International Journal of Mathematics in Operational Research (94 papers in press)

Regular Issues

• A distinct management of Linear Programming in uncertain atmosphere  
  by Tuhin Bera, N.K. Mahapatra 
  Abstract: For a linear programming problem (Lp-problem), a fluctuation of the optimal objective value may occur when some relevant parameters are additionally acted upon the system. An Lp-problem is here structured in the parlance of a number of such parameters to have a fair end. Each parameter corresponds one objective function and thus the problem is multi-objective. The coefficient of objective function is set upon the expert’s past experience and its degree of functionality so that a particular problem can also support the different atmosphere. The experimental data is described by three kinds of single valued triangular neutrosophic number (Svtrn-number) to deal with uncertainty. To manipulate huge number of data in uncertain climate, graded mean integration concept is practiced to find the score of an Svtrn-number. An user friendly algorithm is developed to solve an Lp-problem. The model is applied on a fishery planning to justify its efficiency. The obtained result is analysed, and is compared in existing frames to claim the superiority of this work.
  Keywords: neutrosophic set; single valued triangular neutrosophic number; score function; linear programming in neutrosophic arena.
  DOI: 10.1504/IJMOR.2022.10049822
   
  
• FIXED POINT RESULTS USING MULTIVALUED AND ORBITAL CONTINUOUS MAPPING IN QUASI PARTIAL METRIC SPACE  
  by Lekha Dey, Sanjay Sharma 
  Abstract: The aim of the work is to generalise some fixed-point results for mapping that is multivalued in quasi-partial-metric space. It is an extension of fixed points for dominated mappings in partial metric space. The work modifies and extends all results of partial metric space Ahmad et al. (2013) into quasi-partial metric space. The work also proves some fixed-point theorem for orbitally continuous operators defined in quasi-partial metric space. This paper reveals that both theorems can be given better results in quasi-partial metric space as well as obtained results are associated with the other operators. Finally, we provide an example to support the last theorem.
  Keywords: fixed point theory; partial metric space; quasi partial metric space; multi valued mappings; Cauchy sequence; distance function; orbitally complete QPMS.
  DOI: 10.1504/IJMOR.2022.10050858
   
  
• Equitable coloring and scheduling on identical machines  
  by Sarah Nouri, Mourad Boudhar 
  Abstract: This paper deals in the first place with the problems of two-equitable colouring of a union of complete bipartite graphs and three-equitable colouring of connected bipartite graphs, where their N P-completeness is proved. In the second place, it studies the scheduling problem of conflicting jobs on identical machines, while distributing the load evenly between them. Jobs with conflicting constraints cannot be executed on the same machine, these constraints are modelled by a conflict graph. Such problem with identical processing times can be seen as an m-equitable colouring. If the conflict graph is a star graph or a union of chains, this paper demonstrates that the addressed scheduling problem remains N P-hard. Furthermore, the paper describes mixed integer linear programming formulations, followed by some heuristics. The computational experiments show that one of the MILPs can optimally solve some instances with 100 jobs, and the proposed heuristics perform well.
  Keywords: equitable colouring; scheduling; conflict graphs; heuristics; mixed integer linear programming; MILP.
  DOI: 10.1504/IJMOR.2022.10051040
   
  
• Study of two heterogeneous servers with service feedback, vacation and particular service interruption.  
  by Nitin Mahla, Alka Choudhary, Dinesh Chandra Sharma 
  Abstract: Due to the huge impact on real-life application, queueing models with different types of servers have been studied widely. This paper-based on M/M/2 queues presents the study of two heterogeneous servers with particular service interruption, vacation and maintenance. Feedback facility is provided to the customers which are served by a particular server and this server will be interrupted by reactive maintenance after getting a threshold number of negative feedback. Another server will work simultaneously and no feedback will be recorded for this server. To derive the steady-state probabilities, a detailed computational procedure is followed using the matrix geometric method, and then performance measures are calculated. The economic analysis of the model is done. This model is compared with the M/M/1 model in which the server is interrupted by reactive maintenance after getting threshold number of negative feedback.
  Keywords: M/M/2 queueing model; Feedback; Service interruption; Maintenance.
  DOI: 10.1504/IJMOR.2022.10051407
   
  
• A Greedy Heuristic and a Lower Bound on a Nonlinear Stochastic TSP with Partially Satisfied Node Demand Coverage Constraint  
  by Murat Cal, Senol Altan 
  Abstract: The combinatorial travelling salesman problem (TSP) has driven researchers to find faster ways to solve the problem in reasonable times. As a result, researchers modified and created new TSP combinations such as multi-objective TSP or TSP with stochastic constraints. One of these constraints is the node demand coverage constraint. It makes sure that the demand of each node is satisfied in a route. In this study, we re-modify the node demand coverage constraint to be satisfied by some percentage of the time. This approach is more realistic because a node can be visited without covering its demand, allowing the missing of some nodes during the demand covering process while making our model nonlinear. We then provide a greedy heuristic in MATLAB and a lower bound determination procedure for this model and experiment with some predefined datasets.
  Keywords: travelling salesman problem; TSP; chance constraints; nonlinear optimisation.
  DOI: 10.1504/IJMOR.2022.10051415
   
  
• Availability modeling and analysis of a two-component parallel system under stochastic dependence  
  by Ziyad Bahou, Krimi Issam, Abdessamad AitElCadi, Nizar Elhachemi 
  Abstract: In real-world settings, machines are not available all the time. They can undergo different collapses and malfunctions. This may increase costs and sometimes gravely threaten safety. To face this challenge, it is important to assess the availability based on the different dependencies between their components. The purpose of this paper is to compute exactly the availability of a two-component parallel system considering stochastic dependence. We propose an efficient and user-friendly model, based on Cox proportional hazards model using the generalised Weibull distribution. A calculation framework is presented to compute more realistic system availability even for real systems provided with a history of failures. A numerical example is given to assess the stochastic dependence effect on the availability of the system and to illustrate the model. A managerial insight is provided to allow the practitioners to better estimate this latter in order to develop adequate maintenance strategies.
  Keywords: availability modelling; multi-components systems; stochastic dependence; Cox proportional-hazards model.
  DOI: 10.1504/IJMOR.2022.10051416
   
  
• Analysis of S-shaped, U-shaped and V-shaped Transfer Functions in IoMT datasets using Binary Aquila Optimization Techniques  
  by Surendra Babu Nallagorla, R. Dhanalakshmi 
  Abstract: The Aquila optimisation (AO), a metaheuristic approach, is motivated by the Aquila’s natural behaviour when collecting prey. However, while the method shines at several benchmark functions, it fails to solve the binary optimisation problem. We suggested a binary version of AO (BAO) for feature selection (FS) concerns in classification tasks in this research using internet of medical things (IoMT) datasets. We used 12 (S, U, and V-shaped) transfer functions (TF) to transform continuous data into binary values. The proposed TFs demonstrate that BAO techniques, particularly S2-BAO, outperform alternative transfer functions. According to the results, the suggested approach, as compared to traditional transfer functions, converges to the global minimum in multiple rounds based on the selection of optimal attributes, fitness values, and improved classification accuracy.
  Keywords: Aquila optimisation; classification; feature selection; metaheuristic optimisation.
  DOI: 10.1504/IJMOR.2022.10051483
   
  
• Unreliable single server retrial queueing model with repeated vacation  
  by Ebenesar Anna Bagyam J, SUGANTHI POOMALAI, Visali P 
  Abstract: The steady-state behaviour of a single server retrial queueing model with server breakdown and repeated vacation is analysed. If the server is accessible, the customer gets service immediately; otherwise, the customer waits for his turn. After each service, the server may take a vacation with a certain probability. However, if the system is empty, the server takes repeated vacations until the server finds at least one customer in the system. If the server is prone to breakdown, the repair of the server starts immediately. After the repair, the server continues the service to the same customer. The retrial, service, repair, and vacation times are assumed as arbitrary distributed. The steady-state solutions for various performance measures are determined using the supplementary variable method.
  Keywords: retrial queue; repeated vacation; server breakdown; repair; unreliable server; performance measures; numerical analysis; call centre; multiple vacation; supplementary variable technique.
  DOI: 10.1504/IJMOR.2022.10051524
   
  
• Transient Solution of fractional M/M/c queue  
  by NANDURI SUJATHA, GVSR Deekshitulu 
  Abstract: In queuing models, sometimes the server may not work with full efficiency or may stop working also. Such problems are modelled with the help of fractional differential equations. Differential-difference equations involving fractional derivatives in the sense of Mittag-Leffler function have been employed to model the problems with partial activity of the server. In this paper, transient analysis of fractional M/M/c queue has been carried out analytically and results are obtained using MATLAB. The validity and efficiency of the above model is demonstrated with a numerical example. The results obtained by this new approach are justified by comparing them with solutions of classical queue which are available in the literature.
  Keywords: transient analysis; fractional derivatives; Mittag-Leffler function.
  DOI: 10.1504/IJMOR.2022.10051634
   
  
• Proposing a Novel Integrated OPA-MARCOS Multi-criteria Decision Making Model to Choose the Best Plastic Recycling Method (case study)  
  by Alireza Keshtpour, Elham Shadkam, Hooman Khorsand 
  Abstract: Due to the rapid reduction of natural resources and adverse global environmental changes, it is necessary to preserve natural resources and protect the environment. There are various ways to recycle plastic. Choosing the best plastic recycling method is a multi-criteria decision-making problem. This research investigated the output of reference research and then re-solved it using 17 multi-criteria decision-making methods (such as MAIRCA, ELECTRE I, II, etc.). Then, it examined and compared the answers obtained from these methods. Finally, this study evaluated and ranked plastic recycling methods using the combined OPA-MARCOS method, a combination of the OPA for weighting, and the MARCOS method for ranking the alternatives. The innovation of this research is that it combined the OPA and MARCOS methods for the first time and presented a new model. Finally, after solving the OPA-MARCOS model, the second alternative, i.e., mechanical recycling, is selected as the priority alternative. The results suggested that the multi-criteria decision-making methods and weighting methods used in this study can be used for multi-criteria decision-making in other cases.
  Keywords: ordinal priority approach; OPA; MARCOS; multi-criteria decision making; MCDM; OPA-MARCOS; plastic recycling.
  DOI: 10.1504/IJMOR.2022.10052121
   
  
• Steady state analysis of M/G/1 retrial queue with vacation and server timeout using a Petri net formalism  
  by Lyes Ikhlef, Djamil AÏSSANI, Ouiza Lekadir 
  Abstract: In this paper, we analyse an M/G/1 retrial queue with vacation and server timeout. When the system is empty, the server waits for a random time. At the expiration of this time, if there is no arrival to the system, the server takes a vacation. If there is at least one customer in the system, the server commences service. So, we propose an unbounded Markov regenerative stochastic Petri net (MRSP N) to model this queueing system. For the qualitative analysis of this model, we combine the Markov regenerative approach and the generating function technique. Finally, numerical illustrations are performed.
  Keywords: retrial systems; Markov regenerative stochastic Petri nets; MRSPN; M/G/1; renewal theory; steady state; vacation policy; server timeout.
  DOI: 10.1504/IJMOR.2022.10052124
   
  
• A Markovian risk model with possible by-claims and dividend barrier  
  by Sreeshamim P. P., M.J. Jacob, A.S. Dibu 
  Abstract: A MAP/PH risk model with possible by-claims and a dividend barrier is considered. Along with the main claim, a by-claim also can occur with a certain probability but by-claims are settled only after an inquiry and hence delayed. The model is analysed considering associated Markovian fluid models under the original timeline and an auxiliary timeline. Systems of integro differential equations (IDE) are developed for the Gerber-Shiu function (GSF) and the total dividends paid until ruin. Explicit expressions are obtained for the GSF of the models without and then with the barrier. Expressions are also provided for the moments of the total dividends paid until ruin. A dividends-penalty identity is given. The method is numerically illustrated with a two-phase model and sensitivity analysis of the model is done by varying some of the parameters involved.
  Keywords: MAP claim arrivals; phase type claims; by-claims; risk reserve process; dividend barrier; Lundberg equation; Gerber-Shiu function; GSF.
  DOI: 10.1504/IJMOR.2022.10052301
   
  
• Queuing Models with Customers’ Impatience: A Survey  
  by Sapana Sharma, Rakesh Kumar, Bhavneet Singh Soodan, Pradeep Singh 
  Abstract: Queuing systems with customers’ impatience are highly applicable in many real life situations, for instance, in grocery stores, banks, hospitals, barber shops, call centres, online shopping, computer-communication networks, etc. The aim of this paper is to give a review of recent results on queuing systems with customers’ impatience. In this paper, we present a survey and develop a classification scheme of queuing models with customers’ impatience that includes vacation, feedback, priority service and retention of reneging customers. First, we introduce various queuing models with customers’ impatience in chronological order. Second, we classify various queuing models with customers’ impatience. We also provide some tables to illustrate some special features of these systems.
  Keywords: queuing models; customers’ impatience; classification; research; survey.
  DOI: 10.1504/IJMOR.2022.10052442
   
  
• Cost optimization of a heterogeneous server queueing system with working breakdown using PSO  
  by Radhika Agarwal, Divya Agarwal, Shweta Upadhyaya 
  Abstract: Persuaded by the applicability of queueing models the reliability analysis and cost optimisation of MX/M/2 system consisting of heterogeneous servers (Server1 and Server2) is discussed in this article. The Server1 is steady and reliable which leaves for vacation as soon as there is no client available in the system while Server2 is unreliable and may breakdown while giving service to the client. No sooner the server fails, immediately the repair process starts and the server works at a lower speed instead of halting. The schematic diagram of the model gives the overview of the model. The sensitivity analysis is done for validation of the model by taking a numerical illustration and the results are visualised and validated with the help of graphs. Finally, the optimal service rates are obtained using particle swarm optimisation (PSO) technique for matrix method.
  Keywords: heterogeneous (two) servers; matrix-geometric method; working breakdown; multiple vacations; cost optimisation; particle swarm optimisation; PSO.
  DOI: 10.1504/IJMOR.2022.10052489
   
  
• A New Heavy-Tailed Exponentiated Generalized-G Family of Distributions: Properties and Applications  
  by Gomolemo J. Lekono, Broderick Oluyede, Lesego Gabaitiri 
  Abstract: In this paper, we introduce a new family of heavy-tailed distributions called the type-I heavy-tailed exponentiated generalised-G (TIHTEG-G) family of distributions. A special model of the proposed family, namely the type-I heavy-tailed exponentiated generalised-log-logistic (TIHTEG-LLoG) model is studied in detail. Statistical properties of the new family of distributions are presented. These include, among others, the hazard rate function, quantile function, moments, distribution of order statistics and R
  Keywords: heavy-tailed; exponentiated generalised-G; family of distributions;properties; applications; simulation; actuarial measures.
  DOI: 10.1504/IJMOR.2022.10052525
   
  
• Uncertain Bottleneck Assignment Problem Using Credibility Theory  
  by Debapriya Dey Sarkar, Shyamal Kumar Mondal, KAJLA BASU 
  Abstract: In this paper, two types of generalised bottleneck assignment problem (BGAP) namely task-BGAP and agent-BGAP have been considered with fuzzy costs, capacities and resources. In reality, most of the data are uncertain or vague in nature. The objective of this paper is to formulate and solve a more realistic model under uncertainty. A robust counterpart of these two BGAP models have been constructed using credibility measure theory to solve these optimal mini-max regret problems. Credibility theory helps the actuaries to understand the risk associated with historical data and try to reduce the losses for any organisation. So, by this approach, chance constrained programming (CCP) models have been developed. Finally, the CCP models are solved to get the optimal solution using LINGO software. The method has been illustrated using a real life application of a production factory in Section 5.
  Keywords: trapezoidal fuzzy number; bottleneck assignment problem; confidence interval; credibility measure theory; robust optimisation.
  DOI: 10.1504/IJMOR.2022.10052534
   
  
• Local cone approximations in nonsmooth K-univex multiobjective programming problems  
  by Tadeusz Antczak, Kalpana Shukla 
  Abstract: In this paper, we have established some results for a new class of non-smooth multi-objective problems with both inequality and equality constraints are considered. Several definitions of non-smooth (generalised) K-univex functions are gathered in a general scheme by means of the concepts of K-directional derivative and the K-subdifferential. Then, local cone approximations are used to obtain optimality and Mond-Weir duality results for aforesaid non-smooth multi-objective problems with (generalised) K-univex functions. The results established in this paper extend similar results existing in the literature to new classes of non-convex non-differentiable multi-objective programming problems. Some examples are also given for our findings.
  Keywords: non-smooth multi-objective programming; K-subdifferential; local cone approximations; K-directional derivative; K-univex function.
  DOI: 10.1504/IJMOR.2022.10052600
   
  
• APPROXIMATELY OPTIMUM STRATA BOUNDARIES UNDER SUPER POPULATION MODEL  
  by Faizan Danish, S.E.H. Rizvi 
  Abstract: In the present investigation, a methodology has been developed under super population model for obtaining approximately optimum strata boundaries (AOSB) on highly related variable with the variable under consideration which is applicable for the situation having more than one study variables with product estimator. Minimal equations have been obtained under certain assumptions by minimizing the generalized Variance expressions. Under this complex nature we developed Cum?(R_5 (x)) Rule or obtaining the AOSB. Empirical studies have also been made on certain density functions, which showed remarkable gain in precision.
  Keywords: Product estimator; Super population; Optimum strata boundaries; Optimum stratification.
  DOI: 10.1504/IJMOR.2022.10052805
   
  
• A Single Server Markovian Differentiated Working Vacation Queue With Server BREAKDOWN  
  by V. Karthick, V. Suvitha, R. Kalyanaraman 
  Abstract: A single server Markovian queue with server breakdown has been considered here. In addition, the server goes on two types vacation namely type-I and type-II. Type-I vacation is taken after busy period of non-zero duration and type-II vacation is happen, at the completion of type-I vacation when there is no customers in the system, where both type-I and type-II vacations are working vacations. Also in type-I vacation the server may breakdown and immediately the repair takes place. We analysed as a quasi-birth-and-death (QBD) process, using the matrix geometric method, the steady state probability vector of the number of people in the queue and the stability conditions are produced. There are some system performance measures found. The effects of various parameters on the system performance measures are illustrated numerically.
  Keywords: single server; differentiated vacation; breakdown; repair; QBD process.
  DOI: 10.1504/IJMOR.2022.10053027
   
  
• Risk analysis on Product quality improvement and supply chain performance for return contract with warranty  
  by Shirsendu Nandi 
  Abstract: Products which require after sales services and associated with a warranty clause often pass through a series of quality checks and quality control measures. Improvement of quality of the product is an ongoing exercise and the manufacturer and the channel coordinator are expected to explore the impact of any initiative for quality improvement on the profitability and performance of the supply chain. It is important to carry out a risk benefit analysis before undertaking such quality improvement initiatives since it requires major financial investment. It is necessary to redesign the contract parameters after successful implementation of any quality improvement programme. The paper analyses the impact of the quality improvement initiative upon the profitability of the supply chain and describes how to redesign the contract parameters when return contracts are practised. It also does a risk analysis of the parties and the entire supply chain when return contract is practised along with warranty. It examines how change in order quantity and warranty length impacts supply chain risk as measured by variance of profit.
  Keywords: warranty; quality; risk analysis; supply chain contract; return contracts; supply chain performance; redesign; supply chain risk.
  DOI: 10.1504/IJMOR.2022.10053331
   
  
• Optimal order quantity and credit period for a time-dependent deteriorated green item under two-level trade credit with reminder cost: A new approach  
  by Gautam Kumar, Sukhendu Bera, GURUPRASAD SAMANTA, Manoranjan Maiti 
  Abstract: Nowadays, people prefer to buy green products. In the present competitive market, the wholesalers and retailers offer trade credit to their downstream customers. Against retailers’ offers, some customers become defaulters. In rural India, money landers engage some people to remind the defaulters for payment. Following this idea, we introduce reminder costs in trade-credited systems to reduce default risk, though this system negatively affects the demand. Along with the conventional, a new approach for a two-level trade-credited EOQ model with a time-dependent deteriorated green item is presented, allowing default risk and reminder cost and solved by using the generalised reduced gradient method through LINGO 19.0. The new approach gives better results than the conventional ones, and in both approaches, the introduction of reminder cost gives more profit. The nature of profit and its dissection concerning decision variables are presented. Some managerial decisions are derived.
  Keywords: inventory; two-level trade credit; deterioration; default risk; reminder cost; new approach.
  DOI: 10.1504/IJMOR.2022.10053351
   
  
• AN EOQ INVENTORY POLICY VARYING WITH EXPONENTIAL- CONSTANT-EXPONETIAL DEMAND AND SHORTAGES  
  by Itishree Rout, Trailokyanath Singh, A.K. Nayak 
  Abstract: In real market situations, it is often seen that the demands of the most of the seasonal commodities run through three different phases, e.g., growth, steady and decline. The demand and the deterioration are taken as exponential-constant-exponential functions of time and constant, respectively. The model is divided into three policies according to the occurrence of the shortages period. The main purpose of the present paper is to investigate the effect of exponential-constant-exponential demand with seasonal commodities within the economic order quantity (EOQ) framework. Shortages as well as complete backlogged demand have been taken into consideration. A simple analytical procedure is presented to compute the optimal solutions of each policy. The model is well-explained with the help of three numerical examples. Finally, sensitivity analyses of all examples have also been performed to study the effectiveness of several system parameters on optimal solutions.
  Keywords: backlogging; deterioration; economic order quantity; EOQ; exponential-constant-exponential type; replenishment.
  DOI: 10.1504/IJMOR.2023.10053905
   
  
• New Population-Based Simple Algorithms for Solving Global Optimization Problems  
  by BASKAR AMALADOSAN, M. Arunachalam Sai Balaji, Jitendra Kumar Katiyar, Bharti Nagpal, J. Rajesh Babu 
  Abstract: Heuristic algorithms have effectively been used for solving global optimization problems in a continuous space. It can be applied to both constrained and unconstrained problems. Presently, several population-based algorithms were proposed by researchers and available in the literature but those are not enough to solve the issues. Therefore, this study has proposed five new populations base simple algorithms that do not require any tuning parameter. A different strategy was used for updating the solution set. Unlike other algorithms, the solution set is constructed using three or four expressions to ensure effective search and move towards the optimal/ near-optimal solution. Each expression is used to build the population partially and the best one is selected for the next iteration. Further, it is compared with the recent popular Arithmetic Optimization Algorithm (AOA) using different benchmark functions. The dimensions are varied from 2 to 1000. Five real-world problems with constraints are also analyzed.
  Keywords: Population-Based; Benchmark Function; Arithmetic Optimization Algorithm; Trigonometric Algorithm; Constrained Optimization; Unconstrained Optimization.
  DOI: 10.1504/IJMOR.2023.10053957
   
  
• A BACKORDER INVENTORY MODEL CONSIDERING PRICE-SENSITIVE AND STOCK-DEPENDENT DEMAND  
  by Dharma Lesmono, Taufik Limansyah, Ignatius A. Sandy 
  Abstract: In the inventory management system, time and quantity are crucial factors to be considered in relation to inventory costs. Demand is another external factor that influences the availability of goods for customers. In fact, demand varies from time to time, being dependent on price, time, stock or other relevant factors. The dynamics of this condition can be described by developing a mathematical model. In this paper, we develop a backorder inventory model considering price-sensitive and stock-dependent demand. From the model, we determine the cycle length and the time when the inventory drops to zero as decision variables in order to minimize the total inventory cost. Based on the sensitivity analysis, we found that generally speaking, changes in certain parameter values will substantial affect the decision variables of the model. Having this information at their disposal, retailers can determine which specific parameters should be managed in order to minimize the total inventory cost.
  Keywords: inventory; price- and stock-dependent demand; backorder.
  DOI: 10.1504/IJMOR.2023.10054048
   
  
• Optimal Server Analysis of M/M/c Queueing Model to Reduce the Waiting Time of Patients in Healthcare Service  
  by Preethi Sowndharya Kumar, Ebenesar Anna Bagyam J 
  Abstract: Queueing system is a mathematical design known to be theory of overcrowding. Healthcare organization is one of the applications for queueing theory. This paper provides about the healthcare setting at the Arathana ortho local hospital at Pollachi. The proposed queuing model has used the multi-server system with a first come, first server queue discipline. The arrival rate follows Poisson distribution and service rate follows an exponential distribution. The actual data were collected in the ortho hospital and examined using the windows based TORA optimization technique. Performance measures and optimal number of server were found. The result shows that the optimal server to serve the patients and also to reduce the waiting time of patients. The technique is manageable to utilize in the hospital.
  Keywords: service cost; Patients waiting time cost; optimal server level,Service time.
  DOI: 10.1504/IJMOR.2023.10054051
   
  
• Mean Time to Failure Modeling and Sensitivity Analysis of Mixed Standby Serial Systems  
  by Ibrahim Yusuf, Muhammad Sagir Aliyu, Mus'abu Musa 
  Abstract: Abstract: In this article, we investigate and compares the mean time to failure (MTTF) of series-parallel systems. This paper considers four different configurations with each having exponential failure and repair time. Each configuration consisting of the main, warm and cold standby units. A cold standby unit is included in Configuration 1 together with two warm standby units. Two cold standby units and one warm standby unit make up Configuration 2. In configuration number three, there are four primary units, two warm standby units, and one cold standby unit. The configuration 4 consists of six primary units, one warm standby unit, and two cold standby units. First order linear differential difference equations are used to produce a mathematical formula for mean time to failure (MTTF) for each configuration, which is then verified through analytical and numerical testing. Through the analytical and ranking experiment, Configuration 1 is found to be optimal.
  Keywords: Keywords: Mean time to failure; mixed standby; redundancy; series-parallel.
  DOI: 10.1504/IJMOR.2023.10054094
   
  
• Decision-Making Analysis for a new variant of the classical Secretary Problem  
  by Y.U. WU 
  Abstract: In this paper, a new variant of the classic secretary problem is studied, in which the interviewer has a look-ahead privilege to observe partial future candidates before making a decision each time. Different from the classic problem, a decision can be deferred till some subsequent candidates are interviewed in this variant. We define the degree of look-ahead privilege on one candidate as how many candidates are sequentially interviewed from when this candidate is interviewed to when its decision is made. We first propose a general optimal decision strategy framework that can maximize the probability of successfully selecting the best candidate. Then, focusing on one specially structured look-ahead privilege, we apply the proposed strategy framework and obtain the probability of success in a closed function, to which an explicit solution will give the concrete optimal strategy; and further, through computational experiments, we study relationships between related parameters.
  Keywords: Secretary Problem; Look-ahead Privilege; Optimal Strategy.
  DOI: 10.1504/IJMOR.2023.10054145
   
  
• Statistical-based Multi-Criteria Decision Making Approach for prediction of the grade of an Institution in NAAC.  
  by SUKARNA D.E.Y. MONDAL, Dipendra Nath Ghosh, Pabitra Kumar Dey 
  Abstract: In the modern era, innumerable colleges and universities have been established in India but sometimes quality education is not imparted by the authority of colleges/universities. It has been a major challenge for the Indian government to assess the quality education in India. Through a well-versed assessment procedure, National Assessment and Accreditation Council (NAAC) was established to assist higher education institutions in identifying their assets, strengths, and weaknesses. In this paper, an innovative mathematical model is proposed to calculate and justify the NAAC grading of a well-known Engineering College while taking into consideration the NAAC grading of nine other well-known affiliated colleges/autonomous colleges/universities. This model is making a prediction based on the data obtained from SSR (Self Study Report) of them after DVV (Data Validation and Verification) and the result of the model is found very accurate while comparing the overall NAAC grade of the college given by NAAC.
  Keywords: NAAC Grade; MCDM techniques; ANOVA test; P-test; Combined MCDM techniques; and Linear Regression method.
  DOI: 10.1504/IJMOR.2023.10054189
   
  
• Multi-objective perishable multi-item green inventory models with uncertain finite time horizons and constraints by neutrosophic optimization approach  
  by Chaitali Kar, Manoranjan De, Manoranjan Maiti, Pritha Das 
  Abstract: The business period of seasonal products, such as mango, broccoli, etc. is finite over the years due to their availability, which is again uncertain for seasonal variations. According to FAO, about 40% of India’s fruits and vegetables perish before reaching consumers. Due to global warming, firms have incorporated carbon management into business decisions. The resources in business are always limited and uncertain. Considering these facts, multi-objective perishable multi-product EOQ models with stock-dependent demand are formulated under crisp, uncertain (fuzzy, random, rough and neutrosophic) time horizons and constraints. The objective is to maximise total profit while minimising wastage costs and carbon emissions. Proposed models are solved using neutrosophic optimisation approach. The multi-objective problems are transformed into single ones using the weighted-sum method and solved through GRG (LINGO 11.0) method. Models are illustrated with numerical examples, and some sensitivity analyses are presented. A trade-off between profit and carbon emission is depicted.
  Keywords: inventory; seasonal products; uncertain time horizon; carbon emission; neutrosophic optimisation.
  DOI: 10.1504/IJMOR.2023.10054810
   
  
• Aspiration level-based non-dominated sorting genetic algorithm- II & III for multi-objective shortest path problem in trapezoidal environment  
  by Aniket Todkar, Jayesh Dhodiya 
  Abstract: The present article provides aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and AL-based NSGA-III utilising an exponential membership function (EMF) with possibility distribution to tackle fuzzy multi-objective shortest path problem (FMOSPP). In this study, fuzzy judgement for trapezoidal fuzzy number is classified for the decision maker (DM) to optimise fuzzy objective function scenarios like optimistic, most likely lower, most likely upper, and pessimistic at the same time, utilising ?-level sets. A numerical demonstration and a dataset have been offered to portray the application of the recommended methodologies. This study suggests that AL-based NSGA-II and AL-based NSGA-III can handle FMOSPP effectively and efficiently with optimal outputs. These methods provide solutions as per DM’s AL. Thus it is very effective to manage real-world multi-objective shortest path problems (MOSPPs).
  Keywords: multi-objective shortest path problem; MOSPP; aspiration level; exponential membership function; EMF; ?-level set; trapezoidal fuzzy number; genetic algorithm.
  DOI: 10.1504/IJMOR.2023.10054856
   
  
• Dependability Prediction of a Hybrid Multi Client Computer Networking System Using Gumbel-Hougaard Family Copula  
  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  
  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  
  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 ”  
  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  
  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  
  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  
  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
   
  
• An EOQ Model for Seasonal Product with Ramp-type Time and Stock dependent demand, Shortage and Partial Backorder  
  by Prokash Mondal, Pritha Das, Sudhansu Khanra 
  Abstract: This study analyses an EOQ model for a seasonal product with ramp-type time and stock dependent demand function under permissible shortages. In the model, deterioration of seasonal products is considered with partial backlog, variable backlog rate, and backlog rate as a function of time until the next replenishment partial backlogging and the backlogging rate is variable and is dependent on waiting time for the next replenishment. Using the optimal control approach, we analytically derive the optimal total average cost and inventory strategy for the retailer over a finite time horizon. We analytically determine the best total average cost and inventory strategy for the merchant over a limited time horizon using the optimal control approach. A numerical application and sensitivity analysis demonstrate practical applicability.
  Keywords: inventory; time-stock dependent demand; backlogging; deterioration.
  DOI: 10.1504/IJMOR.2023.10056039
   
  
• Economic Order Quantity Model for Pareto distributed decaying products with Quadratic Demand and Salvage Value  
  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  
  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  
  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  
  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  
  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  
  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.  
  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  
  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 single server finite buffer Geom/G/1/K queue with L limited service and multiple vacation policy  
  by Karabi Sikdar 
  Abstract: This paper investigates a Geom/G/1/K queueing system with L limited service and multiple vacation in which the packets arrive under the Bernoulli process. The lengths of service and vacation times are integral multiples of the slot duration. The server goes for a vacation if either the system is empty or L packets have been served during each busy period. The queue length distribution at service completion and vacation termination epochs is obtained using the imbedded Markov chain technique. Based on the supplementary variable technique, we develop the system of difference equations to derive the queue length distribution at random epoch. The waiting-time analysis for an arrival packet and other performance measures are also examined. We execute several numerical results, but only a few of them are added in the form of tables and graphs. The results of this research could be useful in understanding the performance of a service system.
  Keywords: discrete-time queue; finite-buffer; limited service discipline; imbedded Markov chain; multiple vacation policy.
  DOI: 10.1504/IJMOR.2023.10056631
   
  
• A neutrosophic application to the transportation problem with Mixed Constraints using single-valued trapezoidal neutrosophic numbers  
  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  
  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  
  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
   
  
• Multi-goal Multi-product Fuzzy Solid Transportation Problem via Goal Programming Technique  
  by Prathyusha G, Udaya Kumar K. N, Vatsala G. A 
  Abstract: This paper investigates a Multi-Goal Multi-Product Solid Transportation Problem (MGMPSTP) with fuzzy coefficient variables for the objective functions and, therefore, the constraints under linear and non-linear membership functions. The primary objective is to analyse the multi-goal multi-product fuzzy solid transportation problem (MGMPFSTP) using the Goal Programming (GP) technique through the membership functions and compare the results among the compromise solutions to obtain an optimal compromise solution of multi-objectives. The uncertain cost coefficients of the fuzzy numbers are initially De-fuzzified to the equivalent crisp MGMPSTP using the a-cut method. Finally, a numerical illustration has been examined to support the tactic.
  Keywords: Goal Programming: Fuzzy Solid Transportation Problem: a-cut Method: Triangular Fuzzy Numbers: Trapezoidal Fuzzy Numbers.
  DOI: 10.1504/IJMOR.2023.10056660
   
  
• A Marketing-Oriented Production Inventory Model under Hybrid Carbon Policy with Carbon Emission Origin-Based Green Investments  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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)  
  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  
  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  
  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  
  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  
  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  
  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
   
  
• Cyprinus Carpio Feed Cost Optimization Using Linear Programming Technique: A Case Study in Iraq  
  by Qusay Mohammed Abdulateef, Syariza Abdul-Rahman, Hazem Sabri 
  Abstract: Common carp (Cyprinus carpio) is the usual dietary meat in Iraq, as it is reasonably priced for consumers compared to other high-cost fish. However, the relative price increment in recent times has alienated some consumers. The high price is due to the feed, an essential component of the fish farming project. The main ingredients of fish feed consist of concentrated animal protein, yellow corn, soy flour, barley, and wheat bran. Moreover, the feed additive enhancer, i.e., barley sprout powder is also incorporated into the feed, since it can increase fish weight significantly. Therefore, this study proposed a linear programming formulation to ascertain the optimal cost of fish feed. The optimal total feed cost was 41 cents per kilogramme, and the amount of the ingredients in the mixture was: animal protein concentrates (0.10114); yellow corn (0.17077); soybean meal (0.39521); barley (0.12037); wheat bran (0.2); premix (0.01); and barley sprout powder (0.0025).
  Keywords: Cyprinus Carpio; feed formulation; linear programming; optimization; aquaculture.
  DOI: 10.1504/IJMOR.2023.10058643
   
  
• Solving an Exploitation based Marxian fuzzy EOQ Model  
  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  
  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  
  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  
  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  
  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.  
  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  
  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  
  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  
  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  
  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  
  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  
  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  
  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
   
  
• A QUEUEING SYSTEM WITH HETEROGENEOUS ARRIVALS, TWO KINDS OF VACATIONS AND IMPATIENT CUSTOMERS  
  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
   
  
• Classification and feature selection for microarray cancer dataset using an improved African vulture optimisation algorithm  
  by K. Balakrishnan, R. Dhanalakshmi 
  Abstract: The African vulture optimisation algorithm (AVOA) is a recently developed metaheuristic algorithm that imitates the eating and movement patterns of authentic African vultures. AVOA's convergence accuracy and stability, like that of various state-of-the-art metaheuristics, will degrade as optimisation problems get more complicated and variable. Furthermore, the traditional AVOA only searches in one direction, limiting its convergence capacity and causing stagnation at local minima. To address these shortcomings, this work offers LOBL-AVOA, a better version of AVOA hybridised with the lens opposition-based learning (LOBL) technique for classification. The LOBL enhances global exploratory capacity while preventing premature convergence. The suggested LOBL-AVOA findings are compared to traditional AVOA results. The efficacy of LOBL-AVOA is assessed employing six high-dimensional microarray datasets and three distinct classifiers such as support vector machine (SVM), K-nearest-neighbour (KNN) and random forest (RF). As an outcome, the proposed method surpasses traditional AVOA in terms of convergence capability, statistical analysis and classification accuracy.
  Keywords: African vulture optimisation algorithm; AVOA; classification; feature selection; microarray dataset.
  DOI: 10.1504/IJMOR.2022.10049046
   
  
• Solving bi-level linear fractional programming problems with fuzzy interval coefficients using game matrix  
  by Nejmaddin A. Sulaiman, Gulnar W. Sadiq, Basiya K. Abdulrahim 
  Abstract: In this paper, a bi-level linear fractional programming problems (BILLFPP) with fuzzy interval coefficients (FIC) was considered where all of it is coefficients in the goal function and constraints are fuzzy intervals (FIs). Firstly, to resolve this issue, we construct two LFPP with fuzzy coefficients one of these problems is a LFPP where all of it is coefficients are upper approximations of (FIs) and the other is a LFPP, where all of it is coefficients are lower approximations of (FIs) secondly, the BILLFPP are converted in to a single objective LFPP and QFPP. At the end, and we use game matrix technique which yields an efficient resolution of the original BILLFPP with fuzzy interval, the single objective LFPP or QFPP is resolved by modified simplex technique. Finally, numerical examples are given to demonstrate the results.
  Keywords: LFPP; BILLFPP; FBILLFPP; BILLFPP with fuzzy interval; FBILLFPP with fuzzy interval; modified simplex technique.
  DOI: 10.1504/IJMOR.2022.10049735
   
  
• A model on an EOQ optimal ordering policy varying with time-dependent cubic demand and variable deterioration under delay in payment conditions  
  by Sephali Mohanty, Trailokyanath Singh 
  Abstract: The main objective of the proposed paper is to extend Khanra et al. 's (2011) model with the following characteristics: 1) delay in payment is acceptable; 2) demand is a generalised demand pattern and is a cubic function of time; 3) deteriorating items follow a variable deterioration rate, which is a linear function of time; 4) neither partial backlogging nor complete backlogging has been taken into consideration. For settling the account, the formulation of the model is derived under two main approaches: case 1 - the grace period is less than the time period of the system or case 2 - the grace period is greater than the time period of the system. Finally, results are analysed and presented with the help of several numerical examples. Sensitivity analysis of all of the system parameters of the proposed model is discussed.
  Keywords: delay in payment; deteriorating items; EOQ; time-dependent cubic demand; variable deterioration.
  DOI: 10.1504/IJMOR.2022.10049205
   
  
• On the existence of the tracking model for N-dimensional Brownian particle in the fluid  
  by Mohamed Abd Allah El-Hadidy, Alaa Awad Alzulaibani 
  Abstract: In this work, an existential study of the tracking technique of N-dimensional Brownian particle in the fluid has been discussed. A set of nano-robot sensors start the tracking process from the origin of N-dimensional space. Besides giving the conditions which present the finiteness of the expected value of the first meeting time between one of the nano-robot sensors and the particle, we provide the computational expected value of this time.
  Keywords: probabilistic methods; statistical physics; mathematical analysis; N-dimensional Brownian motion; purify impurities.
  DOI: 10.1504/IJMOR.2022.10049299
   
  
• An algorithm for solving a min-max problem by adaptive method  
  by Aghiles Azizen, Kahina Louadj, Mohamed Aidene 
  Abstract: Min-max problems occupies an important place in linear programming (LP), as it addresses a large number of optimisation problems, in various fields of science. In this study, an algorithm using adaptive method is proposed for solving the min-max problem in linear programming. It consists on finding the maximum of the minimum of a function (where the essential constraints are in equality and the direct constraints are bounded) in a minimum execution time. A solving algorithm is built using the principle of the adaptive method and it is based on the concept of the support matrix of the problem. Necessary and sufficient conditions for the optimality of a support feasible solution are established and sub-optimality criterion is derived. This algorithm allows to solve directly the considered problem, without modifying it and avoids the drawbacks of the increase in the number of the variables and the constraints, thus, improve the convergence speed of the method. Its performance is tested on a numerical example.
  Keywords: min-max problem; linear programming; adaptive method; sub-optimality estimate; change of support; optimisation; feasible solution; optimality criterion.
  DOI: 10.1504/IJMOR.2022.10050676
   
  
• Throughput optimisation in reentrant circular regular robot cells  
  by Ali Khebouche, Mourad Boudhar, El-Sedik Lamini 
  Abstract: We consider robot cells of type reentrant circular flow shop served by a single-gripper central robot having the ability to swap. The objective is to find a cyclic sequence of robot moves that minimises the cycle time of one-unit required to produce a part or, equivalently, that maximises the throughput. We analysed three-machine robot cells in-depth showing that four of the feasible one-unit cycles dominate the remaining 17 cycles. We determined the parameter regions in which each of the four cycles is optimal. In the case of m machines, we gave two new lower bounds with an emphasis on four cycles that are specific among all one-unit cycles. Initially, cycle time formulas are created for the four cycles of one-unit. In addition, we established the parameter regions where each of the cycles is best. Finally, we showed that a specific cycle provides a 3/2-approximation for the remaining unique region.
  Keywords: circular robot cells; chain-reentrant; throughput maximisation; cyclic production; flow-shop scheduling.
  DOI: 10.1504/IJMOR.2022.10050068