Forthcoming articles

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 (49 papers in press)

Regular Issues

  • Analysis of Batch Arrival Bulk Service Queue with Additional Optional Service Multiple Vacation and Setup Time   Order a copy of this article
    by G. Ayyappan, T. Deepa 
    Abstract: This paper studies an M[x]/G(a,b)/1 queueing system with additional optional service, multiple vacation and setup time. After completing the first service, the customers may opt for the second service with probability or leave the system with probability . After completing a bulk service, if the queue size is less than `a', then the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than `a', he leaves for another vacation and so on. This process continues until he finds at least `a' customer in the queue. After a vacation, if the server finds at least `a' customer waiting for service, he requires a setup time 'G' to start the service. After this setup he serves a batch of customers (). Using supplementary variable technique, the probability generating function of the queue size, expected queue length, expected waiting time, expected busy period and expected idle period are derived. Numerical illustrations are presented to visualize the effect of system parameters.
    Keywords: Batch arrival; Bulk service; Additional optional service; Multiple vacation; Setup time.

  • Comments on the Polynomial formulation and heuristic based approach for the k-Travelling Repairman Problem   Order a copy of this article
    by Imdat Kara, Bahar Y. Kara 
    Abstract: The paper Polynomial formulation and heuristic based approach for the k-Travelling Repairman Problem claims to present the first polynomial formulation for the k-travelling repairman problem (k-TRP). We first make some corrections on this formulation and we show that the first polynomial size formulation for k-TRP is the one proposed by Kara et al. (2008).
    Keywords: Repairman problem; k-Traveling Repairman problem; minimum latency problem; delivery man problem.

  • Solution of Fuzzy Multi Objective Generalized Assignment Problem   Order a copy of this article
    by Supriya Kar, Aniruddha Samanta, Kajla Basu 
    Abstract: In this paper, Multi Objective Generalized Assignment Problem (MOGAP) with fuzzy parameters has been solved using three different approaches. Here we consider three objective functions which are to be minimized. In the first approach, weighted sum method has been used and the problem is converted into a single objective one and then solved by Extremum Difference Method (EDM) to get the optimal assignment. In the second one, Modified Fuzzy Programming Technique (MFPT) has been used for the same problem. Application of linear and exponential membership functions give comparative results with the goal that the better alternative can be obtained. The third one describes Multi Objective Genetic Algorithm (MOGA) to find the solution surface and the Pareto Optimal front including the optimal assignment. The methods are demonstrated by a suitable numerical example.
    Keywords: FMOGAP; EDM; MFPT; MOGA.

  • A Cryptosystem Based on Chaotic Maps and Factoring Problems   Order a copy of this article
    by Nedal Tahat, Eddie Esmail, Ashraf Aljammal 
    Abstract: A cryptosystem allows a sender to send any confidential or private message using a receiver's public key and the receiver next confirms the integrity and validity of the received message using his own secret key. Cryptosystem algorithms can be categorized based on the type of security suppositions, for example discrete logarithm, factorization, and elliptic curve hard problems, which are all currently believed to be unsolvable in a reasonable time of period. Recently, cryptosystems based on chaotic maps have been proposed. Due to some subtle and close relationship between the properties of traditional cryptosystems and chaotic-based systems, the idea of using chaotic in cryptography has received a great deal of attention from many cryptographys researchers. Therefore, to enhance system security, we explore the implementation of a cryptosystem algorithm based on both cryptographic and chaotic system characteristics. We also provide security against known cryptographic attacks and discuss the performance analysis of the developed system.
    Keywords: Cryptography; Cryptosystem; Factorization; Chaotic maps.

  • A Matheuristic Approach for the Split Delivery Vehicle Routing Problem: An Efficient Set Covering-Based Model with Guided Route Generation Schemes   Order a copy of this article
    by Nurul Huda Mohamed, Said Salhi, Gabor Nagy, Nurul Akmal Mohamed 
    Abstract: The Split Delivery Vehicle Routing Problem (SDVRP) is a relaxed version of the classical VRP where customers can be visited more than once. The SDVRP is also applicable for problems where one or more of the customers require a demand larger than the vehicle capacity. Constructive heuristics adapted from the parallel savings and the sweep methods are first proposed to generate a set of solutions which is then used in the new and more efficient set covering-based formulation which we put forward. An effective repair mechanism to remedy any infeasibility due to the set covering problem is presented. A reduced set of promising routes is used in our model, instead of the original set of routes, proposing and using well defined reduction schemes. This set covering-based approach is tested on large data sets from the literature with encouraging results. In brief, 7 best solutions including ties are found among the 137 SDVRP instances.
    Keywords: split deliveries; vehicle routing; set covering; hybrid method; matheuristic.

  • Exact Stationary Solution for a Fluid Queue Driven by an M/M/1 Queue with Disaster and Subsequent Repair   Order a copy of this article
    by Vijayashree K.V., Anjuka A 
    Abstract: This paper deals with the stationary analysis of a fluid queueing model driven by an M/M/1 queue subject to disaster and subsequent repair. Further, arrivals are allowed to join the background queueing model during the period of repair at a slower rate as compared to the arrivals during regular busy period of the server. Such a model was analysed earlier by Sherif. I. Ammar cite{sherif}, however the model formulation and hence the main results are found to be incorrect. In this paper, the assumptions are suitably modified to ensure correctness, detailed mathematical analysis is carried out to find an explicit analytical expression for the buffer content distribution. The underlying system of differential difference equations that govern the process are solved using Laplace transform and generating function methodologies. Closed form expressions for the joint steady state probabilities of the state of the background queueing model and the content of the buffer are obtained in terms of modified Bessel function of the first kind.
    Keywords: Generating function;Laplace Transform;Steady State Probabilities;Buffer Content Distribution.

  • Inventory model for deteriorating items with incremental holding cost under partial backlogging   Order a copy of this article
    by Sanjay Singh, Seema Sharma, Shiv Raj Pundir 
    Abstract: The present paper deals with an inventory model for deteriorating items with dynamic demand. Shortages are allowed and partially backlogged. The demand has been considered as the function of inventory level during storage period and function of time during shortage period. Storage period is divided into n distinct time periods. In practice, longer storage period requires additional specialized equipment and facilities to keep the products away from deterioration. So, it is assumed that holding cost is increasing step function. The model has been discussed for n arbitrary distinct time periods of storage time and a numerical example has been solved for n = 1 and 2. The sensitivity analysis has been performed in order to examine the effect of various costs and parameters on optimal policy.
    Keywords: Inventory; Holding cost; Deterioration; Partial backlogging.

    by E. Rameshkumar 
    Abstract: In this paper, a queueing system in which the server follows multiple adaptive vacations, server breakdown without interruption and closedown time with controllable arrival is considered. In a single server model, after completion of a bulk service, if there is no breakdown with probability (1- ѱ) and queue length is greater than or equal to a, then the bulk service continues, otherwise, the server performs closedown work. At the end of bulk service, if there is a breakdown occurs with probability (ѱ), then the server performs renovation process. After a renovation process, if the queue length is greater than or equal to a, then he performs bulk service otherwise the server is doing closedown work and the server avails a vacation of random length. At the end of a vacation, if the queue length is less than a, then the server takes at most M vacations successively. After M vacations, if the queue length is still less than a, then the server remains in the system till the queue length reaches a. However, the customers enter the service station with probability p (0 ≤ p ≤1) during multiple adaptive vacations. At a vacation, service and dormant period completion epoch, if the queue length ξ, is at least a customers, then the server serves a batch of min(ξ, b) customers, where b ≥ a. The Probability Generating Function (PGF) of queue size and performance measures are obtained and cost model is developed. The wide-range of algebraic results for the various particular cases is obtained.
    Keywords: multiple adaptive vacation; closedown times; server breakdown; renovation times; controllable arrival.

  • Minimizing Vehicle Distribution Duration Considering Service Priority   Order a copy of this article
    by Dimitra Alexiou 
    Abstract: A Vehicle Routing Problem (VRP) is dealt with, where a fleet of vehicles serve (distribution/pickup) a given subset of demand locations in an urban network. A service time priority degree is given to a subset of demand locations. The aim of this paper is to find the least possible overall service time for vehicles to all the demand locations and particularly those that have a high degree of priority. The problem is dealt with in the context of graph theory and a corresponding method is proposed. The paper incorporates a numerical example of the proposed method.
    Keywords: distribution; graph theory; vehicle routing; priority service; network.

  • Modelling and Analysis of Two-Unit Hot Standby Database System with Random Inspection of Standby Unit   Order a copy of this article
    by Amit Manocha, Gulshan Taneja, Sukhvir Singh, Rahul Rishi 
    Abstract: Stochastic model for a two-unit hot standby database system comprising of one operative (primary unit) and one hot standby unit has been developed. The primary unit acts as production unit which is synchronized with hot standby unit through online transfer of archive redo logs. Data being saved in the primary unit gets simultaneously stored in the hot standby unit. Different modes of failure of primary database have been considered. To avoid loss of data, random inspection of the standby unit is carried out by a database administrator (DBA) to see as to whether redo log files are created/updated in standby unit or not. The repair of the failed unit and creation/updation of redo log files are also done by the DBA. The system is analyzed using semi-Markov process and regenerative point technique. Mathematical expressions for various performance measures of the system have been obtained along with cost-benefit analysis of the system. Numerical analysis has been done to validate the derived results. Bounds for various parameters have also been obtained with regard to profitability of the system.
    Keywords: database system; hot standby; random inspection; semi-Markov process; regenerative point technique; stochastic modelling; measures of system effectiveness; cost-benefit analysis; profitability; bounds.

  • A Hybrid Metaheuristics Approach for a Multi-Depot Vehicle Routing Problem with Simultaneous Deliveries and Pickups   Order a copy of this article
    by Sonu Rajak, P. Parthiban, R. Dhanalakshmi 
    Abstract: Multi-Depot Vehicle Routing Problem with Simultaneous Deliveries and Pickups (MDVRPSDP) is a variant of classical Vehicle Routing Problem (VRP), which has often encountered in real-life scenarios of transportation logistics; Where, vehicles are required to simultaneously deliver the goods and also pick-up some goods from the customers. The current scenario importance of reverse logistics activities has increased. Therefore it is necessary to determine efficient and effective vehicle routes for simultaneous delivery and pick-up activities. MDVRPSDP, which is very well-known Non-deterministic Polynomialhard (NP-hard) and Combinatorial Optimization (CO) problem., which, requires metaheuristics to solve this type of problems. In this context, this article presents a hybrid metaheuristic which combines Simulated Annealing (SA), Ant Colony Optimization (ACO) and along with long-arc-broken removal heuristic approach for solving the MDVRPSDP. The preliminary results show that the proposed algorithm can provide good solutions.
    Keywords: K-means Clustering; Vehicle routing problem; Simulated annealing; Ant colony optimization; Long-arc-broken removal heuristic.

  • A modified two-step method for solving interval linear programming problems   Order a copy of this article
    by Mehdi Allahdadi 
    Abstract: In this paper, we propose a new method for solving interval linear programming (ILP) problems. For solving the ILP problems, two important items should be considered: feasibility (i.e., solutions satisfy all constraints) and optimality (i.e., solutions are optimal for at least a characteristic model). In some methods, a part of the solution space is infeasible (i.e., it violates any constraints) such as the best and worst cases method (BWC, proposed by Tong in 1994) and two-step method (TSM, proposed by Huang et al. in 1995). In some methods, the solution space is completely feasible, but is not completely optimal (i.e., some points of the solution space are not optimal) such as modified ILP method (MILP, proposed by Zhou et al. in 2009) and improved TSM (ITSM, proposed by Wang et al. in 2014). Firstly, basis stability for the ILP problems is reviewed. Secondly, the solving methods are analyzed from the point of view of the feasibility and optimality conditions. Later, a new method which modifies the TSM by using the basis stability approach is presented. This method gives a solution space that is not only completely feasible, but also completely optimal.
    Keywords: Basis stability; Feasibility; Interval linear programming; Optimality; TSM.

  • Effects Of Product Reliability Dependent Demand In An EPQ Model Considering Partially Imperfect Production   Order a copy of this article
    by J.K. Dey 
    Abstract: In this article, an economic production quantity (EPQ) model with partially imperfect production system has been considered where both perfect and imperfect quality items are produced and demand has been assumed as a function of selling price, reliability of the product and advertisement. In fact, every manufacturing sector wants to produce only perfect quality items to maximize his profit but due to long run process several kinds of problem like labor, machinery, technology etc. arise and therefore, system becomes out of control state and consequently it produces both perfect and imperfect quality items simultaneously. Perfect quality items are ready for sale but imperfect quality items are reworked at a cost to become perfect one. Reworking cost, reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the time dependent development cost and also by improving the quality of the raw material used in the production system. Under such circumstances, a profit function has been developed and maximized by optimizing the reliability parameter of the manufacturing system, reliability of the product and duration of production. Finally, the model has been illustrated with some numerical examples exploring the sensitivity analysis with respect to some parameters to illustrate the feasibility of the model.
    Keywords: Inventory; Imperfect production; Production time; Reliability parameter; Product reliability.

  • A new approach for solving fully fuzzy linear programming problem   Order a copy of this article
    by Sapan Das, Diptiranajan Behera, Tarni Mandal 
    Abstract: This paper presents the limitations of Kumar and Kaur [1] for solving a FullyrnFuzzy Linear Programming (FFLP) problem. And accordingly to overcomernthese limitations a new method has been proposed by using the rankingrnfunction. We have considered a FFLP problem with mixed constraints whererndecision variables are represented by non-negative fuzzy numbers. Triangularrnconvex normalized fuzzy sets are considered for the analysis. To illustraternthe applicability and eciency of the proposed method various numericalrnexamples have been solved and obtained results are discussed.
    Keywords: Fully fuzzy linear programming; fuzzy optimal solution; triangularrnfuzzy numbers; ranking function.

  • MAP/PH(1),PH(2)/2 Finite Retrial Inventory System with Service Facility, Multiple Vacations for Servers   Order a copy of this article
    by Suganya Chokkalingam, Sivakumar B 
    Abstract: In this paper, we consider a retrial $ (s, S) $ inventory system with multiple server vacations for two heterogeneous servers. We have assumed that the customers arrive according to a Markovian arrival process and two parallel servers who provide heterogeneous phase type services to customers. The lead times for the orders are assumed to have independent and identical exponential distributions. The vacation times of both servers are assumed to be independent and identically distributed exponential random variables. The arriving customer who finds both servers are busy or both servers are on vacation, joins an orbit of finite size. These orbiting customers retry for their demand after a random time, which is assumed to be exponential distribution. The joint probability distribution of the inventory level, the number of customers in the orbit and the server status is obtained in the steady state. Some important performance measures are obtained and the optimality of an expected total cost rate is shown through numerical illustration.
    Keywords: service facility; heterogeneous servers; multiple vacations; retrial customers.

  • Generalized Linear Search Plan for a D-Dimensional Random Walk Target   Order a copy of this article
    by Mohamed El-hadidy 
    Abstract: In this paper, we present a mathematical search model that studies the generalized linear search plan for detecting a d-dimensional random walk target. The target will be met one of n searchers where each searcher starts its motion from any point rather than the origin on n-disjoint real lines in ℝⁿ. Rather than, finding the conditions that show the finiteness of this search plan, we study the existence of the optimal search plan that minimizes the expected value of the first meeting time between one of the searchers and the target.
    Keywords: Linear search method; d-dimensional random walk; finite search plan;rnoptimal search plan; semi continuous mapping.

  • A Boundary-point LP Solution Method and Its Application to Dense Linear Programs   Order a copy of this article
    by Chanaka Edirisinghe, William Ziemba 
    Abstract: This paper presents a linear programming solution method that generates a sequence of boundary-points belonging to faces of the feasible polyhedron. The method is based on a steepest descent search by iteratively optimizing over a two-dimensional cross section of the polyhedron. It differs from extreme point algorithms such as the simplex method in that optimality is detected by identifying an optimal face of the polyhedron which is not necessarily an extreme point. It also differs from the polynomial-time methods such as the ellipsoid algorithm, or projective scaling method that avoids the boundary of the feasible polyhedron. Limited computational analysis with an experimental code of the method, EZLP, indicates that our method performs quite well in total solution time when the number of variables and the density of the constraint matrix increase.
    Keywords: Linear programming; steepest descent; orthogonal projections.

  • The Efficiency of Greedy Best Response Algorithm in Road Traffic Assignment   Order a copy of this article
    by Lahna Idres, Mohammed Said Radjef 
    Abstract: In this work, we investigate the problem of the integer road traffic assignment. So, we model the interaction among the road users sharing the same origin-destination pair, as a symmetric network congestion game. We focus on Rosenthals results to guarantee the existence of a Pure Nash Equilibrium (PNE). Then, we study the behaviour of an algorithm based on Greedy Best Response (GBR) in finding PNE. In previous studies, the efficiency of GBR to compute a PNE of a symmetric network congestion game in series-parallel networks is proved. In ourwork, another approach is used to demonstrate its efficiency in more general networks. It is shown that the non-series parallel networks can be classed into two types. The conditions that make GBR succeeds for each type is then drawn. The advantage of GBR-algorithm is that provides a better approximation of the equilibrate assignment, since it is integer.
    Keywords: Road traffic assignment; Congestion Game; Nash Equilibrium; GBR-Algorithm.

  • A New Ranking Technique On Heptagonal Fuzzy Numbers to Solve Fuzzy Transportation Problem   Order a copy of this article
    by Malini Ramki 
    Abstract: In this work a general fuzzy transportation problem model is discussed and proposed a new ranking procedure to the heptagonal fuzzy numbers using which convert any fuzzy valued transportation problem to a crisp valued transportation problem which then could be solved using the MODI method. The proposed method serves as an efficient method in ranking Heptagonal fuzzy numbers which is illustrated through a numerical example. The purpose of this paper is to give a new ranking index to rank fuzzy numbers effectively. Fuzzy numbers cannot be easily ordered as ordinary real numbers. Several proposals have addressed this problem, each with some drawbacks and limitations. This paper renounces to the idea of finding a universal ordering method for fuzzy numbers.
    Keywords: Heptagonal Fuzzy numbers; Fuzzy Transportation Problem.

  • Using a multi-criteria decision making approach to select the optimal freeway rout (Case Study: Isfahan Shiraz Freeway)   Order a copy of this article
    by Jalil Heidary Dahooie 
    Abstract: Road construction problems are one of the important factors in countries. The reason for this is the effective role of road transportation in economic development. Considering the high cost of constructing and repairing freeways, principled and optimal design is one of the most important steps in creating a transport infrastructure, especially freeways. On the other hand, the effects of multiple variables and parameters on the decision making process to determine the optimal route have made this choice a difficult and specialized issue for decision-makers. In this regard, this paper aims to select the optimal variant route for Isfahan Shiraz freeway using multi- attribute decision-making approaches. For this purpose, in the first stage, by reviewing the literature and organizing a panel of experts, the indices for evaluation of the optimal variant route have been extracted. In the following, in order to weight and select the optimal variant route, the extended dynamic fuzzy GRA method is used. The results show that road longevity, views of the NGOs, route integrity and ease of tracking are identified as the highest-weighted criteria in the prioritization of the route variant. To evaluate the validity of the results of the GRA method, the problem is examined by using the, COPRAS-IVIF, ARAS-IVTF, WASPAS-IVIF,TOPSIS-IVIF and Multimoora-IVIF methods. Also, Route 3 that takes priority over others is also chosen, in practice, as the main basis for the work.
    Keywords: Variant route Selection; Freeway; Multi Attribute Decision Making (MADM); dynamic fuzzy GRA.

  • On differentiable harmonic univex fuzzy mappings and its applications to fuzzy mathematical programming problem   Order a copy of this article
    by Minakshi Parida, Sunita Chand 
    Abstract: In this paper, harmonic preunivex (H-preunivex) and harmonic preunicave (H-preunicave) fuzzy mappings have been introduced and several interesting results have been obtained related to generalized convexity. By using the concept of differentiability with H-preunivex and H-preunicave fuzzy mappings, harmonic univex (H-univex) and harmonic unicave (Hunicave) fuzzy mappings have been obtained respectively. Furthermore, H-univex and pseudo H-univex fuzzy mappings have been applied to study the sufficient optimality conditions and the duality results for Harmonic univex fuzzy programming problem (HUFP). Moreover, KKT conditions for the HUFP have been studied by using the H-univex fuzzy mappings. Suitable examples have been given to illustrate the results.
    Keywords: Fuzzy optimization; H-preunivex; H-preunicave; H-univex; H-unicave; Fuzzy mappings; Sufficient optimality conditions; Duality results.

  • Solid Transportation Problem under Fully Fuzzy Environment   Order a copy of this article
    by Abhijit Baidya, Uttam Kumar Bera 
    Abstract: Transportation policy seeks to improve agency freight and cargo management and enhance sustainable, efficient and effective transportation operations. In this paper, the profit maximization solid transportation problem under fully fuzzy environment is formulated. In this model formulation the unit transportation costs, purchasing costs, loading costs, unloading costs, selling prices, fixed charges, availabilities, demands, conveyance capacities, vehicle weight and volume capacities, desired total budget are considered as fuzzy in nature. When items are transported from sources to destinations, then due to bad road condition, hilly region etc. few items should be damaged. The unknown quantities those are transported from source to destination with different mode of conveyances are also considered as fuzzy. Also, an additional new constraint on the complete budget at each destination is imposed. Five new approaches are proposed to defuzzify the fully fuzzy model. The nearest interval approximation is used to convert the fully fuzzy model into its equivalent interval form. The interactive fuzzy satisfying technique and different interval approaches are used to determine the crisp equivalent of the objective function and constraints of the proposed model. The reduced deterministic model was solved using generalized reduced gradient techniques (GRG technique). A numerical example is provided to illustrate the model and methodology and finally, the obtained results are compared.
    Keywords: Fully fuzzy solid transportation problem; complete budget constraint; interval approaches; nearest interval approximation; interactive fuzzy satisfying technique.

  • Monohull ship hydrodynamic simulation using CFD   Order a copy of this article
    by Javier Martinez, Paul Martinez Gómez, Jessica Constante, Gabriela Chavez 
    Abstract: This research analyses the performance of a ship monohull at Galapagos real conditions using ANSYS FLUENT. In order to achieve these analyses, tide charts at Santa Cruz Island coast in Galapagos Islands were considered, since similar motorboats provide services as taxi boats in this area. These analyses were made in order to validate ships behaviour existing in Galapagos Islands. In addition, through simulation is not necessary to build these ships, in a way to obtain same results using less economic and technical resources. The hydrodynamic analysis of a monohull was simulated in static and dynamic conditions. Static analysis considers water and air flows hitting the boat bow which is resting (anchored boat). While dynamic analysis considers both the boat and water flow speed (sailing boat). Main results were: static and dynamic pressures, water height achieved by flow and ship speed variation, turbulence intensity, and simulation convergence residuals.
    Keywords: Monohull; hydrodynamics simulation; ANSYS-FLUENT; Computational Fluid Dynamics (CFD).
    DOI: 10.1504/IJMOR.2019.10015742
  • Optimization of multi-objective commercial bank balance sheet management model: A parametric T-set approach   Order a copy of this article
    by Arindam Garai, Tapan Kumar Roy, Bappa Mondal 
    Abstract: In this article, we consider optimisation of multi-objective model with fuzzy coefficients in imprecise environment. In 2016, we introduced T-set to supersede fuzzy set for representing impreciseness. It followed our observation that some constraints of existing classical fuzzy optimisation method compel membership values of fuzzy objective functions and constraints to fall in range between zero and one. So we cannot always attain most preferable Pareto optimal solution to it. Again existing constraints in this method sometimes show models as infeasible. Here we introduce parametric T-set. Next we consider multi-objective optimisation model with fuzzy cost coefficients and present general algorithm to arrive at parametric Pareto optimal solution to it. In numerical application, we illustrate usefulness of proposed algorithm by considering commercial bank balance sheet management model with fuzzy cost coefficients in parametric T-environment. Also we perform sensitivity analysis of parameters and present key managerial insights. Finally we draw conclusions.
    Keywords: commercial bank balance sheet management; fuzzy coefficients; multi-objective optimization; Pareto optimal solution; parametric T-characteristic function; parametric T-set.
    DOI: 10.1504/IJMOR.2019.10015743
  • An effective algorithm to solve cost minimizing transportation problem   Order a copy of this article
    by S.M. Abul Kalam Azad, Mohammad Kamrul Hasan 
    Abstract: The developed algorithm in this article provides an initial basic feasible solution (IBFS) of the transportation problem (TP) of the linear programming problem. The proposed method, which involves fewer calculations and fewer steps or iterations, is able to provide a better approximate solution to the TP than classical methods, especially Vogel's approximation method (VAM). This method is also easier and more effective than some recent methods to solve TPs, which were introduced by various researches. This article illustrates the simplicity and effectiveness of the developed algorithm by providing a good number of examples.
    Keywords: IBFS; TP; VAM; Transportation Table; Cost Unit.
    DOI: 10.1504/IJMOR.2019.10016190
  • Multi-Release Software Reliability Growth Assessment: An approach incorporating Fault Reduction Factor and Imperfect Debugging   Order a copy of this article
    by Anu G. Aggarwal, Neha Gandhi, Vibha Verma, Abhishek Tandon 
    Abstract: In the last few decades, a plenty of software reliability growth models with diverse parameters have been formulated and proposed to assess software trustworthiness. Fault reduction factor (FRF) is one such significant factor which has been incorporated in numerous reliability modelling researches in past and results have proved its importance on reliability growth phenomenon. To keep pace with rising demands of the market, software development firms keep upgrading their products in terms of new features and by providing rectification of previously reported defects. In this paper, an SRGM based on NHPP integrating imperfect debugging and time-variable FRF is proposed for multi-release software systems. The model is then tested on the failure datasets of multiple releases of Tandem Computers and Firefox OSS. The experimental results for each release are compared with their corresponding perfect debugging model. Results illustrate that the proposed model fits the failure data well, outperforming perfect debugging model.
    Keywords: Software Reliability Growth Model; Imperfect Debugging; Multi-Release; Fault Reduction Factor; Least Square Estimation.
    DOI: 10.1504/IJMOR.2019.10016194
  • Numerical Methods for First Order Uncertain Stochastic Differential Equations   Order a copy of this article
    by Justin Chirima, Eriyoti Chikodza, Senelani Hove-Musekwa 
    Abstract: Uncertain stochastic calculus is a relatively new sub discipline of mathematics. This branch of mathematical sciences seeks to develop models that capture aleatory and epistemic features of generic uncertainty in dynamical systems. The growth of uncertain stochastic theory has given birth to a novel class of differential equations called uncertain stochastic differential equations (USDEs).Exact and analytic solutions to this family of differential equations are not always available. In such cases, numerical analysis provides a gateway to approximate solutions.This paper examines a Runge-Kutta method for solving USDEs. Before examining and applying the Runge-Kutta method, the paper states and proves the existence and uniqueness theorem. The Runge-Kutta method is then applied to solve an American call option pricing problem. This numerical algorithm proves to be effective and efficient because it produces almost the same results as compared to Chen's analytic formula and the classical Black-Scholes model.
    Keywords: Uncertain Stochastic Differential Equations; Aleatory Uncertainty; Epistemic Uncertainty; American Call Option; Runge-Kutta Method.
    DOI: 10.1504/IJMOR.2019.10016984
  • Transient solution of an M/M/? queue with system's additional tasks and impatient customers   Order a copy of this article
    by A. Azhagappan, Sudhesh R 
    Abstract: This paper studies the impatient behaviour in an infinite server queue with additional tasks assigned to the system. Whenever the system becomes empty, the system as a whole is assigned a secondary task of duration U whose distribution is exponential. Any arrival during the period U becomes impatient due to the unavailability of service facility. Each individual waiting customer activates an independent impatience timer of duration T which is exponentially distributed. When the system comes back after the completion of U, before T expires, the waiting customers are simultaneously taken for service and they leave the system after the completion of service. If T expires before the completion of task U, the customers abandon the system and never to return. The transient system size probabilities of this model are derived explicitly for both single and multiple task cases. The time-dependent mean and variance of system size are also derived. Further, numerical simulations are also presented to analyse the effect of system indices.
    Keywords: Infinite server queue; Single and multiple tasks; Impatient customers; Transient probabilities.
    DOI: 10.1504/IJMOR.2019.10017561
  • An Application of Bilevel Optimization to the Waste Collection Centers Location Problem   Order a copy of this article
    by Massimiliano Caramia, Mattia Dalla Costa 
    Abstract: In this paper, we show an application of bilevel programming to the problem of locating waste collection centres inside a municipal area. In our study, the latter problem possesses a hierarchical structure, i.e., there are two decision makers one of which acts as a leader and the other behaves as a follower. Therefore, we exhibit a bilevel optimisation program able to capture this hierarchy and propose an iterative algorithm to solve the problem. This solution proposal is then tested on data derived from a real scenario. Experimental results reveal that the approach is effective in this kind of decision problems.
    Keywords: bilevel programming; facility location; waste collection.
    DOI: 10.1504/IJMOR.2019.10017779
  • Selection of materials by multi-criteria methods applied to the side of a self-supporting structure for light vehicles   Order a copy of this article
    by Javier Martinez, Juan Carlos Rocha, Edilberto LLanes, Rodger Salazar 
    Abstract: The selection of materials is an important stage in the design and development of products, but considering the enormous amount of materials available on the market that have different properties and characteristics, defining suitable and ideal alternatives is a difficult task. Within the automotive area there is a tendency to develop vehicles with greater efficiency and capacity, keeping aside the economic implications without underestimating the functionality of the materials. The use of multi-criteria methods (MCDM) allows the establishment of a reliable selection methodology, due to the interaction between each of the criteria with statistical methods that converge in a single solution. The methodology used in this study was based on the application of MCDM methods, and the comparison between them to determine a convergence in the alternatives of greater potential for the structural section of vehicles. Four methods were evaluated: TOPSIS, COPRAS, VIKOR, PROMETHEE II, obtaining that for all the methods the best material corresponds to the Martensitic Steel YS1200, being this the most appropriate one when fulfilling structural requirements, as well as providing a reduction of weight and price.
    Keywords: Lateral structure; weighting method; multi-Criteria method; MCDM; Material selection.
    DOI: 10.1504/IJMOR.2019.10017783
  • New class of estimators of the population mean using the known population median of the study variable   Order a copy of this article
    by Dinesh K. Sharma, S.K. Yadav, Kate Brown 
    Abstract: In this paper, we propose an improved class of estimators of the population mean using the population median of the study variable. We study the properties of the sampling distribution of the proposed class of estimators up to the approximation of order one. Different values of the two characterising constants in the new estimators affect the mean squared error (MSE) of the proposed family of estimators. Finding the optimum values of the constants to minimise the MSE of the suggested class of estimators provides the least MSE of the recommended family for these optimal values of the characterising scalars. We compare the proposed family of estimators with other competing estimators of the population mean. The theoretical findings are justified with an empirical example and reveal that the proposed class of estimators performs more efficiently than other competing estimators of the population mean under a simple random sampling without replacement (SRSWOR) scheme.
    Keywords: Main variable; known variable; ratio estimators; bias; MSE; efficiency.
    DOI: 10.1504/IJMOR.2019.10019246
  • A robust bi-objective programming approach to environmental closed-loop supply chain network design under uncertainty   Order a copy of this article
    by Zahra Homayouni, Mir Saman Pishvaee 
    Abstract: Imposition of strict environmental protection acts and the imperative need of the best possible allocation of resources have given birth to the concept of low carbon logistics. Environmental laws force the manufacturers to extend their existing supply chains to form a closed-loop supply chain (CLSC) through the setup of an efficient recovery system. In this paper, a multi-objective robust optimisation model is proposed for the design of CLSC network under uncertainty. First, a deterministic bi-objective mixed integer linear programming (BOMILP) model is developed for designing a CLSC network. Then, the robust counterpart of the proposed BOMILP is presented to cope with the real-world uncertainty. The first objective aims to maximise the total profit generated in the CLSC network and the second objective minimises the environmental pollution of the CLSC network. The proposed bi-objective model is solved using a multi-choice goal programming (MCGP) approach.
    Keywords: Closed-loop supply chain; Environmental issues; Robust optimization; Multi-choice goal programming.
    DOI: 10.1504/IJMOR.2019.10019291
  • Data Analytics for Relative Ranking of Factors to Optimize Blood Bank Supply Chain   Order a copy of this article
    by Parthiban Palanisamy, J. Arul Valan, E. Baburaj 
    Abstract: Healthcare systems are supported by blood service operations. Restricted usage limit of 21 days and stochastic nature of demand against the supply are the challenges in the field and results in complex situations. The paper focuses on the model mentioned for which a regionalised blood banking system is considered. Typically, it consists of hospitals, regional blood banks, in addition to central blood banks. The 20 factors that influence is weighed and raked using multiple criterion decision making (MCDM) methods. Interpretive structural modelling (ISM) gives the influence of a factor on another and determines weights. Fuzzy-TOPSIS is used to quantify the qualitative values systematically and rank the alternatives. The relative ranking enables to identify best alternative. The procedure for a single central blood bank executed may be extended to similar central blood banks. Supply chain optimisation of perishable products is possible with the framework proposed, with suitable modifications.
    Keywords: Influencing factors; Relative ranking; Interpretive Structural Modeling; Fuzzy TOPSIS.
    DOI: 10.1504/IJMOR.2019.10019464
  • Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game   Order a copy of this article
    by Yasuhito Tanaka, Atsuhiro Satoh 
    Abstract: About a symmetric three-players zero-sum game we will show the following results. A modified version of Sion’s minimax theorem with the coincidence of the maximin strategy and the minimax strategy are proved by the existence of a symmetric Nash equilibrium. The existence of a symmetric Nash equilibrium is proved by the modified version of Sion’s minimax theorem with the coincidence of the maximin strategy and the minimax strategy. Thus, they are equivalent. However, without the coincidence of the maximin strategy and the minimax strategy there may exist an asymmetric equilibrium in a symmetric three-players zero-sum game.
    Keywords: three-players zero-sum game; Nash equilibrium; Sion's minimax theorem.
    DOI: 10.1504/IJMOR.2019.10019543
  • A Hybrid Direction Algorithm for Solving a Convex Quadratic Problem   Order a copy of this article
    by Mohand Ouamer Bibi, Nacira Ikheneche, Mohand Bentobache 
    Abstract: In this paper, we propose a new algorithm for solving convex quadratic programming problems with bounded variables. Instead of using the standard direction of the adaptive method, which is constructed by minimising only the linear part of the objective function increment, we will suggest a new descent direction, called hybrid direction. This latter is constructed by minimising a quadratic part of the increment. Furthermore, we define a quantity called optimality estimate from which we derive sufficient and necessary conditions of optimality. On the basis of this new concept, we construct an algorithm for solving convex quadratic programs. In order to compare our method with the active-set method implemented in MATLAB, numerical experiments on randomly generated test problems are presented.
    Keywords: Convex quadratic programming; Adaptive method; Bounded variables; Hybrid direction; Optimality estimate; Numerical experiments.
    DOI: 10.1504/IJMOR.2019.10019963
  • Material Selection using Multi-criteria decision making (MCDM) methods for geomembranes   Order a copy of this article
    by Javier Martinez, Cristian Chingo, Ricardo Narvaez 
    Abstract: The present work aims to be an useful information about the novel MCDM methods applied on geomembranes in order to select the best alternative for construction. Qualitative and quantitative information will be used to do the best choice. AHP method is used to calculate the weight (importance) of the different criteria which uses the subjective information to assign numeric values among 0 and 1, being better weights with values near to 1. COPRAS-G, OCRA, TOPSIS, VIKOR, EXPROM II and ORESTE methods are applied as MCDM methods in order to perform the more accurate selection using relevant information about the features of different materials. These methods use the weight obtained by AHP for ranking the best alternative, whose result contains subjective and objective information. Finally, all methods are standardised with a unique equations template, which makes easier to understand all of them to subsequent applications.
    Keywords: geomembranes; Material selection; MCDM; qualitative; quantitative; standardized; weight.
    DOI: 10.1504/IJMOR.2019.10020233
  • Holistically addressing uncertainty in group decision-making: the case of a   Order a copy of this article
    by Lanndon A. Ocampo, Eppie Clark, Anthony Shun Fung Chiu, Raymond Tan 
    Abstract: This paper presents a methodology that holistically captures the uncertainty of judgment in 'quasi-collaborative' group decision-making in the context of the analytic hierarchy/network process. The proposed method is motivated mainly by the two uncertainty approaches that seemingly diverge in literature: the simulation approach and the fuzzy set theory (FST) approach. In the proposed method, FST is used to handle the judgmental uncertainty of individual decision-maker while simulation addresses randomness and uncertainty when individual judgments are aggregated as a group decision. An illustrative problem is presented in this paper along with a numerical experiment that attempts to compare the efficacy of the proposed methodology with existing methods. Results show that the method is more capable of handling uncertain group decisions through simulation runs and it can perform sensitivity analysis which is essential in testing robustness of judgment results. Finally, the proposed method can identify non-expert member of the group.
    Keywords: analytic hierarchy process; analytic network process; simulation; fuzzy set theory; sensitivity analysis.
    DOI: 10.1504/IJMOR.2019.10020350
    by Murshid Kamal, Srikant Gupta, Irfan Ali 
    Abstract: This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.
    Keywords: Multi-objective Optimization; Sustainable Supply Chain; Supplier Selection Problem; Fuzzy Goal Programming; Intuitionistic Fuzzy Number.
    DOI: 10.1504/IJMOR.2019.10020422
  • On the distribution of an infinite-buffer queueing system with versatile bulk-service rule under batch-size-dependent service policy: M/G^(a,Y)_n/1   Order a copy of this article
    by Sourav Pradhan  
    Abstract: Batch-service queues have a wide range of noteworthy applications in wireless telecommunication to deal with the multimedia type of data, manufacturing systems, group testing procedure, etc. The knowledge of both the queue and server content distributions helps the system designer to evaluate the efficiency of the queueing system in a better way. We analyse a single server infinite-buffer batch-size-dependent service queue with Poisson arrival and versatile batch-service rule. Based on supplementary variable technique, a bivariate probability generating function, the entire spectrum of new contributions, of queue content and number in a served batch at departure epoch is derived. Moreover, we perceive the complete queue and server content distribution at departure as well as arbitrary epochs. The utility of analytical results is illustrated by the inclusion of some numerical examples, which also includes the investigation of multiple zeros.
    Keywords: Batch-service; Versatile-bulk-service; Batch-size-dependent; Multiple roots; Queueing; Server content.
    DOI: 10.1504/IJMOR.2019.10020516
  • An M^[X]/G(a,b)/1 queue with unreliable server, second optional service, closedown, setup with N-policy and multiple vacation   Order a copy of this article
    by Nirmala Marimuthu 
    Abstract: Batch arrival bulk service queueing system has been effectively used to model many real life systems like production, manufacturing, transportation as well as telecommunication. Characteristic like second optional service, service interruption, closedown time, multiple vacation, setup time with N policy etc have been respectively considered in such models. So far no comprehensive combination of these characteristics have been reported in the literature. This paper deals with the analysis of a non-Markovian batch arrival bulk service queue with a general combination of all the above mentioned characteristics.
    Keywords: General bulk service; Unreliable server; Closedown; Multiple vacation; Setup with N-policy; Optional service.
    DOI: 10.1504/IJMOR.2019.10020612
  • Evaluation the Branches of Iran Insurance Corporation based on Data Envelopment Analysis-Free Disposal Hull in the Presence of Weight Restrictions   Order a copy of this article
    by Mohammad Reza Fathi, Hossein Safari, Abdol Hossein Jafarzadeh 
    Abstract: This study reviews the concepts of performance evaluation in the insurance industry based on data envelopment analysis. In this study to deal with the problems that exists in conventional DEA model, a new DEA model is introduced and applied based on FDH and weight restrictions to evaluate Insurance Corporation’ branches. In this study, non-parametric frontier technologies for data analysis are mainly discussed. It combines several models with non-parametric frontier technology to suggest a new model for analysing the data. This paper is based on a combination of the two frontier technology, DEA and free disposal hull. As it is mainly based on DEA and benchmarking based on DEA. The proposed method was successfully conducted in a case study about Iran Insurance Corporation; secondly, the paper depicts the insurance company evaluation process through a DEA model, while allowing for incorporating the preferences of decision maker. According to result, 26 branches are efficient and achieved efficiency score is equal to 1.
    Keywords: Insurance; performance evaluation; non-parametric analysis; DEA; data envelopment analysis; FDH; free disposal hull; benchmarking; weight restrictions; discernment power.
    DOI: 10.1504/IJMOR.2019.10021405
  • Mathematical Modelling and Performance Analysis of Single Server Queuing System   Order a copy of this article
    by E. Mamatha, S. Saritha, Chandra Sekhar Reddy, P. Rajadurai 
    Abstract: Classical queuing theory is playing vital role to study and analyse the performance analysis of real-time servicing systems, production inventory and manufacturing systems, telecommunication systems, modern information and communication technology systems and computing sector. In recent decays, bounded and immeasurable queues have been intensively studied; due to its attractive mathematical features with wide spread applicability. Such a system describes units of work, e.g., particles or customers, arriving at a resource, that stay present for some random duration that is independent of other customers. The aim of this paper is to evaluate the performance measures with a single server queuing system. Mathematical model has been developed to study the probability live time of the server using algebraic eigenproperties. These models are indispensable in real-time systems, manufacturing and communication queuing systems, including wireless networks, mobility, and randomly arriving traffic.
    Keywords: Markov Process; Server live probability; Latent values and vectors; Matrix Geometric approach; Single server queuing system.
    DOI: 10.1504/IJMOR.2019.10021946
  • Evaluating fuzzy risk based on a new method of ranking fuzzy numbers using centroid of centroids   Order a copy of this article
    by Phani Bushan Rao Peddi 
    Abstract: This paper describes a method to rank fuzzy numbers based on centroid of centroids of fuzzy numbers and emphasises the use of the subjectivity of the decision maker's view point, such as optimistic or pessimistic. Using the decision maker's view point and index of modality, a ranking index of each fuzzy number is calculated which serves as a criterion for ranking fuzzy numbers. The proposed fuzzy ranking method is used to analyse the fuzzy risk involved in manufacturing products by different companies, where the probability of failure of a product is represented by a fuzzy number. The proposed method is more flexible than the existing methods as it takes into consideration the degrees of confidence of decision maker's opinion in both the stages.
    Keywords: centroid points; index of optimism; index of modality; fuzzy risk analysis; fuzzy numbers.
    DOI: 10.1504/IJMOR.2019.10022356
  • Design optimisation of cost of the pressure vessel through MATLAB and simulation through ANSYS   Order a copy of this article
    by S. Elizabeth Amudhini Stephen, D. Christu Nesam David, A. Joe Ajay 
    Abstract: The objective functions used in engineering optimisation are complex in nature with many variables and constraints. Conventional optimisation tools sometimes fail to give the global optimal points. Very popular methods like genetic algorithm, pattern search, simulated annealing, and gradient search are useful methods to find global optima related to engineering problems. This paper attempts to use new non-traditional optimisation algorithms which are used to find the minimum cost of designing a pressure vessel to obtain global optimum solutions. The cost, number of iterations and the total elapsed time to complete the problems are all compared using these ten non-traditional optimisation methods. The validation is done through simulation using ANSYS.
    Keywords: pattern search; simulate annealing; GODLIKE; cuckoo search; firefly algorithm; flower pollination; ant lion optimiser; gravitational search algorithm; multi-verse optimiser; simulation ANSYS.
    DOI: 10.1504/IJMOR.2019.10022357
  • Geolocation of electric bikes recharging stations: City of Quito study case   Order a copy of this article
    by Geovanna Villacreses, Javier Martínez-Gómez, Paola Quintana, Ricardo A. Narváez C. 
    Abstract: The aim of this research was to develop a geographical information system with multi-criteria decision making methods for selecting the most feasible location to install electric bikes recharging stations in the City of Quito. For such purpose, the ideal solution-similarity preference ranking and weighted overlay techniques have been used as multi-criteria decision making methods. In addition, the analytic hierarchy process method was performed for calculating the weights of each criterion. Moreover, a standardisation process that consists of establishing an overall performance index to evaluate the results was applied. Finally, the Pearson correlation coefficient was used to analyse mutual correspondence between multi-criteria decision making methods. The resulting Pearson correlation coefficients indicate that the two selected multi-criteria decision making methods provided similar results. In this context, the methods analysed covered similar solutions and indicated that multi-criteria decision making methods are a powerful tool to select ideal locations for electric bikes recharging stations.
    Keywords: optimal location; e-bikes; geographic information systems; GIS; multi-criteria decision making; MCDM methods.
    DOI: 10.1504/IJMOR.2019.10022358
  • Analysis of bulk queue with additional optional service, vacation and unreliable server   Order a copy of this article
    by Charan Jeet Singh, Sandeep Kaur, Madhu Jain 
    Abstract: The present investigation deals with the performance analysis of group input queueing system with unreliable server. The server is capable of rendering essential as well as optional services. After getting essential service, the customer may choose any one of the available optional services if required. The server has choice either to avail the vacation for the short period after completion of the service or may continue to provide the service to other customers. The server may fail at any instant of the essential/optional service and undergoes repair immediately. The queueing model is developed by introducing the supplementary variables corresponding to elapsed setup time, service time, and repair time and vacation duration for obtaining the queue size distribution. The maximum entropy principle is employed to determine the approximate results of the system state probabilities and the waiting time of the customers in the queue. The numerical simulation and sensitivity analysis are performed by taking the numerical illustration to study the effect of system parameters on the various performance measures and cost function.
    Keywords: bulk queue; unreliable server; repair; essential service; optional service; vacation; supplementary variable.
    DOI: 10.1504/IJMOR.2019.10022359
  • Resource portfolio problem under relaxed resource dedication policy in multi-mode multi-project scheduling   Order a copy of this article
    by Umut Beşikçi, Ümit Bilge, Gündüz Ulusoy 
    Abstract: The most common approach in the multi-project scheduling literature considers resources as a common pool shared among all projects. However, different resource management strategies may be required for different problem environments. We present the relaxed resource dedication (RRD) policy, which prevents the sharing of resources among projects but allows resource transfers when a project starts after the completion of another one. We treat the case where the available amounts of resources - namely, the capacities - are decision variables subject to a limited budget. This capacity planning problem, called the resource portfolio problem, is investigated under the RRD policy employing both renewable and non-renewable resources with multiple modes of usage. A mixed integer linear programming model to minimise total weighted tardiness is proposed. To obtain some benchmark solutions for this hard problem, the branch and cut procedure of ILOG CPLEX is modified by customised branching strategies, feasible solution generation schemes and valid inequalities.
    Keywords: multi-mode resource constrained multi-project scheduling; resource dedication; resource portfolio allocation; branch and cut.
    DOI: 10.1504/IJMOR.2019.10022360
  • On phase type arithmetico-geometric process and its application to deteriorating systems with warranty   Order a copy of this article
    by Y. Sarada, R. Shenbagam 
    Abstract: This research article makes an attempt to introduce a phase type arithmetico-geometric process and illustrate its applicability to a deteriorating system with fixed warranty. Properties, renewal function, second moment and variance of the underlying counting process are derived analytically and supplemented numerically in the case of three distributions: exponential, Erlang distribution of order 3 and Coxian distribution of order 2. Sensitivity analysis and graphical illustrations are provided to highlight the effect of various cost parameters on the expected warranty cost by means of the Exponential and Erlang distribution of order 2.
    Keywords: phase type distribution; arithmetico-geometric process; fixed warranty.
    DOI: 10.1504/IJMOR.2019.10022361
  • Parameter estimation for partially observed linear stochastic system   Order a copy of this article
    by Chao Wei 
    Abstract: This paper is concerned with the problem of parameter estimation for a partially observed linear stochastic system. The state estimator is obtained by using the continuous-time Kalman linear filtering theory. The likelihood function is given based on the innovation theorem and Girsanov theorem, the parameter estimator and error of estimation are derived. The strong consistency of the parameter estimator and the asymptotic normality of the error of estimation are proved by applying ergodic theorem, maximal inequality for martingale, Borel-Cantelli lemma and the central limit theorem for stochastic integrals.
    Keywords: linear stochastic system; parameter estimation; state estimation; strong consistency; asymptotic normality; incomplete observation; operational research; Kalman linear filtering; error of estimation; likelihood function.
    DOI: 10.1504/IJMOR.2019.10022362