ranks in optimal TSP solutions generally follows a power law distribution. This knowledge suggests that statistical information about a solution may be sufficient to inform an observer about the quality of a solution.
    Keywords: optimisation; travelling salesman problem; TSP; graph theory; edge ranking.
    DOI: 10.1504/IJMOR.2023.10059334
  • Pricing a Guaranteed Minimum Maturity Benefit in Uncertain Markets   Order a copy of this article
    by Justin Chirima, Frank Ranganai Matenda, Mabutho Sibanda 
    Abstract: This paper examines the problem of pricing a guaranteed minimum maturity benefit (GMMB) in uncertain markets. Several uncertainties are encountered in financial markets. The pricing process of a GMMB does not exhibit randomness alone, but also nonrandom uncertainties. We introduce uncertainty theory into pricing a GMMB. The assumption is that the stock price process, St, interpreted as an index for the fund assets, is driven by an uncertain differential equation (UDE). The solution to this UDE is regarded as a geometric canonical Liu process. We apply the UDE in pricing the GMMB problem and assume that the stock price evolution is driven by the canonical Liu process. Utilising the uncertain Liu option pricing approach, we formulate and examine a framework for pricing a GMMB in uncertain markets. Numerical computations are exemplified as well. The results of the study show that this approach is capable of pricing a GMMB.
    Keywords: uncertainty; uncertainty distribution; canonical Liu process; guaranteed minimum maturity benefit; GMMB; insurance policyholders; stock price.
    DOI: 10.1504/IJMOR.2023.10059337
    by Yohapriyadharsini R. S, V. Suvitha, Rakesh Kumar 
    Abstract: We consider an M/M/1 queueing system with two kinds of vacations and impatient customers. The server begins the 1st kind of vacation each time the system becomes empty after serving all the customers. If the system is empty, when returning from this vacation it takes the 2nd kind of vacation. When the server comes back from either 1st kind or 2nd kind of vacation, if there is at least one customer in the system, the server immediately starts the service. If the server is busy or on 1st kind of vacation when a customer arrives at the system, it activates an impatience timer. If the customer’s service has not been finished before the customer’s timer perishes, the customer leaves the system and never returns. The balance equations of the model are all derived using a state-transition diagram. Probability generating functions (PGFs) technique has been used to derive the steady-state probabilities. Various measures of performance are presented and numerical illustrations are also provided.
    Keywords: busy state; vacations; steady state; performance measures.
    DOI: 10.1504/IJMOR.2023.10059372
  • Optimal mean-variance portfolio selection with uncertain time horizon in a regime-switching market when asset returns are market path-dependent   Order a copy of this article
    by Reza Keykhaei 
    Abstract: In a financial market, the state of the underlying economy and investors’ mood affect market trends and consequently asset prices movements. Regime-switching models are used to describe changes in market states and trends. The main assumption in regime-switching models is that asset returns depend on the current state of the market. We generalises this assumption to the case where market states in the past, as well as the current state, affect asset returns. In fact, we assume that asset returns are market path-dependent. Under this assumption, we study a multi-period mean-variance portfolio selection problem in a Markovian regime-switching market when the time horizon is uncertain. Using the stochastic dynamic programming approach, we obtain the path-dependent optimal portfolio strategy and the mean-variance efficient frontier in a closed form. We show that the results obtained under conventional regime-switching model, can be obtained as special cases of the present model.
    Keywords: mean-variance portfolio selection; regime-switching; market path-dependent; uncertain time horizon; stochastic dynamic programming.
    DOI: 10.1504/IJMOR.2023.10059431
  • Uncertain Multi-objective Student Project Assignment Problem by Fuzzy Programming Technique   Order a copy of this article
    by Sunil Bhoi, Jayesh Dhodiya 
    Abstract: This paper presents mathematical zero-one integer programming model of uncertain multi-objective student project assignment problem based on uncertain preferences of students and supervisor over projects or pairs of student and project. To develop this uncertain model, preferences are computed based on supervisor feedback and student result analysis, which are uncertain in nature. Two ranking criteria are utilised to deal with these uncertain preferences, which are expected value and optimistic value. Thereafter, uncertainty theory is applied to these uncertain model to transform uncertain models into deterministic form. Fuzzy programming technique with linear and exponential membership functions is utilised to solve deterministic multi-objective models and results are obtained using LINGO software. To check the strength and efficiency of proposed models, numerical data-based case is studied and results are discussed.
    Keywords: student project assignment; multi-objective optimisation; 0-1 integer programming; uncertain programming; fuzzy programming technique.
    DOI: 10.1504/IJMOR.2023.10059470
  • Cost analysis of a transient Markovian queueing model with provision of options between regular and working vacation   Order a copy of this article
    by Mayank Singh, Madhu Jain, A. Azhagappan 
    Abstract: A transient Markov queue is investigated that provides options for two types of server vacations. When the server becomes idle after serving the last customer, he has the choice to take a complete vacation (CV) or a working vacation (WV). New arrivals can join the system in CV or WV mode with different arrival rates, which are dependent on the state of the system. During CV, the server remains idle, while during WV, he serves at a slower rate. After returning from the CV (or WV), the server immediately starts the service if some customers are waiting in the system; otherwise, he waits for the arrivals. The transient queue size distribution and other queueing indices are determined using continued fractions and probability generating function techniques. The stationary distribution is also derived from the transient distribution. Numerical analysis is conducted using a practical application to display the analytical results in real-life scenarios.
    Keywords: transient analysis; vacation; working vacation; continued fractions; probability generating function; queue size.
    DOI: 10.1504/IJMOR.2023.10059600
  • Reduction of bounded variables in integer linear programming problems   Order a copy of this article
    by Abdelkrim Rezzag, Mohand Ouamer Bibi, Abdelhek Laouar 
    Abstract: In this paper, we suggest a new technique for reducing the number of variables in general integer linear programming problems with bounded variables. This technique involves fixing certain variables of the problem's optimal solution at one of their bounds, either lower or upper. A numerical illustrative example is presented, numerical experiments have been conducted to compare the execution time of the original problem with the execution time of the reduced problem and the pre-solving procedure.
    Keywords: integer linear programming; bounded variables; presolving procedure; numerical results and comparisons.
    DOI: 10.1504/IJMOR.2023.10059652
  • New Weibull-Pareto Poisson Distribution: Properties, Actuarial measures, and Applications   Order a copy of this article
    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
  • On the Numerical Solution and Mathematical Modelling of the Global Warming Data from the years 1970 to 1994 and from 1995 to 2019   Order a copy of this article
    by Zuhair Al-Hemyari, Jamal Alabasi 
    Abstract: In this paper, the numerical method, and modelling of a big data set related to global warming are developed using several techniques. The data is collected of daily temperatures from several cities over a 50-year period. To study the existence of the global warming precisely, the collected data is to be divided into two equal secondary periods. In addition, several methods of analysis and modelling will be applied in this paper. The analytical and modelling methods applied to the global warming in this paper are unique. In addition, the results on this paper are comprehensive, prominent and describe the essence of the problem and its perspective in the future. In specific, the results have shown that the changes occurring in the climate in the studied cities are significant and more severe than the changes occurring in the past (before 1970) and in other countries of Middle East region.
    Keywords: numerical solution; modelling; global warming; fitting; mixture distributions; EM algorithm.
    DOI: 10.1504/IJMOR.2023.10059729
  • Joining Strategy for Double Orbit Retrial Queue with Imperfect Service and Vacation under N-policy   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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
  • Cost Optimization of MMAP/PH(1), PH(2)/1 Pre-emptive Priority Retrial Queueing model with Standby Server, Orbital Search, Server Breakdowns, Phase Type repairs and Impatient Customers   Order a copy of this article
    by AYYAPPAN Govindan, Thilagavathy Karthikeyan, Rakesh Kumar 
    Abstract: In this paper, we examine a single server queueing model in which priority customers arrive based on the marked Markovian arrival process (MMAP) and their corresponding service process is based on phase-type (PH) distribution. The primary server provides service to high priority or low priority customers, who may be affected by a breakdown, the standby server takes over service until the primary server has been repaired. Whenever either the primary or the standby server becomes idle, an orbital search of low priority customers is performed. We have established the stability condition for the model. Utilising the matrix-analytic method (MAM), the model is solved under steady state. Further, the busy period analysis of the model is carried out. Finally, the cost model is presented and the total cost of the system is analysed with the change in system parameters.
    Keywords: MMAP; PH-distribution; standby server; impatient customers; busy period analysis; retrials.
    DOI: 10.1504/IJMOR.2023.10060048
  • Optimized Variable Step-Size Algorithm for the Solution of Dynamical Systems   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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
  • Quasi-Birth-and-Death Processes to determine Economic Order Quantity of a Queueing Inventory System with Impatient Customers   Order a copy of this article
    by Sivasamy R, Setlhar K, Mokgware Olebogeng 
    Abstract: The proposed investigation is an inventory system tied to a single-server M/M/1/N facility that allows impatient customers according to the ordering policy (r, Q). The order is triggered when the stock level drops to a positive integer r < Q for a fixed number Q of units. Here: 1) queueing inventory system (QIS) with lost customers; 2) QIS with back-order are investigated. For each type, we study the long-run moments of the X variable representing the observed queue length, and the Y variable representing observed inventory level. We show that the combined sequence Z = (X, Y) constitutes a level-dependent quasi-birth and death process (LDQBD) in the state space E = {(n, j): n = 0, 1, ..., N, and j = 0, 1, ..., (Q + r)}. We obtain the general probability distribution of the Z process by matrix analysis. Numerical illustrations are provided to find the economic order quantity.
    Keywords: queueing inventory; queue length; inventory level; customer impatience; stationary distribution; expected cost; economic order.
    DOI: 10.1504/IJMOR.2023.10061420
  • Job Shop Scheduling in Wafer Fab with Random Job Arrivals using Hybrid Tabu Search   Order a copy of this article
    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
  • Fuzzy Multi-objective Solid Transportation Problem: Genetic Algorithm Based Solution Approach   Order a copy of this article
    by Shubha Agnihotri, Jayesh Dhodiya 
    Abstract: This article addresses the structure of the fuzzy multi-objective solid transportation problem (FMOSTP) under the aegis of a hybrid genetic algorithm. Here, solid transportation problems (STP) are three-dimensional transportation problems in the sense that the mode of transportation is taken into account along with demand and supply constraints. Furthermore, the data structure considered in this article is assumed to be fuzzy because of the argument that the crisp data, in principle, is nearly hypothetical, and for this reason, the theory of fuzzy numbers is employed to account for the inherent impreciseness/uncertainty of the underlying system. Against this backdrop, the authors propose a matrix-based stochastic algorithm that efficiently generates an initial population. In this connection, two STPs are also posed for illustration purposes and solved using a hybrid genetic algorithm. In addition, the obtained results are compared with the fuzzy programming technique (FPT).
    Keywords: multi-objective solid transportation problem; fuzzy theory; fuzzy programming technique; FPT; genetic algorithm; hybrid GA.
    DOI: 10.1504/IJMOR.2023.10061481
  • Optimizing inventory in business environments: Combining matrix analytic methods with a working vacation, cancellation policy, and working breakdown   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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.   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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
  • On Phase Inventory Model for (Non)Co-Operative Games   Order a copy of this article
    by Sujit Kumar De, Mrinmoyee Das 
    Abstract: This article develops an economic order quantity (EOQ) inventory model with infinite exhaustive cycle time. In this study the supply chain itself is viewed as the flow of current in the well-known L-C-R circuit of the physics discipline. We have shown that, those items which are not sold for an infinite time duration can easily be managed with the help of (non)cooperative games of the management followed by strategy of Nash-equilibrium solution. A schematic diagram of (non)cooperative game and a novel algorithm has also been presented to justify the new approach. However, our findings reveals that the arithmetic-geometric mean for the cases of non-cooperative games approach might be more beneficial of the decision maker than any other existing methods rather than cooperative games. Finally, numerical experimentation, sensitivity analysis and graphical illustrations are done to validate the model.
    Keywords: EOQ model; phase inventory; (non)cooperative game; Nash equilibrium; optimisation.
    DOI: 10.1504/IJMOR.2024.10063161
  • Non-linear fuzzy programming - a case study   Order a copy of this article
    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
  • A Novel Approach to find Simple, Pragmatic Solutions to Transportation Problems   Order a copy of this article
    by Satakshi Singh, Vishal Henry 
    Abstract: The transportation problem is a special case of a linear programming problem (LPP), and its goal is to determine the least/optimal shipping cost that satisfies both the supply and demand constraints simultaneously. An initial basic feasible solution (IBFS) is used to determine the optimal solution. Many methods can be found in the literature to find IBFS. Some of them are Vogel's approximation method (VAM), least cost method (LCM), and North West corner method (NWCM). Among these methods, VAM provides a better solution than other existing methods. This paper proposes a new transportation method (SVAM), inspired by VAM to find IBFS. SVAM performs better than VAM with respect to computation time as it takes very less computation time compared to VAM. The SciLab (V6.1.1) programming is used to implement the algorithm for solving the examples and finding the computation times of all the methods. To establish the correctness of the proposed method, many examples are solved and checked for SVAM and compared with VAM and LCM.
    Keywords: transportation problem; initial basic feasible solution; IBFS; Vogel’s approximation method; VAM; least cost method; LCM.
    DOI: 10.1504/IJMOR.2023.10063407
  • Dynamic service management and priority handling in dual server queuing systems with breakdowns   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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   Order a copy of this article
    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