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International Journal of Mathematics in Operational Research

International Journal of Mathematics in Operational Research (IJMOR)

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International Journal of Mathematics in Operational Research (72 papers in press)

Regular Issues

  • Solution of Interval-valued Matrix Games Using Intuitionistic Fuzzy Optimization Technique: An Effective Approach   Order a copy of this article
    by Mijanur Rahaman Seikh, Shibaji Dutta 
    Abstract: In most of the cases in the real world scenario, there are many situations where the payoffs of a matrix game may vary within specific ranges and may be considered as interval numbers. In this paper, we developed an effective solution concept of the interval-valued matrix game using intuitionistic fuzzy optimization technique (IFOT) with non-linear membership and non-membership functions. In this proposed approach, we first convert the formulated game problem into a deterministic model by splitting the single interval type objective function into multi-objective functions. Then, IFOT with non-linear membership and non-membership functions is used to solve the reduced model. Finally, we consider one numerical example to illustrate the methodology. A comparative study implies the fact that the proposed approach gives a better result and is more effective than the results obtained previously by the existing methods.
    Keywords: Matrix game; interval number; intuitionistic fuzzy optimization technique; multi-objective optimization.
    DOI: 10.1504/IJMOR.2020.10032648
  • A Periodic Review Decision Model for an Inventory System with Two Demand Types   Order a copy of this article
    by The Jin Ai, Ririn Diar Astanti, Huynh Trung Luong 
    Abstract: This paper presents a decision model for finding the best policy in a single item inventory system incorporating two kinds of demand, in which each demand type is modeled as an independent compound Poisson process. Some critical model assumptions are infinite planning horizon, infinite replenishment rate, zero lead time, and shortage backorder. A periodic review inventory model is utilized, in which decision variables of the optimization problem considered in the model are replenishment period and maximum inventory after replenishment. After the mathematical model is developed, optimal decision variables can be obtained.
    Keywords: inventory; periodic review; compound poisson process; model; optimization.
    DOI: 10.1504/IJMOR.2020.10033397
  • Solving Quadratic Programming Problems through a Fully Rough Scheme and Its Applications   Order a copy of this article
    by Amr Abohany, Rizk Masoud, Diana Mousa, Aboul Ella Hassanien 
    Abstract: Real-life problems are generally solved with some uncertain parameters Naturally, these parameters may be determined based on the opinions of experts Therefore, all consenting and opposing opinions should be considered The aim of this work is to present an approach for solving quadratic programming (QP) problems The proposed approach combines the merits of the slice sum method (SSM), linearization, and the Frank and Wolfe algorithm to find optimal solutions The proposed approach has two features: first, it elicits four crisp problems from the fully rough QP (FRQP) problem using the SSM Second, the proposed method employs a linearized Frank and Wolfe algorithm for solving crisp problems Finally, a numerical example and a case study of the economic dispatch (ED) problem of a power system are investigated The obtained results prove that the proposed methodology can serve as a significant tool for decision makers to handle several types of logistic problems with rough parameters.
    Keywords: Quadratic programming; Rough set theory; Rough intervals; Slice sum method.
    DOI: 10.1504/IJMOR.2020.10034131
  • A Fuzzy DEA Approach on the Extended Transportation Problem   Order a copy of this article
    by Deepak Mahla, Shivi Agarwal 
    Abstract: The transportation problem is a part of supply chain management. It aims to minimise the cost of transportation costs. The existing methods to solve the transportation problem either use only a single attribute or multiple attributes with crisp data, to obtain the optimal solution. In solving real-life transportation problems, we often face the state of uncertainty in data, as well as multiple attributes, play the role to find out the optimal transportation plan. In this study, the fuzzy DEA approach has been utilised on the extended transportation problem to solve both limitations, as mentioned above. A numerical example has been explained to illustrate the effectiveness of the proposed study. The lower and upper bound maximum efficiency is 66.158 and 68.293, respectively. The results obtained by Amirteimoori's extended transportation problem for the crisp model lies in between these bounds.
    Keywords: Transportation Problem; Data Envelopment Analysis; Decision-Making Units; Fuzzy Set Theory; Alpha-cut Approach.
    DOI: 10.1504/IJMOR.2020.10034416
  • Evolutionary Multi-objective Optimization: A Bibliometric Study   Order a copy of this article
    by Zied Bahroun, Mohamed Amine ABDELJAOUAD, Slim Bechikh 
    Abstract: Evolutionary algorithms are among the most popular methods for solving optimization problems. The use of metaheuristics emulating the natural evolution of living organisms dates back to the 1970s. In this study, a particular focus is put to use these evolutionary techniques to solve multi-objective optimization problems. Based on a bibliometric and network analysis, the paper provides a review of 5549 scientific publications (journal articles and book chapters) on the field before June 2019. The top contributing authors, journals, organizations, and countries are identified, as well as the most used key-words related to the topic. Then, the most influential papers are compared on the basis of citations and PageRank. The established research clusters and emergent research directions are also discussed.
    Keywords: bibliometric; evolutionary; metaheuristic; multi-objective; network analysis.
    DOI: 10.1504/IJMOR.2020.10034589
  • Robust control of pricing and inventory in a two-level supply network with competing retailers and delays in decision   Order a copy of this article
    by Azeddine Zemzam, Jamila El Alami, Nourddine El Alami 
    Abstract: In this paper, we construct a type of dynamic joint pricing and inventory supply model with switching time-varying delays and weights in pricing, scarcity effect in inventory and the uncertainties of parameters and customers demand. This model is consisted of one distributor and two retailers under stock and price-dependent demand. Based on the rule of bounded rationality, the uncertain switched nonlinear system is approximated by the Takagi-Sugeno fuzzy model. Meanwhile, the fuzzy robust control method is introduced to minimise the bullwhip effect (BE), and a sufficient condition for the stability is presented utilising switched and delayed H-infinity state-feedback controller. The parallel distributed compensation is used to design the controller for the overall T-S fuzzy model. Finally, a simulation example is provided to investigate the influence of the different parameters as well their relative uncertainties on the complex dynamic characteristics of the system and to illustrate the effectiveness of the proposed method. Moreover, the influence of the competition/partnership interactions on the dynamics and robustness is examined.
    Keywords: Fuzzy robust control; Switched TakagiĀ–Sugeno fuzzy model; Bullwhip effect; Interaction; Stock and Price -dependent demand.
    DOI: 10.1504/IJMOR.2020.10034680
  • A generalized censored least squares and smoothing spline estimators of regression function   Order a copy of this article
    by Ilhem Laroussi 
    Abstract: In this work, new regression function estimators based on the combination of two approaches are proposed. The first one is the general censorship which gather the left, right, twice and the double censorship in the same context. The second approach is inspired from non parametric estimation methods. The least squares and smoothing spline techniques are chosen in this paper. Moreover, the almost sure convergence of the proposed estimators to the optimal value is established. The main results extend and improve the obtained results in [1] and [4] allowing for a more flexible methodology to deal with different censorship models including the four types of censoring (left, right, twice and double). Simulation study illustrates the performance of these estimators. We only considered a model subject to twice censorship because the other cases have already been studied in previous works.
    Keywords: Regression estimators; least squares; smoothing spline ; censored data; convergence in the L2-norm.
    DOI: 10.1504/IJMOR.2020.10034886
  • A Globally Convergent Interval Newton’s Method for Computing and Bounding Real Roots of a Function with One Variable   Order a copy of this article
    by Yosza Dasril, Ismail Bin Mohd 
    Abstract: It is known that Newton’s method is locally convergent, involves errors in numerical computations, and requires an initial guess point for calculating. This initial guess point should be closed enough to the root or zeros otherwise this method fails to converge to the desired root. The method of interval mathematics should overcome these issues and be used to make Newton’s method as globally convergent. This paper shows how to use interval mathematics for computing and bounding the simple and multiple roots of multimodal functions. It shows how to solve the problem when zero is in the given interval. The numerical computations for the two examples show the ability of newly proposed methods and satisfactory computational behaviour and convince us that Newton’s method is able to solve nonlinear problems statement.
    Keywords: interval mathematics; global convergence; root finding; Newton’s method; nonlinear; Alefeld’s method; algorithm.
    DOI: 10.1504/IJMOR.2020.10035174
  • Optimal Order Quantity with Endogenous Discounted Partial Advance Payment and Trade-credit for Inventory Model with Linear Time varying Demand   Order a copy of this article
    by Swati Agrawal, Snigdha Banerjee, Rajesh Gupta 
    Abstract: When buyers seek extended credit periods from relatively less secure suppliers, the supplier requires co-operation from the buyer for purchase of raw materials, etc., in terms of partial advance payment. For a single buyer single supplier supply chain, we develop an inventory model with a hybrid payment policy combining discounted advance payment to supplier with the supplier permitting interest free delay period to the buyer when buyer has the option to make advance payment. For the advance, supplier offers discount and may allow the buyer to set the discount rate and the advance proportion. For a linear demand function in such a scenario, we maximise buyer’s net profit rate through optimal choice of payment policy and the buyer’s replenishment. We consider two situations with discount: 1) exogenous; 2) endogenous for the buyer. Optimal solution is characterised theoretically. Numerical example reveals that by choosing advance proportion appropriately, the profit rate in the endogenous case can be higher than that in the exogenous case even with lower discount.
    Keywords: inventory; supply chain; endogenous discount; advance payment; credit period; linear time dependent demand rate.
    DOI: 10.1504/IJMOR.2020.10035233
  • Numerical methods for the optimal control of the heel angle of a rocket   Order a copy of this article
    by Mohand Bentobache, Mohamed Aliane, Nacima Moussouni 
    Abstract: In this work, we calculated the optimal heel angle trajectory of a rocket which have a constant mass and moves with a nonrectilinear motion from an initial point to a final one with a known altitude. The objective of the study is to maximise the lateral offset of the rocket. This problem is modelled as a nonlinear optimal control problem, where the control represents the heel angle of the rocket. In order to find a numerical solution to the problem, we applied the shooting method which is based on the Pontryagin’s maximum principle, and the Euler discretisation method, then we developed an implementation with the MATLAB programming language. Finally, we presented simulation results which compare the two numerical methods.
    Keywords: optimal control; heel angle of a rocket; Pontryagin’s maximum principle; shooting method; Euler discretisation method; nonlinear programming.
    DOI: 10.1504/IJMOR.2020.10035320
  • Developing a cost-effective and heuristic tool to solve cut order planning problems in the apparel industry   Order a copy of this article
    by Sandeep Prasad, Monika Panghal, Tesfamichael Molla Ali 
    Abstract: Cut order planning (COP) plays a vital role in the proper utilisation of fabric in the garment manufacturing process. It is because its major goal is to develop the most effective cutting plan considering the various decision variables in a purchase order, namely quantity, size and colour. However, the major challenge faced by SMEs is to develop the best mix of cut plans while ensuring the optimum use of the material, machine, and labour in the absence of any sophisticated software. This result in under-utilisation of fabric because of
    Keywords: COP; Solver; Macros; Python; Area; Marker Efficiency; Garment Industry; Marker Planning; Optimization.
    DOI: 10.1504/IJMOR.2020.10035753
  • Fuzzy reliability appraisal of a system using probabilistic dual hesitant fuzzy element emphasizing score function   Order a copy of this article
    by Deepak Kumar, S.B. Singh, Pawan Kumar 
    Abstract: Present paper introduces a new technique for analysing fuzzy reliability of a system under probabilistic fuzzy environment, where the reliability of a component/unit of a system is represented by probabilistic dual hesitant fuzzy element for handling uncertainty like hesitancy in real life situation. With the help of the proposed approach, in this study, we have evaluated the fuzzy reliability of some complex systems having series, parallel and bridge configurations using score function and deviation degree. Additionally, a numerical example is taken for better demonstration of the proposed technique.
    Keywords: fuzzy reliability; probabilistic dual hesitant fuzzy element; bridge configuration; score function; deviation function.
    DOI: 10.1504/IJMOR.2020.10035755
  • On the Linear Cooperative Search Technique for a Lost Target with Multiple Searchers   Order a copy of this article
    by Mohamed El-hadidy, Hamdy Abou-Gabal 
    Abstract: We discuss the linear cooperative search model to detect a hidden and randomly located target on one of the n-intersected roads (real lines). The searching process starts from the origin with n searchers. Each one of these roads has one unit speed searcher. We get the expected value of the searching time until the (n-1) searchers return to the origin after the target has been detected by the other searcher. We obtain the optimal distances for these n searchers to get the optimal search strategy which minimises the expected time of return. An interesting case with numerical results is studied when the target’s position has a truncated normal distribution.
    Keywords: cooperative search model; probability of detection; truncated normal distribution; optimal search plan.
    DOI: 10.1504/IJMOR.2020.10036156
    by K. A. M. Kotb, Hassnaa A. El-Ashkar 
    Abstract: This paper provides the quality control policy to improve the performance and the effectiveness of the machining system with standbys (spares) from the viewpoint of the queuing theory. The unit in the system is called a customer to whom the service should be rendered. An inspector is used to control the inspection process of the serviced unit. Under steady-state situation and the feedback concept, we obtained some performance measures and the probability when the system is empty or it has n units. Some important special cases and some analysis about the economic optimisation model with illustrative numerical examples, are performed.
    Keywords: quality control; spares; feedback machining system; steady-state solution; economic optimisation model.
    DOI: 10.1504/IJMOR.2020.10036159
  • An Inventory Model for Decaying Items with Pareto Distribution, Time- Dependent Demand and Shortages   Order a copy of this article
    by Varun Mohan, Mahadev Ota, Ashok Kumar 
    Abstract: In this paper, we develop an EOQ model for time-varying demand with deterioration. We assumed that the deterioration of commodity follows a generalised Pareto distribution. Also, the shortage is allowed and fully backlogged. Keeping these assumptions under consideration, the mathematical expressions are obtained for carrying cost, shortage cost and deterioration cost. Inventory costs were used to constitute the total cost function. Subsequently, optimal time to consume physical stock, cycle time, and total cost per cycle were determined. The results are discussed with the help of numerical examples followed by a comparative analysis between quadratic demand rate and equivalent linear demand rate. A comparison of results obtained from numerical examples concludes that the optimum cost for quadratic demand is less than that of the linear demand model. Finally, sensitivity analysis is presented to describe the influence of changes in the parameters on optimal policies.
    Keywords: EOQ model; inventory; shortages; stock out cost; cycle time; deteriorated units; positive stock.
    DOI: 10.1504/IJMOR.2020.10036163
  • A nonparametric estimation of the conditional quantile for truncated and functional data   Order a copy of this article
    by Halima Boudada 
    Abstract: In this paper, we propose a local linear estimator for the conditional distribution function in the case where the real response variable is subject to left-truncation by another random variable (r.v.) and the covariate is of functional type. Under regular assumptions, both of the pointwise and the uniform almost sure convergences, of the proposed estimator, are established. Then, we deduce the uniform almost sure convergence of the obtained conditional quantile estimator. A simulation study is used to illustrate the performance of our estimator with respect to the kernel method.
    Keywords: truncation; functional type covariate; local linear method; conditional quantile function; rate of almost-sure convergence; simulation.
    DOI: 10.1504/IJMOR.2020.10037454
  • Hierarchical Groups DEA Cross-efficiency and TOPSIS technique: An application on mobile money agents locations   Order a copy of this article
    by Jacob Muvingi, Arshad Ahmud Iqbal Peer, Farhad Hosseinzadeh Lotfi, Volkan Soner Ozsoy 
    Abstract: Ranking of efficient decision-making units (DMUs) allows a further analysis of the data envelopment analysis (DEA) efficient DMUs, where otherwise a high number of efficient DMUs can be identified. The current research seeks to segregate the efficient DMUs through the use of seven cross-efficiency (CE) ranking approaches. The choice of using those CE approaches was meant to reduce bias associated with the use of a single criterion. The seven approaches were extended to suit a situation were DMUs are structured in a two-level hierarchical grouping. The CE of level 1 DMUs was adjusted with the performance of the level 2 DMUs. Variations in the seven adjusted CE ratings were observed. In a bid to ensure complete ranking, the technique for order preference by similarity to ideal solution (TOPSIS) ranking method was combined with the adjusted CE ratings. The results from a real-world example revealed complete ranking for the majority of DMUs.
    Keywords: data envelopment analysis; DEA; hierarchical; groups; cross-efficiency; TOPSIS; locations; mobile money agents.
    DOI: 10.1504/IJMOR.2020.10037455
  • A novel decomposition approach to set covering problems by exploiting special structures   Order a copy of this article
    by Maryam Radman, Kourosh Eshghi 
    Abstract: The Set Covering Problem (SCP) has quite a large coefficient matrix in practical problems, but due to its low density, most of its entries are zero. Drawing on this observation, some methods can be developed to exploit special structures of the coefficient matrix of an SCP in such a way that they contain smaller dense subproblems. Against this backdrop, in this paper, three structures, namely "partitioned", "semi-block angular", and "block angular", are proposed. To begin with, some heuristic methods are presented to exploit these structures of the coefficient matrices of SCPs; then, by optimally solving the smaller subproblems of these structures, their solutions are used to solve the whole problem based on the proposed theorem. Our approach has been tested using well-known instances from OR-Library and shown to be comparable with some of the recently-developed methods to solve SCPs.
    Keywords: Set covering problem; Constraint partitioning; Decomposition techniques; Special structures; Clustering methods.
    DOI: 10.1504/IJMOR.2021.10037688
  • Optimal Generalized Searls Estimation Procedure of Population Mean Under Ranked Set Sampling Scheme   Order a copy of this article
    by Dinesh K. Sharma, S.K. Yadav 
    Abstract: Searls (1964) concluded that some constant multiple of a sample mean is an improved estimator of the study variable’s population mean. Further, it is well established that the proper use of auxiliary information elevates the estimator’s efficiency. In this study, a novel, more generalised family of Searls type estimators is suggested to enhance the estimation of the main variable’s population mean utilising known auxiliary parameters under ranked set sampling (RSS) scheme. The bias and mean squared error (MSE) expressions are studied up to first-order approximation. The optimal values of Searls constants are derived, which minimises the MSE of the introduced estimator. The minimum MSE of the proposed estimator is also obtained. The introduced family of estimators is compared with the competing estimators of the population mean. The efficiency conditions of the proposed class over the competing estimators are also derived. These efficiency conditions are verified through numerical and simulation studies. The comparison is made based on the estimators’ MSEs, and the estimator with the least MSE is recommended for practical applications.
    Keywords: ranked set sampling; RSS; main variable; auxiliary variable; Searls estimation; bias; mean squared error; MSE; percentage relative efficiency.
    DOI: 10.1504/IJMOR.2021.10037915
  • Selection of rear axle tip alternative material of a car by multicretria means   Order a copy of this article
    by Henry Toledo, Javier Martínez-Gómez, Juan Francisco Nicolalde 
    Abstract: In Ecuador some automotive spare parts are not manufactured in the country and must be imported, the reason for this is that some materials cant be found in the market, which is why this research aims to find an alternative material for the rear axle tip of a car, in order to find this material, first an original part is characterised under the ASTM E415 standard for chemical composition testing, where 0.5770.603 per cent of C was obtained, the hardness is determined with the ASTM E18 standard obtaining a hardness 322.77 HB. Tensile strength is found through the ratio of hardness vs. tensile strength, obtaining 115.05 kg / mm squared. Subsequently, a multicriteria analysis is carried out with the entropy, simple management and CRITIC methods the weights of each criterion are measured and with the EXPROM II, TOPSIS and VIKOR method the material is selected, where it was established that the optimal option is the AISI 5115 Steel compared to the original material characterised.
    Keywords: automotive; multicriteria; mechanics; materials; simulation.
    DOI: 10.1504/IJMOR.2020.10037916
  • A two-echelon supply chain contract under advertisement and retail price-dependent demand   Order a copy of this article
    by Rubi Das, Abhijit Barman, Pijus Kanti De 
    Abstract: In this study, we have considered the coordination issues of a supply chain system composed of a supplier and a retailer. The supplier offers a single product to the retailer, and the customer demand for the product at the retailer’s end is advertisement and retail price dependent. We have investigated the behaviour of the two-layered supply chain under the integrated and non-integrated scenario. Both models’ nature provides significant perceptions to an organisation’s manager to achieve optimum strategy under price and advertisement dependent demand. The main objective is to maximise the supply chain’s overall profit by optimising selling price, wholesale price, order quantity, and replenishment time. We have established the decentralised structure under the Stackelberg game approach to find the optimal values of each channel member. A numerical example and study of sensitivity analysis are provided to validate our proposed model.
    Keywords: inventory; advertisement; price; supply chain; centralised; decentralised; Stackelberg game.
    DOI: 10.1504/IJMOR.2020.10037929
  • Modeling and Analysis of Cascading failures in Interoperable Critical Infrastructure Systems   Order a copy of this article
    by Shohreh Ajoudanian, Moslem Fattahi 
    Abstract: Studying the behaviour and structure of the critical infrastructure systems (CISs) and the interdependency among them is of special significance, and if it is not determined properly, in addition to failure and cascading failure, there will be a national catastrophe. One of the reasons for not using the proper technique for critical infrastructure modelling is not to specify the entire sample space of the system and express all its limitations so that in addition to displaying accurate infrastructure behaviour, cascading failures can be prevented to an acceptable extent. Therefore, there is a need for a CIS formal specification modelling to develop different instances of a CIS and selecting the best and the failure-free instance of it. In this paper, we provide a formal declarative specification of CIS that supports detection and prevention of failure and cascading failure automatically in using Alloy. Since failures and cascading failures occur in dynamic and time-dependent environments, the proposed model considered dynamic aspects of CISs. The results show that using Alloy Analyser, all the models made and the current failures in infrastructure are determined using counter-examples and the best instance in terms of minimum and even without failure can be selected.
    Keywords: critical infrastructure system; CIS; formal modelling; cascading failure; Alloy modelling language.
    DOI: 10.1504/IJMOR.2021.10038293
  • Fuzzy optimization of a Production Model with CNTFN Demand Rate under Trade-Credit Policy   Order a copy of this article
    by Neelanjana Rajput, R.K. Pandey, Anand Chauhan 
    Abstract: The presented article deals with an economic production quantity model with a trade-credit policy. The classical (crisp) model presented with a fuzzy demand rate under a cloudy fuzzy environment. The concept of fuzziness affects the inventory model as well as inventory cost, profit, lot size, and all other factors. The centroid method has been used for the defuzzification of the model with triangular fuzzy demand in a general fuzzy environment. To avoid the effect of non-random uncertainties of demand rate in the production, the cloudy fuzzy model has been used here to provide a profitable business under several circumstances. And the Yager’s ranking method has been used for defuzzification for the cloudy fuzzy model. The cloudy fuzzy model gives better results instead of deterministic models for the long-run production cycle. Finally, the sensitivity analysis and graphical illustrations of a numerical example justify the model.
    Keywords: uzzy optimisation; cloudy normalised triangular fuzzy number; CNTFN; EPQ inventory model; trade-credit scheme; triangular fuzzy number; TFN.
    DOI: 10.1504/IJMOR.2020.10038419
  • Service pricing and customer behaviour strategies of Stackelberg's equilibrium in an unobservable Markovian queue with unreliable server and delayed repairs   Order a copy of this article
    by Kamel MEZIANI, Fazia RAHMOUNE, Mohammed Said Radjef 
    Abstract: In this paper, we model as a Stackelberg game the service pricing of server and the strategic behaviour of customers in a totally unobservable M/M/1 queueing system subject to random breakdowns and delayed repairs, under a reward-cost structure. For this, we first use the partial generating functions to determine the steady-state condition and the sojourn time of a customer in the considered queueing system. The analytical forms of the service price and the customer entrance strategies of the Stackelberg equilibrium of the game are given. Through numerical examples, we illustrate the effect of the price and the reliability parameters on the entrance probability of customers and the server profit. Finally, we define and solve the corresponding social welfare problem. This study has not only a theoretical aspect, but also a practical one, and it can be adapted to several real-life situations.
    Keywords: unreliable queue; delayed repairs; pricing; strategic behaviour; Stackelberg game; equilibrium.
    DOI: 10.1504/IJMOR.2021.10038485
  • A Load Balancing Algorithm Inspired by the Honey Bee Behavior to Reduce Waiting Time in a Perinatal Network   Order a copy of this article
    by Hudson Henrique De Souza Lopes, Ricardo Bruno Osés De Oliveira, Flávio Geraldo Coelho Rocha 
    Abstract: This article proposes a solution to a problem of mixed-integer linear programming for efficient resource allocation in the admission and scheduling process of pregnant women to a perinatal network composed of two maternity hospitals with heterogeneous capacities. For this, a load balancing algorithm based on the metaheuristic of honey bee behaviour is used. It is shown, through the results obtained in the simulations, that the proposed algorithm reduces the mean turnaround time of the system and the waiting time for pregnant women who enter the perinatal network, in comparison with other load balancing algorithms, based on classic queue theory, that are found in the literature.
    Keywords: load balancing; honey bee behaviour; perinatal; maternity.
    DOI: 10.1504/IJMOR.2021.10038637
  • Optimal Procurement and Pricing Policy for Deteriorating Items with Price and Time Dependent Seasonal Demand and Permissible Delay in Payment   Order a copy of this article
    by Ashish Sharma, Amit Kumar Saraswat 
    Abstract: In practice, items like food, nursery plants, medicines, etc. are seasonal and deteriorating in nature. For such class of products, permissible delay in payment is a common business policy which is used to increase in the sell volume and to develop trust in buyer-seller relationship. In this paper we developed an inventory model for time dependent deteriorating seasonal items with the permission of delay in payment. Shortages are permitted and partially back ordered. Our aim is to find optimal selling price and ordering quantity simultaneously. Concavity of profit function with respect to decision variables has been discussed analytically. A solution procedure followed by a numerical example and sensitivity analysis along with managerial insights are provided. Numerical analysis predicts that delay in payment profit policy is a better decision in order to maximise the profit or in order to get more profit.
    Keywords: inventory; deterioration; price and time dependent demand; delay payment; seasonal demand.
    DOI: 10.1504/IJMOR.2021.10038693
  • Multilevel Evidence on How Policymakers May Reduce Avoidable Deaths due to Covid-19: The Case of Brazil   Order a copy of this article
    by Rafael Freitas Souza, Luiz Paulo Lopes Fávero, Michel F. C. Haddad, Luiz Corrêa 
    Abstract: We propose a hierarchical linear method to investigate the effectiveness of social distancing measures. By considering the COVID-19 data as a two-level structure, we are able to demonstrate a significant reduction of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases as a direct consequence of lockdown measures adopted by some states in Brazil. The multilevel modelling is the most appropriate method for the case of Brazil due to the fact that political battles between federal and State government leaders have led to the adoption of lockdown measures with distinct levels of flexibility adopted by each of its 27 states. During the outbreak of such a novel and highly contagious disease, decisions made by policymakers either prevent or increase the number of avoidable deaths. Thus, our results are also potentially useful to convince policymakers to adopt reasonable policy measures to shorten the COVID-19 pandemic in the biggest Latin American country.
    Keywords: COVID-19; emerging countries; lockdown; multilevel modelling; SARS-CoV-2.
    DOI: 10.1504/IJMOR.2021.10038813
  • Fuzzy multi-criteria lead and zinc plant site location considering environmental criteria (A case study in Iran)   Order a copy of this article
    by Hassan Bagheri, Javad Behnamian, Samaneh Babaie Morad 
    Abstract: The aim of this study is to determine the location of the lead and zinc site considering environmental criteria. Within a radius of 5-10 km of the province under study, there are about 150 lead and zinc plants, which increase the pollution of the city and various diseases. If the plants are closed, about 3,500 people will be unemployed, and industry, mines, and national capital will be destroyed. Another option is to move these plants to a radius of 100 km in the province, which will cost a lot. Since the fuzzy sets theory method has been widely applied to the uncertain decision-making problem in the real-world, in this study for the first time, to select the appropriate option according to the criteria affecting environmental pollution, disease prevalence, income, unemployment rate, corruption, and cost, a multi-criteria decision-making technique with a hybrid fuzzy approach has been used. The proposed method is a hybrid of the TOPSIS fuzzy technique and a fuzzy hierarchical process that takes advantage of both of them. The results obtained in the case study show that using the proposed method, the best option is moving plants within a radius of 100 km from the city.
    Keywords: location problem; fuzzy multi-criteria decision-making; lead; zinc; hybrid approach; Iran.
    DOI: 10.1504/IJMOR.2021.10038814
  • A simple way to enhance the efficiency of Nguyen-Widrow method in neural networks initialization   Order a copy of this article
    by FAIZA SAADI, Ahmed Chibat 
    Abstract: The choice of the initial values of neural network parameters is of crucial importance for the conduct and successful completion of training. The most known and most used method to perform this task is the Nguyen-Widrow method. It has brought a well-established advantage over the traditional method of purely random choice. However, this advantage is not always guaranteed. A hidden defect can appear in some situations leading to a quality deteriorate of training. In this work, the existence of this hidden defect is revealed and the way to remedy this is proposed. We show how a simple procedure, built on conditional resets, eliminates unsuitable starting conditions and ensures the steadiness of good training quality. In this way, the search for the optimal architecture of a network when processing any given problem becomes faster and more reliable.
    Keywords: neural networks; weight initialisation; function approximation; regression.
    DOI: 10.1504/IJMOR.2021.10038815
  • Single Numerical Algorithm Developed to Solving First and Second Orders Ordinary Differential Equations   Order a copy of this article
    by John Kuboye, Bamikole Gbenga Ogunware, Olusola E. Abolarin, Chika O. Mmaduakor 
    Abstract: A potent numerical algorithm for solving first and second orders initial value problems is examined in this paper. Interpolation and collocation approach was applied in the derivation of the new method with the use of power series approximate solution as interpolating polynomial. The two numerical integrators that formed the block were derived by evaluating the non-interpolating points within the selected interval of integration. To examine the effectiveness of the block, it was tested on some first and second orders ordinary differential equations and results generated performed better when compared with existing methods in terms of accuracy.
    Keywords: block method; collocation; hybrid; interpolation; power series; first order IVP; second order IVP.
    DOI: 10.1504/IJMOR.2021.10038999
  • Establishment of EOQ strategy for time   Order a copy of this article
    by Rakesh Tripathi 
    Abstract: The retailer makes a decision, the initial holding cost at the beginning of each replenishment cycle and then concludes whether and how to change the carrying costs during the cycle. Thus, during each cycle, items are sold before and after the carrying cost modification at two costs: the initial holding cost and the used holding cost. Of course, the two prices may be the same if the retailer chooses not to change prices. In this study, an inventory model is established under time linked demand and deterioration. Carrying cost is considered exponential time dependent. Mathematical formulation is given to build up the model . The numerical examples are discussed to authenticate the model projected in this study. Some results based on optimal solution are also discussed. We then show that the total cost is curved upward by means of cycle time. The sensitivity investigation is also established.
    Keywords: inventory; deterioration; demand; exponential holding cost; credit period.
    DOI: 10.1504/IJMOR.2021.10039103
    by Ahmed R. Abubakar, Hamisu A. Adamu, Asuku Abdulsamad, Yusuf A.Sha’aban 
    Abstract: This paper presents the development of a second-order polynomial model for the prediction of power of a typical miniature neutron source reactor (MNSR). Using the least-squares method, the model coefficients were generated from thermal power and reactor core coolant temperature as dependent and independent variables, respectively. Operational data were collected at 1-minute intervals, for a total of 100 minutes each for 6.20 kW, 15.50 kW, and 31.0 kW. The mean absolute deviation (MAD) obtained during validation using the developed model (QModel), at 6.2 kW, 12.4 kW, 15.5 kW, 18.6 kW, 24.8 kW and 31 kW were: 0.51, 0.25, 0.38, 0.29, 0.44, and 0.50 respectively while the corresponding results from earlier work were 3.03, 3.36, 3.49, 2.24, 1.24, and 5.71. The QModel gave a better power prediction with an error deviation of less than±5%.
    Keywords: miniature neutron source reactor; MNSR; Nigeria research reactor-1; NIRR-1.
    DOI: 10.1504/IJMOR.2021.10039300
  • Modelling a shared-resource network DEA with bad output in measuring technical efficiency of banking system   Order a copy of this article
    by Khac-Thanh Mai, Manh-Trung Phung, Bao-Ngoc Tong, Cheng-Ping Cheng, Son-Tung Le 
    Abstract: This paper develops a serial three-stage network data envelopment analysis (DEA) model to estimate the efficiency of banks who transform their resources into final products, incomes. Different from previous studies, which oversimplified the banking’s production, we divide it into three stages, namely, capital organisation, capital allocation, and capital turnover. The shared resources and undesirable outputs are also integrated into the evaluation framework to better reflect the nature of banking business. The novel contribution of our network structure is its ability to disclose the inefficient of each stage as well as its relative importance in the whole operation. The model is then employed to appraise the technical efficiency of 35 banks in Taiwan. Some managerial implications are offered to optimise their performance.
    Keywords: data envelopment analysis; DEA; network structure; shared resources; undesirable outputs.
    DOI: 10.1504/IJMOR.2021.10039489
  • Optimization of an inventory Model for Conclusive and Inconclusive Cost Parameters using Triangular and Trapezoidal Fuzzy Numbers   Order a copy of this article
    by Renu Sharma, Anubhav Pratap Singh, Ritu Arora, Anand Chauhan 
    Abstract: Volatility in the prices of crude oil creates a very complicated situation for the management of an inventory system. As result, an unexpected shift in cost parameters occurs. A model of economic order quantity (EOQ) is developed to control the inventory in that situation when a decision-maker is not able to clearly express the cost parameters at the beginning of system design. Such type of situation is created due to volatility in the price. The purpose of the article is to study the impact of inconclusive cost parameters on total average cost. The holding cost, ordering cost, deterioration cost, and shortage cost are assigned by fuzzy numbers. Then, graded mean integration method (GMIM) is used to defuzzified the total average cost. A comparative study in a crisp environment and fuzzy environment is validated as an explicit condition to control the inventory for reducing the optimum cost.
    Keywords: economic order quantity; EOQ; trapezoidal fuzzy number; triangular fuzzy number; graded mean integration method.
    DOI: 10.1504/IJMOR.2021.10039506
  • An Optimal Inventory Model for a Deteriorating Item with Multivariate Demand Function   Order a copy of this article
    by Mahsa Ghandehari, Mohsen Karimi-Lenji 
    Abstract: Managing the inventory of perishable items is a vital task in the supply chain. The demand for some deteriorating items is influenced by many factors that make their management a complicated task. Therefore, it is important to take multiple key factors into account to develop a more realistic model. In this paper, an inventory model for non-instantaneous deteriorating items is proposed, for the case where the quality and quantity of the item decrease over time. The demand is an additive, continuous, and differentiable function of price, stock level, and also age of the product. The deterioration starts after a fixed period with a constant rate, and the shortage is not allowed. Permissible delay in payment and time value of money are also considered in the model. First, we formulate the problem in a piecewise mixed-integer nonlinear programming model. We then propose an algorithm to solve a number of examples.
    Keywords: replenishment policy; deteriorating items; multivariate demand function; delay in payment.
    DOI: 10.1504/IJMOR.2021.10039543
  • On multi-objective extensions of the classical assignment model with fuzzy parameters and fuzzy goals   Order a copy of this article
    by Lanndon A. Ocampo, Enrico Enriquez, Carmelita Loquias, Reuella J. Bacalso, Grace Estrada 
    Abstract: This study advances the limitations of current fuzzy multi-objective assignment models by exploring some formulations with fuzzy parameters and fuzzy goals. The first formulation expresses the coefficients of the objective functions and constraints as fuzzy sets. Two crucial fuzzy transformations were adopted, along with the computational process of the epsilon-constrained multi-objective optimization. On the other hand, the second formulation assumes the fuzzy coefficients of objective functions and constraints and extends such fuzziness by introducing fuzzy constraints. Lastly, the coefficients of the objective functions and the constraints are expressed as crisp sets while allowing permissible constraint violations. The symmetric fuzzy linear programming solution concepts in the domain literature were adopted as part of the computational process in arriving at a model solution. Actual case examples aided these formulations to gain insights into their computational complexity, efficiency, scalability, and flexibility.
    Keywords: assignment; multi-objective optimisation; fuzzy optimisation.
    DOI: 10.1504/IJMOR.2021.10039694
  • Detection Model for a Suitable Waiting List with Maximizing the Discount Effort Reward Search Under the Quality Control Process   Order a copy of this article
    by Mohamed El-hadidy 
    Abstract: The economic benefits of the company are increased by improving the quality of its services. At the same time, the customers aimed to get the service with minimum cost. In this paper, we provide a detection model which satisfies these purposes. The customer chooses the suitable engineering consultancy company from independent companies. Each company has a Markovian waiting list of customers with size N. The customer arrives to the waiting list with Poisson process and its service time has an exponential distribution. Under the quality control process and some concepts like balking and reneging of each waiting list, we provide the optimal decision to consider the suitable company. We consider the searching effort is bounded by a random variable with a known probability distribution. After applying the discount effort reward search function, we solve a difficult stochastic optimisation problem to get the maximum values of the service rate, discount effort reward and the minimum value of the detection cost. A case study is provided to get these optimal values and the optimum performance measures which give the optimal expected profit.
    Keywords: detection model; services quality; waiting list; performance measures; decision-making; maximum discount effort reward.
    DOI: 10.1504/IJMOR.2021.10039787
  • A Hybrid Fuzzy Stochastic Model for Fractional Multi-commodity Network Flow Problems   Order a copy of this article
    by Salim Bavandi, Seyed Hadi Nasseri 
    Abstract: In this paper, we aim to introduce a class of multi-commodity network flow problems. Here, we deal with a multi-commodity flow problem with a fractional objective function that is investigated in a fuzzy random hybrid environment. This paper aims to provide a model that manages unknown coefficients in fractional multi-commodity networks. In this problem, the coefficients of the objective function in the numerator of the fraction and the arc capacity are assumed to be fuzzy random variables and the coefficients of the objective function in the denominator of the fraction are assumed to be fuzzy variables. Since this problem is investigated simultaneously in both random and fuzzy environments, we use a probability-possibility approach to convert the problem to a deterministic form. Next, we get the problem out of the fractional mode using the variable transformation method and finally, examine the efficiency of the proposed method by providing some numerical examples.
    Keywords: fractional programming; fuzzy random variable; multi-commodity flow problem; probability-possibility approach; decision making under uncertainty.
    DOI: 10.1504/IJMOR.2021.10039999
  • Optimizing fully interval integer two-stage transportation problems   Order a copy of this article
    by A. Akilbasha, Natarajan G 
    Abstract: The study proposes a novel technique namely, divided-united method which is framed based on the zero point method in order to optimise the fully interval integer two-stage transportation problem (FIITSTP). The proposed method offers more than one optimal solution to fully interval integer two-stage transportation problems. The optimal values of decision variables and the objective function of the fully interval integer two-stage transportation problems provided by the proposed method are interval integers. A numerical example is illustrated for a better understanding of the solution procedure of the proposed method. Since the proposed method offers more than one optimal solution therefore it is highly helpful for the decision makers when they are handling logistic models of real life situations involving interval integer parameters. Further, this method is likely to determine the perfect and effective optimal solution for fully interval integer transportation problems in a simple manner.
    Keywords: two-stage transportation problem; optimal solution; interval integers; divided-united method.
    DOI: 10.1504/IJMOR.2021.10040215
  • Efficient classes of estimators for population variance using attribute   Order a copy of this article
    by Shashi Bhushan, Anoop Kumar, Sumit Kumar 
    Abstract: This article deals with the problem of estimating population variance of study variable by using information on auxiliary attribute in simple random sampling. We have adapted the procedure of Kadilar and Cingi (2006) and established some efficient classes of estimators for population variance. The performance of the proposed estimators have been assessed by an empirical study using two real populations and the results demonstrate that the proposed estimators present an extensively greater efficiency when compared with the usual mean estimator, classical ratio, regression and exponential estimators suggested by Singh and Kumar (2011), Singh and Malik (2014) estimators, Zaman and Kadilar (2019) type estimators, Zaman (2020) type estimator and Cekim and Kadilar (2020) type estimator.
    Keywords: bias; mean square error; efficiency; auxiliary attribute.
    DOI: 10.1504/IJMOR.2021.10040442
  • The New Family of Ristic-Balakhrishnan Marshall Olkin-G Distributions with Properties and Applications   Order a copy of this article
    by Peter O. Peter, Broderick Oluyede, Nkumbuludzi Ndwapi, Onkabetse Mabikwa, Huybrechts F. Bindele 
    Abstract: In this paper, we develop and study in detail a new family of distributions called Risti ´ c — Balakhrishnan Marshall Olkin-G (RBMO-G) distribution. We obtain some mathematical and statistical properties of this distribution such as hazard and reverse hazard functions, quantile function, moments and incomplete moments, moment generating functions, R´ enyi entropy and order statistics. The model parameters are obtained through method of maximum likelihood. We finally illustrate the usefulness of this family of distributions via simulation experiments. Furthermore, we apply a special case of this family of distributions to some real data to assess and compare its performance with other non-nested models.
    Keywords: Ristic-Balakhrishnan; Marshall-Olkin; distributions; moments; maximum likelihood; simulations.
    DOI: 10.1504/IJMOR.2021.10040443
    by S. Maragathasundari, S. Kishore Eswar, Somasundaram RS 
    Abstract: This paper manages the Queuing issue of various vacation Policies. Clients showing up in clumps follow a Poisson distribution. Administration following general distribution is rendered in two phases of administration, in which the second phase of administration is discretionary. Here, during vacation period the support work of the server is completed. Here get-away is presented in two classifications, viz. compulsory vacation and broadened vacation both follow general conveyance. Expanded vacation is given regarding two phases in which the second phase of broadened get-away is of server's decision. Set up time arrange is presented in earlier of expanded vacation and the idea of reneging occurs during the second phase of broadened vacation. The issue is solved by strengthening variable technique and the Queue measures including the force parameter, the mean inactive time, the mean number of clients, the mean waiting time in the queue and in the system are determined. Also the numerical depiction and a graphical appraisal support the model.
    Keywords: multi vacation; composite materials; reneging; extended vacation; two stages of service.
    DOI: 10.1504/IJMOR.2021.10040468
  • An Optional Arrival Process of the Oscillatory Demands in the Inventory System with Queue Dependent Service Rate   Order a copy of this article
    by Jeganathan Kathirvel, Selvakumar Subramanian 
    Abstract: In this paper, we study a classical retrial queueing-inventory system (CRQIS) with an optional arrival process of an oscillatory customer (OC) who may enter into the waiting hall or an infinite orbit directly under Bernoulli trials. The orbital customer emulates their requirements through the waiting hall only over the classical retrial policy (ClRP) whenever it is less than its capacity and the service rate of customer depends on the queue length at an epoch. This system contains a perishing item, too, and replenishment can be done following the (s, Q) ordering policy. The server can do an orbital search which follows Bernoulli process. Neuts approach is applied for the matrix-geometric approximation (MGA) to find a stationary probability vector and the Laplace-Stieltjes transform method (LSTM) is used to derive waiting time of both arrivals. Also, sufficient numerical problems are to be explored for the assumed model.
    Keywords: optional arrival process; oscillatory customer; queue dependent service rate; QDSR; classical retrial policy; waiting time.
    DOI: 10.1504/IJMOR.2021.10040594
  • Neutrosophy based transportation problem and its solution approach.   Order a copy of this article
    by Tuhin Bera, N.K. Mahapatra 
    Abstract: This study designs a transportation problem (T p-problem) by taking the transportation cost, availabilities, demands and quantity of goods to be transported as single valued trapezoidal neutrosophic number (svtn-number). Then experts can include their hesitancy in decision making independently in uncertain climate. The proposed form of T p-problem is solved in four distinct methods and, optimality test of their initial outcomes are performed. The respective algorithms are developed with the help of existing crisp notions. A parameter-based linear ranking function of svtn-number is drawn here in order to that. This parameter of ranking function helps to incorporate the relevant characters involved indirectly in a T p-problem beside the provided constraints in its solution approach. The way of treatment of uncertainty and the incorporation of relevant character in a T p-problem designed here make its outcome more realistic and acceptable to the experts. The efficiencies of proposed concepts are tested in real ground. The optimal values are analyzed to opt the better method applicable for that problem.
    Keywords: single valued trapezoidal neutrosophic number; svtn-number; ranking of svtn-numbers; neutrosophy-based transportation problem; N t-problem.
    DOI: 10.1504/IJMOR.2021.10040595
  • Solution of Linear Programming Problem with Trapezoidal Fuzzy Coefficients using Score functions   Order a copy of this article
    by Lakshmana Gomathi Nayagam Velu, Jagadeeswari Murugan, Suriyapriya K 
    Abstract: Numerous real-life problems depend on incomplete and implausible information. To overcome the enigma and obscurity, Zadeh promoted fuzzy set theory in 1965. After introducing fuzzy set theory, many researchers have made numerous developments in engineering and medicine. Different ranking principles on trapezoidal fuzzy numbers are established and are applied by eminent authors in multi-criteria decision-making problems in the literature. Linear programming models are essential tools to solve optimisation problems in healthcare, production planning, financial sectors, etc. The ranking principle plays a vital role in the constraints. Recently, a complete ranking principle on the class of trapezoidal fuzzy numbers was suggested in 2018. This study proposes a method to solve the fuzzy linear programming problem whose coefficients are trapezoidal fuzzy numbers using the total ordering principle by score functions defined in 2018. Here, we formulate an equivalent multi-objective linear programming problem for the given fuzzy linear programming problem to attain the optimal solution. Furthermore, the proposed method’s efficiency is illustrated through numerical examples and comparison with the existing techniques is also discussed.
    Keywords: linear programming problem; trapezoidal fuzzy coefficients; total ordering principle.
    DOI: 10.1504/IJMOR.2021.10040627
  • Estimating Weight of Stocks using Ambiguity Index and its Application to Type-2 Intuitionistic Fuzzy Portfolio Selection   Order a copy of this article
    by Anusha Vulimiri, Sireesha Veeramachaneni 
    Abstract: In this paper a method to find the weight of stock in the portfolio is developed when the stock preferences are given in type-2 intuitionistic fuzzy numbers. Taking into the fact that ambiguity can significantly bring the outcome of weight; in this paper we compute ambiguity in the valuation of each stock and then used in weight determination process. The proposed technique allows the decision maker to assign the weights for stocks, which leads to select reliable portfolio for investment. The advantages are discussed by citing appropriate numerical examples.
    Keywords: portfolio selection; stock weights; ambiguity index; type-2 intuitionistic fuzzy set; T2IFS; Jaccard distance measure.
    DOI: 10.1504/IJMOR.2021.10040628
  • A MAP/PH1, PH2/1 system with two types of heterogeneous service, setup, closedown, vacation, immediate feedback, breakdown and repair   Order a copy of this article
    Abstract: In this article, we examine a classical queueing model with single unreliable server who can offer two types of heterogeneous services namely, types I and II. Customers reach the system by following the Markovian arrival process (MAP). The service times of both types of services are considered to be phase-type (PH) distributed. We have considered a service clock which begins at the commencement of the service after the setup/repair process and immediate feedback for the unsatisfied customers. If the service clock expires, the server will start the closedown process and consequently goes on vacation. The assumptions of our model have greater significance on small scale industries. By utilising the matrix-analytic method, we have examined our model and investigated the active period and the waiting time distribution of our model. We have also carried out the cost analysis for our model. To the end, some numerical and graphical exemplifications are presented for clear insight into our model.
    Keywords: PH distribution; Markovian arrival process; MAP; two types of services; vacation; service clock; setup; closedown; immediate feedback.
    DOI: 10.1504/IJMOR.2021.10040826
  • Inventory Policies for Monotonic Change in the Purchase Price   Order a copy of this article
    by Suresha Kharvi, T.P.M. Pakkala 
    Abstract: This article considers an optimal inventory policy for monotonic change in the purchase price where price change depends on the number of orders made. The planning horizon is considered as finite and yearly demand is assumed to be constant and known. A closed-form solution is obtained for the optimal order lengths. These closed-form solutions will be very useful to business managers. An algorithm is given to determine the optimal number of orders during the planning horizon. Some of the interesting properties of the optimal order quantities are discussed. A numerical example and sensitivity analysis are carried out to support the theoretical results.
    Keywords: inventory; monotonic price change; optimal policy; optimal cost; optimal order lengths.
    DOI: 10.1504/IJMOR.2021.10040827
  • Develop an optimization model for relief facility location in disaster   Order a copy of this article
    by Amirmasoud Soltanzadeh, Vahid Baradaran, Faezeh Soltanzadeh 
    Abstract: This research was conducted to study the issue of relief facility location hierarchically by consideration of possible road closure during the disaster, road safety, and arrival time of relief facility under disaster circumstances. A multi-objective model was developed to minimise the pre-disaster and pro-disaster costs. The main contribution of this study is road safety and reduction in time taken to have a critical facility in affected areas. To investigate the functional accuracy of the mathematical model, a numerical example with small dimensions was solved using CPLEX solver, and required sensitivity analysis was described. As the facility location-allocation is an NP-hard issue, three metaheuristic algorithms were used to solve numerical representations in real dimensions to examine numerical analyses effectively. Results showed that the grey wolf algorithm had the highest efficiency compared to other developed algorithms. The obtained results can be used as an efficient managerial tool in management organisations involved in the disaster.
    Keywords: hierarchical location; disaster management; multi-objective optimisation model; metaheuristic algorithms.
    DOI: 10.1504/IJMOR.2021.10040858
  • A Simulation Approach to Modified Searls Estimation of Population Mean under Two-Phase Random Sampling   Order a copy of this article
    by S.K. Yadav, Dinesh K. Sharma, Madhulika Dube 
    Abstract: A new extended Searls type estimator is suggested in this paper to assess the population mean of an essential variable more efficiently. The suggested estimator utilises a known supplementary variable in a two-phase (double sampling) design for improved estimation. The bias and mean squared error (MSE) of the introduced estimator are retained to approximate degree one for studying the sampling distribution properties. The Searls constants’ optimal values that provide minimum MSE of the novel introduced estimator have also been acquired. The MSE of the introduced estimator was compared with the MSEs of other estimators in competition under double sampling, and the conditions of efficiency are obtained. The efficiency conditions obtained in theoretical comparison for the proposed estimator are verified using four natural data sets. A simulation study has also been performed using the natural populations’ parameters to see the results’ consistency.
    Keywords: main variable; Searls type estimator; auxiliary variable; bias; mean squared error; MSE; percentage relative efficiency; PRE.
    DOI: 10.1504/IJMOR.2021.10040901
  • Queueing Systems in the Cafeterias at the University of Dodoma, Tanzania   Order a copy of this article
    by Srinivasa Rao Gadde, Evodia Andreas Mnyanga 
    Abstract: The queuing is a common practice to all public service centres where the demand surpasses the supply. The purpose of this study is the performance of queueing systems in the cafeterias at the University of Dodoma, Dodoma Tanzania. Data were recorded in a period of seven days to find the distribution pattern of the arrival and the service time through fitting them in poison and exponential distribution respectively, to determine the average waiting time in a queue by using the M/M/1 mathematical model, and to analyze the waiting time in a system by using statistical quality control chart. The results of the findings showed that the arrival time and service time for all queues in all sessions follows poison and exponential distribution respectively. Also the findings showed that the expected waiting time was high during breakfast, whereas during lunch and dinner the expected waiting time was low compared to breakfast.
    Keywords: queue; restaurant; waiting lines; M/M/1 mathematical model; arrival time and service time; Tanzania.
    DOI: 10.1504/IJMOR.2021.10040971
  • A Sustainable Inventory Model for Setup and Ordering Cost Reduction under a Controllable Lead Time   Order a copy of this article
    by Malleeswaran Balasubramani, R. Uthayakumar 
    Abstract: In this study, we consider an integrated vendor-buyer supply chain (SC) model. This paper investigates the impact of setup and ordering cost reduction in a continuous review inventory policy with controllable lead time. The probability distribution is the most aspect of this model, within free distribution, including as mean and standard deviation. We obtain the annual minimum cost by considering setup and ordering cost reductions. The solution procedure is used to determine the optimal solutions of order quantity, setup cost, ordering cost, lead time, and the number of shipments from the single vendor (SV)-single buyer (SB) in one production run. This model has vital perspectives to present a venture by considering with and without distribution under a controllable lead time.
    Keywords: supply chain management; SCM; logarithmic investment; integrated approach; probability distribution; controllable lead time.
    DOI: 10.1504/IJMOR.2021.10041084
  • A Robust Global Optimization Framework for Stochastic Integrated Refinery Planning with Demand and Price Uncertainties   Order a copy of this article
    by Mahmud Siamizade, Theodore Trafalis 
    Abstract: This study presents a global optimisation framework for the strategic planning of an integrated oil refinery while accounting for the uncertainties in the crude oil and final product demand and market prices. To model the uncertainties, three modelling schemes have been utilised: 1) a robust optimisation framework; 2) a fuzzy possibilistic programming approach; 3) a risk aversion two-stage stochastic model with financial risk management. These methodologies are applied to an industrial case study, comprising an integrated oil refinery with tasks spanning from unloading crude oil at the refinery’s front to distributing refined products to distribution centres by pipelines. The notable feature of this study is developing an optimisation approach with a multi-period mixed-integer nonlinear programming (MINLP) model and solving it through an aggregation/disaggregation linearisation algorithm and obtaining ?-global optimal solutions. The results indicate significant economical and operational advantage of the robust optimisation scheme depending on the decision maker’s risk attitude.
    Keywords: integrated refinery planning; global optimisation algorithms; uncertainty appraisal; robust programming; fuzzy possibilistic programming; stochastic programming; financial risk management.
    DOI: 10.1504/IJMOR.2021.10041135
    by André G. Medeiros, Leandro Resendo 
    Abstract: In this work, mathematical models were developed to maximise oil production in offshore petroleum fields. Wells considered can be equipped with continuous gas-lift, electrical submersible pumps and naturally flowing, and connected by manifold or satellite. Platforms’ fluid processing capacity and operational condition were considered as well. Two nonlinear models were developed: one model that considered the pipeline network as a fixed parameter, analysing the system configuration; and another that allows the assignment of wells to manifolds, analysing production improvement with network changes. Using piecewise linearisation for multidimensional functions, four mixed-integer linear formulations were proposed. Two-variable functions were linearised using the diagonal method and triangle method and three-variable functions were linearised using plane method. Using a real scenario, there were investigated the piecewise refinement, computational complexity, and solutions error. Results shown the models applicability for daily adjustments and indicates the necessity of new investments in pipeline connections.
    Keywords: mixed integer linear programming; MILP; offshore oilfield; linearisation; diagonal method; triangle method; plane method; production optimisation.
    DOI: 10.1504/IJMOR.2021.10041209
  • Modeling time-series process of an agricultural crop production process by EWMA quality control chart   Order a copy of this article
    by Zeina Mohammed  
    Abstract: Control charts are considered to be one of the main tools for analysing and controlling the steps of a product chain process. This research emphasises the control charts’ versatility not only in manufacturing but in taking enough actions for maintaining the quality of the crops with more flexibility. The time-series quality proceedings for crops that utilised the statistical process control (SPC) method serve as a case study in the EWMA control chart. One week of 168 hours of observation data is analysed with a sampling time of one hour. These measurements have been investigated over three models; AR, MA, and ARMA. The results of plotting EWMA for autoregressive (AR), moving average (MA), and ARMA models included eight points at which the process is out of control. It is found that a higher order of AR or MA model shows a lower out-of-control process. This satisfies the concluded point that higher order of the ARMA model means lower out-of-control process points.
    Keywords: statistical process control; SPC; control chart; EWMA; AR; MA; ARMA.
    DOI: 10.1504/IJMOR.2021.10041381
  • The problem of resource leveling in multi-project mode by Cuckoo Optimization Algorithm   Order a copy of this article
    by Elham Shadkam 
    Abstract: Project resource levelling is very important and project managers need a schedule based on the optimal use of resources needed to complete their projects. Most resource levelling research has been done in a single project, while in many organisations several projects are done simultaneously. For this purpose, a mathematical model with the aim of minimising the level of change in various resources of consumption by all projects is presented in this paper. The cuckoo optimisation algorithm has been used for this model, which is one of the newest and most efficient evolutionary optimisation algorithms. The obtained results by solving the problem with the cuckoo optimisation algorithm and comparing it with the exact approach indicate that the exact approach is more appropriate in low dimensions and as the dimensions of the problem increase, the cuckoo optimisation algorithm solves the problem faster and in less elapsed time with the same accuracy. Therefore, this algorithm is more suitable for large-scale problems that are close to the real world problem.
    Keywords: resource levelling problem; cuckoo optimisation algorithm; COA; multi-project control; meta-heuristic algorithms; multi-resources.
    DOI: 10.1504/IJMOR.2021.10041537
  • A Revisit of the Proposed Model for Solving Fuzzy Linear Fractional Programming Problem   Order a copy of this article
    by Nemat Taghi-Nezhad 
    Abstract: Linear fractional programming (LFP) problem is used worldwide in solving real world problems. In real life situations the parameters of the problem are imprecise instead of fixed real numbers. So, a procedure for modelling these impreciseness in mathematical form is required. Fuzzy set theory is a best tool to deal with such situations. In this paper LFP problem with fuzzy parameters are studied. A fuzzy linear fractional programming (FLFP) problem is considered by Das et al. (2018) where a simple ranking approach between two triangular fuzzy numbers is provided. Then, in their study a tri-objective LFP problem is formulated to calculate the upper, middle and the lower bounds of the fuzzy optimal value. There are some errors and shortcomings in Das et al. method. Hence, in this study errors and shortcomings of Das et al. method are pointed out. Also, to overcome these errors, a simple method is presented to obtain optimal solution and fuzzy optimal value of the objective function. Moreover, by solving some numerical examples these errors are demonstrated and using the new proposed algorithm the correct optimal solution and the fuzzy optimal value of objective function are obtained.
    Keywords: linear fractional programing problem; fuzzy number; fuzzy linear fractional programing problem; fuzzy optimal value.
    DOI: 10.1504/IJMOR.2021.10041791
  • Self-adjoint linear maps on C*-algebra   Order a copy of this article
    by Mehdi Tourani, Yasser Khalili 
    Abstract: Let A and B be two unital C*-algebra and let ? : A ! B be a unital self-adjoint linear map that preserves invertibility and locally preserves commutativity, then ? is a continuous Jordan homomorphism. In this paper, we have studied the structure of self-adjoint linear maps on C*-algebras such that they play an important role in continuity Jordan homomorphism. One of the principal techniques to show that under the assumptions a self-adjoint linear map is a Jordan homomorphism is use of the GKZ (Gleason-Kahane- Zelazko) theorem that the famous GKZ theorem states that every unital invertibility preserving linear functional ? on a unitale Banach algebra A is multiplicative.
    Keywords: Self-adjoint; Jordan homomorphism; Locally preserves commutative.
    DOI: 10.1504/IJMOR.2020.10041902
  • Modeling and Performance Evaluation in the (R, s,lnQ) Inventory System   Order a copy of this article
    by Nedjma Aiane, Fazia RAHMOUNE, Djamil Aissani 
    Abstract: In this work, we propose to analyse a periodic review inventory model with an (R, s, lnQ) policy and an instant replenishment via a discrete Markov chain approach. Then, we adopt the strong stability method to evaluate the characteristics of the considered model in the case of the perturbation of some of its parameters (demand rate and demand law). Thus, we find the approximation bounds of the stationary distribution, with an exact computation of the constants, to evaluate the error generated by this approximation. Finally, we study numerically the effect of the perturbation of the arrival rate and the demand law respectively on the average stock and the total cost of the considered inventory model. Several numerical examples have been performed to illustrate the performance of this approach
    Keywords: inventory control; (R; s; lnQ) policy; Markov chains; transition Kernel; strong stability; stability inequalities; stationary distributions; relative error; the error on the average stock; total cost.
    DOI: 10.1504/IJMOR.2021.10042002
  • Multi-queue system with finite shared buffer under Batch Poisson and/or Interrupted Batch Poisson arrivals: a computational analysis   Order a copy of this article
    by Miron Vinarskiy 
    Abstract: This paper studies a model of a multi-queue system with a finite common buffer shared by queues with batch arrivals. The study is performed for a few buffer sharing policies. For batch Poisson arrivals with an arbitrary batch size distribution, the analysis benefits from the fact that the stationary state distribution has a product form. For the special case of geometrically distributed batches, closed form solutions for normalisation constant are obtained. They lead to efficient computational procedures. For bursty interrupted batch Poisson arrivals, it is shown that an exact numerical analytic analysis is only possible for very small models. For real-life sized systems, an approximation method has been developed.
    Keywords: queuing; multi-queue; batch arrivals; finite buffer; losses.
    DOI: 10.1504/IJMOR.2021.10042132
  • Neuro-fuzzy Computing and Optimization Results for Batch Discrete time Retrial Queue   Order a copy of this article
    by Shweta Upadhyaya, Geetika Malik, Richa Sharma 
    Abstract: The present investigation involves the application of discrete time bulk entrance recurrent queuing model on asynchronous transfer mode (ATM) technology. This analysis includes the concept of Bernoulli feedback along with priority and impatient customers wherein server may undergo starting failure. Once a service is accomplished, the service provider/server either waits for succeeding customer or leave for a vacation of random time span. The service period, vacation period and retrial period all are presumed to follow general distribution. Firstly, we calculate necessary performance indices using generating function method. Thereafter, we approximate all calculated results with the help of adaptive neuro-fuzzy interface system (ANFIS). Furthermore, we discuss how this model can solve issues related to traffic management and control in ATM networks. Lastly, to make the system more economical, we have computationally analysed the model via particle swarm optimisation (PSO) and genetic algorithm (GA) techniques.
    Keywords: batch arrival; Bernoulli vacation; starting failure; ATM network; adaptive neuro-fuzzy interface system; ANFIS; cost optimisation.
    DOI: 10.1504/IJMOR.2021.10042136
  • New Hybrid Method for Direct Numerical Solution of Nonlinear Second, Third and Fourth Orders Ordinary Differential Equations   Order a copy of this article
    by Olusola E. Abolarin, Bamikole Gbenga Ogunware 
    Abstract: A novel and efficient algorithm for the concurrent numerical solution of second, third and fourth orders of ordinary differential equations is studied in this article. Collocation and interpolation technique was employed in the derivation of the method and power series approximate solution was used as the interpolating polynomial. The fourth derivative of the power series was collocated at the entire grid and off-grid points, while the fifth and sixth derivatives of the polynomial were collocated at the endpoint only. Proper investigation of the basic properties of the method was done. The results showed that the new block method applied on a nonlinear second, third and fourth orders of ordinary differential equations were better in terms of accuracy than the existing methods. The proposed method takes away the burden of developing a separate method for the solution of second, third and fourth order initial value problem of ordinary differential equations.
    Keywords: hybrid block method; collocation; higher order ODEs; interpolation; power series.
    DOI: 10.1504/IJMOR.2021.10042183
  • ANFIS computing and analysis of cost optimization by upgrading service rate with N-policy, server vacation in M/M/1 model   Order a copy of this article
    by Anamika Jain, Komal Shekhawat, Bhoopendra Pachauri 
    Abstract: This study investigates an M/M/1/? model that emphasises the effect of various system parameters on the cost factor, with respect to upgraded service rates when the system follows N-policy and server vacation. Most often, the reason for customer dissatisfaction is the annoyingly protracted wait for the service. Therefore, given the customer’s total satisfaction with the service, an upgradation in service rates is required. As a result, this study investigates the effect of different parameters on cost factors by considering the upgraded service rates, which help in better decision making. The well-known QBD process of the Markov chain is analysed using a matrix-geometric approach, and the steady-state probabilities are also observed. The system will continue in a working vacation state until the N threshold value is applied, as it follows N-policy. The adaptive neuro-fuzzy inference system (ANFIS) is utilised to approximate the nonlinear function.
    Keywords: optimisation; balking; working vacation; matrix-geometric method; N-policy.
    DOI: 10.1504/IJMOR.2021.10042236
    by Rallabandi L. N. Pradeep Kumar, V. RAVINDRANATH 
    Abstract: In analytic hierarchy process (AHP), pairwise comparison matrix (PCM) is used to rank the alternatives in the decision-making problem. The priority vector, derived from the PCM, is accepted only when the PCM is consistent. However, in many practical situations the PCM obtained by the judgments of expert may be inconsistent. Several indices have been proposed to measure the consistency level of PCM over the years and one among them is cosine consistency index (CCI). In this paper, an algorithm is proposed to improve the consistency of PCM in terms of CCI. For examining the consistency of the given PCM, the new threshold values for CCI are proposed. Correlation and regression analysis is used to derive the relation between CCI and consistency ratio (CR) from which the threshold values of CCI for PCMs of order 3 to 15 are determined. The derived regression models have been validated by using statistical techniques.
    Keywords: cosine consistency index; CCI; pairwise comparison matrix; PCM; consistency ratio; analytic hierarchy process; AHP.
    DOI: 10.1504/IJMOR.2021.10042367
  • A Multi-Item Sustainable Production Inventory Constrained Model to Study and Analyze the Effective Green Investment and Replenishment Quantity   Order a copy of this article
    by Nabajyoti Bhattacharjee, Nabendu Sen 
    Abstract: In the study of supply chain management (SCM) of bioethanol, it is a challenging problem for the manager to regulate the flow of raw material in the production unit and the finished products in the market. Apart from that the several other decision-making processes like the implementation of preservation technologies, green investment, ordering optimum replenishment quantities, etc. are some relevant issues which demand a profound industrial framework to lead the decision-making process, especially when we are dealing with multi-items. In our present research we propose multi-item supply chain production inventory model to study the effect of green investment and optimum replenishment quantity on production cost. Preservation cost is a linear function of time. Energy cost and labour cost is considered together with finite energy supply and definite production capacity. In order to solve the model, we apply weighted PSO with statistical verification. We perform sensitivity analysis and provide managerial implication of the proposed model.
    Keywords: multi-item; production inventory; preservation technology cost; carbon emission; green investment; optimisation; supply chain management; SCM.

  • Optimal Control of an Epidemic by Vaccination using Dynamic Programming Approach   Order a copy of this article
    by Bouremani Touffik, Benterki Djamel, Yacine SLIMANI 
    Abstract: In this paper, we are interested in solving a SIR epidemic model which can be reformulated as a control problem. We use some recent developments of the dynamics programming method to obtain a rigorous solution of the optimal control problem formulated in Tr
    Keywords: optimal control; differential inclusion; Pontryagin’s maximum principle; dynamic programming; Hamiltonian flow; value function; verification theorem.
    DOI: 10.1504/IJMOR.2021.10042624
  • Effect of Disaster and Balking on M/M/1 driven Fluid Queue with Working Vacation   Order a copy of this article
    by Madhu Jain, ANSHUL KUMAR 
    Abstract: The fluid models are suitable for modelling traffic when individual arrival units have little effect on the system’s performance. This paper aims to study the fluid model for the queueing scenario driven by the features of vacationing server, disaster, and balking. By introducing vacation strategy to the fluid model, we can provide greater flexibility for the design and control of input and output rates. By introducing the multiple working vacation strategy to the fluid model, we can provide greater flexibility to design and control the server’s vacationing time and output. Continuing fraction and generating function methodologies are used to solve the fundamental framework of differential-difference equations that regulates the operation. The steady state probabilities for the different states of the fluid model have been found explicitly. The stationary distribution of the buffer content has also been derived in terms of the modified Bessel function of the first kind.
    Keywords: fluid queue; working vacation; disaster; balking; generating function; continued fraction.
    DOI: 10.1504/IJMOR.2021.10042818
  • A Model for Viruses Propagation throughout Networks   Order a copy of this article
    by Anis Rezgui 
    Abstract: In this paper, we propose a model for virus propagation throughout computers’ network. Recently interests for stochastic models have been increasing very fast where stochasticity can be implemented in at least two different ways. The first one consists of considering the same deterministic ODE system to which we add a stochastic noise, the model turns to be governed by a system of stochastic ordinary differential equations (SODEs). The second way, which we have considered in this work, consists of considering each node apart, and assume that its dynamics is governed by a given Markov chain (MC), we have called such model
    Keywords: Markov chain; SDE; stochastic simulation.
    DOI: 10.1504/IJMOR.2020.10042955
  • Numerical Optimization Technique to Solve Imprecisely Defined Nonlinear System of Equations with Bounded Parameters   Order a copy of this article
    by Sukanta Nayak, Pooja J. 
    Abstract: This paper includes an optimisation algorithm to estimate the solution of interval nonlinear system of equations. First, the proposed optimisation algorithm converts interval nonlinear system of equations to unconstrained multivariable optimisation problem with interval uncertainties. Then the interval unconstrained multivariable optimisation problem is investigated by using inner-outer direct search approach. Finally, the obtained solutions are assembled and using the regularity principle, interval solutions are obtained. Considering these steps together, this method is named as inner outer direct search (IODS) algorithm for interval unconstrained multivariable optimisation. Example problems are investigated to demonstrate the IODS algorithm and compared the obtained results with the results by using Krawczyk, vertex and Newton’s methods.
    Keywords: uncertainty; interval nonlinear system of equations; unconstrained multi-variable optimisation; inner-outer direct search; uncertain width.
    DOI: 10.1504/IJMOR.2021.10042970
  • Comprehensive Economic Order Quantity (EOQ) Model for Weibull decline with Negative Exponential Demand under trade credits   Order a copy of this article
    by Rakesh Tripathi, Hari Shyam Pandey 
    Abstract: In the current circumstances, demand for daily useable, useful items fluctuates for the period of supply chain and depends on its nature like sensitivity for the price, degree of freshness and uncertain deterioration. In this study demand is considered negative power of exponential. The deterioration rate is taken Weibull distribution time liked under allowable delay in payment. The trade credit mechanism is the reality of the modern universe in which supplier in each stage has an incentive to offer permissible delay in payments with pushing the sales, while the buyer has an encouragement of shorter working capital cycle with credit method. The mathematical model is provided under two unlike situations: 1) allowable delay in payments is less than cycle time; 2) permitted delay period is greater than cycle time. The optimal total cost is U-shaped, obtained by drawing graphs between total cost and cycle time. The numerical illustrations are pr
    Keywords: trade credits; Weibull distribution; permissible delay; deterioration; inventory.
    DOI: 10.1504/IJMOR.2020.10042974
  • Analysis of MAP/PH_{1}^{E}, PH_{2}^{O} /1 Queue with Standby Server, Second Optional service, Variant arrival rate, Bernoulli Schedule Vacation, Impatient Behavior of Customers, Breakdown, Essential and Optional Repair   Order a copy of this article
    by AYYAPPAN Govindan, Thilagavathy Karthikeyan 
    Abstract: In this article, we consider a single-server queueing model in which customers arrive under three types of arriving rates depends on the situation in the system according to a Markovian arrival process. After receiving essential service from the server, the customers have a choice to pursue the second optional service. The service time follows a phase-type distribution. If the main server completes essential repair who may go for an optional repair option or else return to the service station. Using the Matrix-Analytic Method (MAM), we investigated the total number of customers are present in the system under the steady-state probability vector. The characteristics of the system performance measures are evaluated. We examined the stability condition, the analysis of the busy period and also discussed waiting time distribution. Some Numerical results and graphical representation are provided for a clear view of our proposed model.
    Keywords: Variant Arrival Rate; Phase Type Distributions; Markovian Arrival Process; Standby Server; Impatient Behavior; Second Optional Service and Repair.
    DOI: 10.1504/IJMOR.2021.10043003
  • Third derivative method for solving stiff system of ordinary differential equations   Order a copy of this article
    by Lawrence Osa Adoghe, Ezekiel Omole, Sunday Emmanuel Fadugba 
    Abstract: A continuous integration method based on the hybrid third derivative block method is constructed and used to generate solution for stiff systems of first order ordinary differential equations. The hybrid third derivative method are applied simultaneously to integrate stiff initial value problems by combining them into a single block matrix known as block hybrid third derivative method. The basic properties of block method were examined and were found to be zero-stable, consistence, convergence and A-stable. Some Numerical results produced by the block method show that it is competitive with some existing ones in the literature. The results and comparison are presented in tables and curves.
    Keywords: first order system of equations; ordinary differential equations; hybrid third-derivative; block method; stiff problems; A-stability; zero-stability; convergences.
    DOI: 10.1504/IJMOR.2021.10043086