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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 (61 papers in press)

Regular Issues

  • Stochastically Escaping Model in a Tumor Cell Growth System Driven by a Poisson Process   Order a copy of this article
    by Mohamed El-hadidy 
    Abstract: We present a new model for the stochastic escaping phenomenon from the chemical treatment in a tumour cell growth system subjected to a Poisson process. This phenomenon has the same behaviour of the reneging units in M/M/1/N queue where these units have stochastically grown by a Poisson process. More than finding the statistical distribution of these cells (reneging units), we get the expected value and the variance of these units at any time. This time is depending on the total number of infected cells (N units) in the system. In addition, by knowing the average number of units in M/M/1/N queue, we can get the expected value of the treatment cells (servicing units number).
    Keywords: Statistical physics; Tumor cells growth system; Poisson process; Stochastic growth.
    DOI: 10.1504/IJMOR.2020.10030938
    by V. Lavanya, M. Mohini 
    Abstract: The study focuses on the productivity assessment of Microfinance Institutions incorporating non-performing loans. The study has computed the productivity growth of microfinance institutions through its two components such as catch up effect and frontier shift effect by measuring the variation in efficiency and variation in technology respectively, using 72 Indian MFIs over the period of five years from 2013-2017. We had employed the Data Envelopment Analysis (DEA), Directional distance functional (DDF) model to compute Malmquist Luenberger productivity index (MLPI), output-oriented with undesirable output assuming a constant return to scale. The study also attempted to classify the MFIs into four groups using a categorization rule to infer the relationship between productivity growth, technical changes, and efficiency change components to show a noteworthy comparison. The result of the study indicates that rather than the technical change component, the efficiency changes are significantly contributing more to the productivity growth of MFIs.
    Keywords: Microfinance; productivity growth; DEA; Malmquist Luenberger productivity index; directional distance function; undesirable output.
    DOI: 10.1504/IJMOR.2020.10032165
  • Simulation of a phase change material for an automotive thermal insulation system.   Order a copy of this article
    by Javier Martinez, Juan Francisco Nicolalde, Andrés Méndez 
    Abstract: The temperature that a car can reach inside is between 25 degrees C to 40 degrees C in certain environmental circumstances, for this reason, studies have been carried out in the field of materials science that allows controlling the interior environment of a car. This study proposes the use of paraffin as PCM, which was chosen through multi-criteria given its melting point that is 37 degrees C, the result of simulating this material as a heat insulator is that in a 50 degrees C of incidence in the roof of a vehicle, the internal temperature of the part is kept in 20 degrees C.
    Keywords: automobile; simulation; thermal storage; phase change; alternative materials; comparison; thermal insulation; energy; heat.
    DOI: 10.1504/IJMOR.2020.10032250
  • Characterization and simulation of polymer membrane and PVC HDPE to use in an automotive application.   Order a copy of this article
    by Marcelo Moya, Ricardo Narvaez 
    Abstract: The work aims to determinie the necessary characteristics of the polymer membrane and PVC HDPE, which include good thermal, physical properties low cost and high weatherability and simulated for automotive application. The results obtained from two PVC and HDPE membranes in two different thicknesses are compared, considering controllable variables such as tension, elongation at break, working temperature and others. These tests are subject to ASTM standards which are collated to determine the membrane with better properties. The simulation was performed in software appropriate for calculating the polymer membrane to determine the stress, displacement and the safety factor of the membrane HDPE are superior to ABS and other membranes to the same time by help standards and design manual geosynthetics helped validate and determine that the geomembrane can be used in the automotive industry.
    Keywords: simulation; geomembranes; safety; mechanical characterization.
    DOI: 10.1504/IJMOR.2020.10032252
  • Adaptive Black Widow Optimization Algorithm for Data Clustering   Order a copy of this article
    by Anmar Abuhamdah 
    Abstract: Generally, local search approaches are better than population-based approaches in exploiting the search space and worse for exploration. Recently, the Black Widow Optimization Algorithm (BWO) was proposed for engineering optimization problems as an algorithm balancing between the exploration and exploitation phases. However, the BWO algorithm employed 3 essential parameter rates, in which a different experiment is needed for each problem. The Adaptive Black Widow Optimization Algorithm (ABWO) is proposed to tune the parameters adaptively and accept worse solutions by relying on a local search, using the solutions’ qualities average. Six medical datasets are used as a test domain with two calculations criteria to calculate the minimal distance. In order to evaluate the effectiveness of ABWO, a comparison is made between ABWO, BWO and other methods’ performances that have been drawn from the acknowledged literature. Outcomes show ABWO is capable of obtaining better cluster qualities, thus outperforming many other methods.
    Keywords: Medical Clustering Problem; Distance function; population-based Algorithm; Black Widow Optimization Algorithm; Adaptive.
    DOI: 10.1504/IJMOR.2020.10032253
  • Mathematical Model to Forecast Future Banking Income   Order a copy of this article
    by Taufik Hidayat, Rahutomo Mahardiko 
    Abstract: The positive growth of operating income before pandemic of Covid-19 had been felt by banking industry. The data shows that the pandemic of Covid-19 changes the world condition especially the industry. This paper presents mathematical model on recent data of bank revenue, the number of transactions and the information technology (IT) investment and forecasts future banking revenue, the number of transactions and IT investment for the next few years. The results show that, while there are problems faced in banking industry, the revenue, the number of transactions and the IT investment are significantly increasing. The mathematical model can be used for other industry.
    Keywords: Banking; Covid-19; Future forecast; Markov Chain analysis.
    DOI: 10.1504/IJMOR.2020.10032545
  • 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
  • Optimal Routing Control of a Retrial Queue with Two-Phase Service   Order a copy of this article
    by Zineb Dahmane, Amar Aissani 
    Abstract: Consider the problem of dynamic routing control in a retrial queue with a single server that provides two phases of service. All arriving customers join an ordinary queue and wait to be served. Every customer must receive service in both phases before leaving the system. After completion of the first phase, the server can either continue with the second phase for the same customer or stop the current service sequence in the first phase (to support a new customer that is on hold). In the latter case, the customer is placed in the retrial box, from where he is recalled for the second phase before leaving the system. Using Markov decision theory, we prove that an optimal policy exists that minimises the expected waiting cost for the system. We show that such a policy can be described by a switching curve that divides the state space into two contiguous regions. We present two conjectures regarding the structure of this policy, taking into account two different retrial policies.
    Keywords: Dynamic Routing; Two-phase service; Ordinary queue; Retrial box; Markov decision theory; Threshold policy; Classical retrial; Constant retrial.
    DOI: 10.1504/IJMOR.2020.10033367
  • 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
  • A Multi-Stage Model to Study Inventory Management of Raw Materials with Shortages   Order a copy of this article
    by Nabendu Sen, Nabajyoti Bhattacharjee 
    Abstract: The research on raw material procurement and maintenance in bio-ethanol production together with its socio-economic impact has been done. Most of the studies focuses on sustainable utilisation and procurement policies of raw materials which includes transportations and maintenance of raw material inventory. In this present work we propose a interconnected multistage framework to minimise the cost involved in four stages of raw material procurement such as, purchase and transportation, primary storage without preservation, cleaning room and final storage with preservation. Further we establish that maintenance cost can be minimise by regulating the quantity of raw materials flowing from primary storage to final storage. We provide an algorithm to formulate a linear programming problem to optimise the cost involved in both purchase and transportation together. We perform sensitivity analysis to test flexibility of the model and represent the result graphically.
    Keywords: Multistage modeling; Optimisation; Raw material inventory; Deterioration; Waiting period; Processing period; Transportation problem; Linear differential equation; Linear programming problem; Hessian m.
    DOI: 10.1504/IJMOR.2020.10033398
  • A c-server Poisson Queue with Customer Impatience due to a Slow-Phase Service   Order a copy of this article
    by Peter O. Peter, Sivasamy R 
    Abstract: In this paper, we investigate a queue with c-servers within a Markovian Environment (ME) under two phases Slow (S) and fast (F). We assume that the sojourn times follow an exponential distribution at states S and F with parameters "v" and "n" respectively. Each customer chooses a random relative deadline duration (RDD) which also follows an exponential law with parameter alpha under S-phase but abandons the system as soon as its RDD expires and never returns. When the environment remains under phase j (= S; F), customers arrive according to a Poisson process with rate lambda_j , and are served according to an exponential distribution with rate mu_j where mu_S < mu_F .We formulate the queue length process Y(j;n),(t) representing the number of customers n(t), waiting in the phase j at time t as level dependent quasi birth-death (LDQBD) process in a 2-dimensional space.
    Keywords: Two-phase service; Fast and Slow service phases; Stationary Probability Distribution.
    DOI: 10.1504/IJMOR.2020.10033432
  • A partially backlogged two-warehouse EOQ model with non-instantaneous deteriorating items, price and time dependent demand and preservation technology using interval number   Order a copy of this article
    by Nabendu Sen, Biman Kanti Nath 
    Abstract: In this paper, a two-warehouse EOQ model for non-instantaneous deteriorating item with price and time dependent demand is developed under imprecise environment. To reduce the loss due to deterioration, the concept of preservation technology investment is incorporated. In order to make the model more general, shortages are allowed and are partially backlogged. Further, the impreciseness of the parameters like coefficients of demand rate, holding costs, deterioration costs, shortage cost and lost sale cost are assumed as interval numbers which are made crisp by parametric functional form representation of interval numbers. The objective of this model is to find an optimal ordering policy with a view to minimize total average cost. To illustrate the developed model, a numerical example is taken in its support and also sensitivity analysis is carried out with respect to some important parameters.
    Keywords: two-warehouse; non-instantaneous deteriorating item; partial backlogging; preservation; interval number; parametric functional form.
    DOI: 10.1504/IJMOR.2020.10033485
  • An Inventory Model for Ameliorating and Deteriorating Items with Stock and Price Dependent Demand and Time Dependent Holding Cost with Preservation Technology Investment   Order a copy of this article
    by AJOY HATIBARUAH, Sumit Saha 
    Abstract: An inventory model is developed for ameliorating and deteriorating items considering stock and price dependent demand with completely backlogged shortages. Fast growing animals such as chicken, duck, etc. when are small in size and stock are purchased and raised in the farm. Stock and value of these items increases because of their high growth rate while stock may reduce due to death or other factors. Amelioration rate is assumed to follow Weibull distribution. Deterioration rate is considered to be constant and is controlled through an investment in preservation technology. The objective is to minimise the total cost per unit time and determine optimal selling price, preservation technology investment, time of occurrence of maximum inventory and shortage. To illustrate our model, some numerical examples are solved using an algorithm while convexity is shown graphically. Sensitivity analysis is performed to study the impact of variation of the parameters on optimal solution.
    Keywords: amelioration; deterioration; preservation technology investment; stock and price dependent demand.
    DOI: 10.1504/IJMOR.2020.10033524
  • On the Gerber-Shiu function of a MAP risk model with possible delayed Phase-type By-claims   Order a copy of this article
    by A.S. Dibu, M.J. Jacob 
    Abstract: This paper introduces the delayed claim settlement feature in a MAP risk model. Surplus process of the model incorporates two kinds of Phase-type claims, the main claim and the by-claim. The delay feature is defined in such a way that every main claim may induce a by-claim with probability and payment of the by-claim is delayed until the next claim arrival. An appropriate Gerber-Shiu function under an auxiliary (delayed) timeline is assumed to analyse the Gerber-Shiu function under the primary (original) timeline. Transient analysis of the Markovian fluid flow models is tailored to develop defective renewal equations satisfying Gerber-Shiu functions. An explicit solution for renewal equations is derived in terms of the Lundberg roots. Further, a Neumann series solution is also provided. A numerical example on the moment of surplus before ruin in a two-state model.
    Keywords: Gerber-Shiu function; MAP risk model; PH claims; delayed by-claims; system of Volterra integro-differential equation; matrix Lundberg equation.
    DOI: 10.1504/IJMOR.2020.10033711
  • Neoteric divergence measure for refined interval-valued neutrosophic sets and its application in decision making   Order a copy of this article
    by Adeeba Umar, Ram Naresh Saraswat 
    Abstract: Smarandache originally initiated the theory of neutrosophic sets, who combined non-standard analysis and a tri-component set to handle indeterminate and inconsistent information. To deal with vagueness and uncertainty, the three functions which are truth membership function, indeterminacy membership function and falsity membership function play an important role and the sum of these three membership functions is less than three. This theory is used to depict information more appropriately. The prime aim of this paper is to introduce a novel divergence measure for refined interval-valued neutrosophic sets with the proof of its validity. Some other properties of the proposed divergence measure are given with their proofs. An application of novel divergence measure is shown with illustration for decision making in construction project selection in order to exhibit the legitimacy of the proposed method.
    Keywords: Divergence measure; neutrosophic sets; refined interval-valued neutrosophic sets; decision making.
    DOI: 10.1504/IJMOR.2020.10034000
  • 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
  • Performance Evaluation of Call Admission Control Based on Signal Quality in Cellular Mobile Networks   Order a copy of this article
    by SHRUTI SHRUTI, Rakhee Kulshrestha 
    Abstract: The subscription of cellular networks is continuing to experience a growth at an unprecedented rate. It becomes a significant challenge for the cellular service provider to accommodate huge traffic demands while satisfying the desired quality of service (QoS) level perceived by the users. This paper proposes a new call admission control (CAC) scheme based on the quality of signals to support the guarantees of QoS. The proposed scheme also provides an algorithm to determine the optimal value of acceptance probability of new calls under the fractional guard channel (FGC) scheme which minimises the new call blocking probability. Moreover, there is a provision of finite buffer for handoff calls to further enhance the QoS of handoff users. Also, the paper includes numerical results to validate the effectiveness of the proposed scheme. Overall, this work provides an effective CAC model for optimising the performance of cellular networks.
    Keywords: call admission control; CAC; fractional guard channel; FGC; signal quality; handoff; optimisation; Markov chain; cellular networks.
    DOI: 10.1504/IJMOR.2020.10035321
  • 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
  • A Quadratic Demand EOQ Model for Deteriorating Items with Time-Dependent Shortage   Order a copy of this article
    by Sindhuja. S, P. Arathi, Varun Mohan 
    Abstract: In an inventory model, optimising the time and cost is a challenging task. This article focuses on an economic order quantity model (EOQ model) with a quadratic demand and constant deterioration of items. The aim of the paper is to provide a methodology to minimise the total cost in an EOQ model. This is achieved by increasing the deteriorating items, under the normal market conditions and considering the demand as a quadratic demand. Shortage in cost is similarly considered. A numerical example is discussed and compared with an existing model to illustrate the behaviour of the quadratic demand rate. There is a considerable reduction in total cost in the proposed model when compared with the existing model. Sensitivity analysis concerning the changes in parameters is carried out through the graphical representations. Complex algebraic equations are solved using MATLAB R2013a.
    Keywords: economic order quantity model; quadratic demand rate; inventory; shortage; deterioration.
    DOI: 10.1504/IJMOR.2020.10035761
  • 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
  • Analysis of MAP/PH/1 queueing model with immediate feedback, starting failures, single vacation, standby server, delayed repair, breakdown and impatient customers   Order a copy of this article
    by G. Ayyappan, K. Thilagavathy 
    Abstract: We have analysed the queueing model with a single server in which customers arrive according to the Markovian arrival process, the service process according to phase type distributions and the standby server who is serving at a lower rate also follows the phase type distribution. The total number of customers are present in the system under the steady-state probability vector has been probed by using matrix-analytic method (MAM). We have examined the stability condition, the analysis of the busy period and derived some important performance measures of our model. Numerical results and graphical representation are discussed for the proposed model.
    Keywords: Markovian arrival process; MAP; phase type distributions; immediate feedback; standby server; delay time to repair; single vacation.
    DOI: 10.1504/IJMOR.2020.10039101
  • Stochastic modelling and performance analysis of feeding unit in paper plant   Order a copy of this article
    by Nitin Panwar, Sanjeev Kumar 
    Abstract: In the present paper a probabilistic method for stochastic modelling and performance evaluation of a feeding unit is suggested. The paper plant consists of various units like feeding, pulping unit, bleaching unit, screening unit and paper production unit. Feeding unit is one of the paper plant's most significant functional units, consisting of three repairable subunits. Using Markov process, differential equations are created after drawing transition diagram and these models are then used to discover the feeding unit's availability by considering the repair and failure information acquired from maintenance personnel. Based upon the various performance values obtained for each subunit priority ranking is formulated for blower subunit.
    Keywords: Markovian process; stochastic modelling; steady state availability; criticality analysis.
    DOI: 10.1504/IJMOR.2020.10032406
  • An effective movie recommender system enhanced with time series analysis of user rating behaviour   Order a copy of this article
    by Bam Bahadur Sinha, R. Dhanalakshmi 
    Abstract: Recommender system aims at improvising user satisfaction by taking decision on what movie or item to recommend next. Over time though, learners and learning behaviours shift regularly. This paper introduces a novel behaviour-inspired suggestion algorithm named the TimeFly-PPSE algorithm, which operates on the concept of changing user's motives around time. The suggested model takes temporal knowledge into account and monitors the progression of consumers and items that are useful in providing adequate recommendations. The latter outlines a framework that enrolls the user's shifting behaviour to include guidance for personalisation. TimeFly's findings are contrasted with those of other well-known algorithms. Simulation test on 100K MovieLens dataset shows that utilising TimeFly contributes to recommendations that are exceptionally efficient and reliable.
    Keywords: recommendation; prediction; MovieLens; time-aware; genres; mean absolute error; MAE.
    DOI: 10.1504/IJMOR.2020.10032451
  • Line planning and passenger routing problem with application to the Quito transportation system   Order a copy of this article
    by Ramiro Torres 
    Abstract: An important phase in the strategic planning process of a public transportation system is the line planning problem. It consists in determining a set of lines together with their frequencies such that a given transportation demand is satisfied. In this work an integer programming model for the integrated line planning and passenger routing problem is proposed. The model aims to improve the benefit and comfort of the passengers, namely maximising direct connection trips, and it also proposes to minimise the total cost for the operator. Restricted to linear transportation networks that are relevant for the Quito public transportation system, NP-hardness results and polynomial algorithms for special cases are presented. Performance of heuristic procedures for solving the integrated problem is evaluated over real-world and simulated instances.
    Keywords: public transport optimisation; line planning problem; LPP passenger routing; computational complexity.
    DOI: 10.1504/IJMOR.2020.10031714
  • Cost analysis of N-policy vacation machine repair problem with optional repair   Order a copy of this article
    by Ritu Gupta, Divya Agarwal 
    Abstract: In this paper, we deal with the N-policy machine repairable system with warm spares and two repairmen under optional repair. The first repairman is always available to serve the failed units in the system while the second repairman leaves for a vacation of random length when the number of failed units is less than N. The second repairmen firstly performs essential repair to all failed units and then may provide second optional repair to some failed units which demand for it. We construct the system state governing equations and the system performance measures under transient condition which are examined by using a numerical approach based on Runge-Kutta method of the fourth order. Further, the sensitivity and cost analysis are facilitated to demonstrate the validity of the model by taking a numerical illustration. The effect of different parameters on system performance indices is demonstrated graphically.
    Keywords: machine repair problem; warm spares; N-policy; first essential repair; FER; second optional repair; SOR; reliability; vacation; cost function; Markov process; Runge-Kutta method.
    DOI: 10.1504/IJMOR.2020.10032166
  • Capital heterogeneity, entrepreneurship and two-way capital flows   Order a copy of this article
    by Abdelkader Mohamed Sghaier Derbali, Ali Lamouchi 
    Abstract: This paper examines the drivers of two-way capital flow phenomenon in various developing countries where flows of portfolio investment and direct investment through borders prove contradictory directions. We try to claim that the scarcity of entrepreneurs in fewer developed countries, who improve firm productivity across unobservable (and thus not contractible) entrepreneurship effort, is an essential resource of two-way capital flows. Building upon the context of venture capital studies, this paper describes in a straightforward model that the lack of entrepreneurs would leave some domestic investment opportunities forgone, following in lower investment, lower interest rate, and lower savings compared optimality. Allowing foreign entrepreneurs to raise money from domestic financial market in the form of portfolio investment outflow and then to invest in the domestic firms in the form of direct investment inflow would help alleviate the situation. In this regard, two-way capital flows bring domestic economy benefit of learning through opening-up.
    Keywords: entrepreneurship; two-way capital flows; portfolio investment; direct investment.
    DOI: 10.1504/IJMOR.2020.10032113
  • Detecting outliers in DEA after correcting biases in efficiency scores using simulated beta samples   Order a copy of this article
    by Parakramaweera Sunil Dharmapala 
    Abstract: We address the issue that data used in DEA are possibly contaminated with statistical noise, and as a result, efficiency scores deviate from actual values due to statistical bias. In such situation, detecting outliers could be misleading. Therefore, we propose a method to correct the biases and compute DEA efficiency scores that follow underlying beta distributions, and we use Thompson et al.'s (1996) DEA model with assurance regions. Then, we demonstrate the bias-correction process of the DEA frontier estimates by constructing confidence intervals for the mean scores and use them to detect outliers.
    Keywords: data envelopment analysis; DEA; assurance regions; order statistics; beta distribution; bias-correction; outliers.
    DOI: 10.1504/IJMOR.2020.10031715
  • A modified ranking function of linear programming problem directly approach to fuzzy environment   Order a copy of this article
    by Rajeev Prasad, Sapan Kumar Das, Tarni Mandal, Jatindra Kumar Dash 
    Abstract: This work introduced a modified ranking function which produced crisp linear programming (CLP) problems. A fully fuzzy linear programming (FFLP) problem in its balanced form having all the parameters and variables are triangular fuzzy numbers is taken into account during this study. Within the literature of the sector, the prevailing proposed approaches have many shortcomings, i.e., incorporate the rule of surplus variable and does not satisfy the constraints. Here, we bearing in mind of the prevailing shortcomings, a constructive solution is approached to beat the restrictions. For better exactness of the answer which is proposed by us, we use fuzzy number. Two numerical examples are illustrated and compared with the pre-existing methods.
    Keywords: fully fuzzy linear programming; FFLP; fuzzy optimal solution; triangular fuzzy numbers; ranking function.
    DOI: 10.1504/IJMOR.2020.10032119