International Journal of Mathematics in Operational Research (29 papers in press)
On differentiable harmonic univex fuzzy mappings and its applications to fuzzy mathematical programming problem
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
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
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).
Optimization of multi-objective commercial bank balance sheet management model: A parametric T-set approach
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.
An effective algorithm to solve cost minimizing transportation problem
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.
Multi-Release Software Reliability Growth Assessment: An approach incorporating Fault Reduction Factor and Imperfect Debugging
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.
Numerical Methods for First Order Uncertain Stochastic Differential Equations
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.
Transient solution of an M/M/? queue with system's additional tasks and impatient customers
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.
An Application of Bilevel Optimization to the Waste Collection Centers Location Problem
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.
Selection of materials by multi-criteria methods applied to the side of a self-supporting structure for light vehicles
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.
New class of estimators of the population mean using the known population median of the study variable
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.
A robust bi-objective programming approach to environmental closed-loop supply chain network design under uncertainty
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.
Data Analytics for Relative Ranking of Factors to Optimize Blood Bank Supply Chain
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.
Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game
by Yasuhito Tanaka, Atsuhiro Satoh
Abstract: About a symmetric three-players zero-sum game we will show the following results. A modified version of Sions 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 Sions 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.
A Hybrid Direction Algorithm for Solving a Convex Quadratic Problem
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.
Material Selection using Multi-criteria decision making (MCDM) methods for geomembranes
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.
Holistically addressing uncertainty in group decision-making: the case of a
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.
A DECENTRALIZED MULTI-OBJECTIVE SUSTAINABLE SUPPLY CHAIN MODEL UNDER INTUITIONISTIC FUZZY ENVIRONMENT
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.
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
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.
An M^[X]/G(a,b)/1 queue with unreliable server, second optional service, closedown, setup with N-policy and multiple vacation
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.
Evaluation the Branches of Iran Insurance Corporation based on Data Envelopment Analysis-Free Disposal Hull in the Presence of Weight Restrictions
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.
Mathematical Modelling and Performance Analysis of Single Server Queuing System
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.
Transient analysis of multi-server Markovian queueing system with synchronous multiple working vacations and impatience of customers
by Vijaya Laxmi Pikkala
Abstract: In this paper, we study an infinite capacity multi-server Markovian queue with synchronous multiple working vacations, balking and reneging. It is assumed that customers may balk and/or renege with some probability if all the c servers are busy serving customers either during the regular busy period or working vacation period. The reneging times follow an exponential distribution. The system is modeled by a quasi-birth-death process and the transient-state probabilities of the model are obtained in the Laplace domain using matrix geometric method.
Keywords: Multi-server; multiple working vacations; Balking; Reneging; Transient-state probabilities; Matrix geometric method; Truncation method; Laplace transform.
MAP/PH(1), PH(2)/2 finite retrial inventory system with service facility, multiple vacations for servers
by C. Suganya, B. Sivakumar
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. 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.
A new approach for solving fully fuzzy linear programming problem
by Sapan Kumar Das, T. Mandal, Diptiranjan Behera
Abstract: This paper presents the limitations of citeku for solving a fully fuzzy linear programming (FFLP) problem. And accordingly to overcome these limitations a new method has been proposed by using the ranking function. We have considered a FFLP problem with mixed constraints where decision variables are represented by non-negative fuzzy numbers. Triangular convex normalised fuzzy sets are considered for the analysis. To illustrate the applicability and efficiency of the proposed method various numerical examples have been solved and obtained results are discussed.
Keywords: fully fuzzy linear programming; fuzzy optimal solution; triangular fuzzy numbers; ranking function.
A boundary-point LP solution method and its application to dense linear programs
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 optimising 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; nonlinear programming; steepest descent; orthogonal projections.
The efficiency of greedy best response algorithm in road traffic assignment
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 Rosenthal's 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 our work, 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
by P. Malini
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; fuzzy programming; nonlinear programming.
Using a multi-criteria decision making approach to select the optimal freeway rout (case study: Isfahan-Shiraz Freeway)
by Jalil Heidary Dahooie, Navid Mohammadi, Amir Salar Vanaki
Abstract: Road construction problems are one of the important factors in countries. The effects of multiple parameters on the decision making process to determine the optimal route have made this choice a specialised issue for decision-makers. In this regard, this paper aims to select the optimal route for Isfahan-Shiraz freeway using MADM approaches. For this purpose, in order to weight and select the optimal 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 prioritisation 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. In addition, 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.