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Sankar Kumar Roy - One of the best experts on this subject based on the ideXlab platform.
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multi objective fixed charge solid Transportation Problem with product blending under intuitionistic fuzzy environment
Applied Intelligence, 2019Co-Authors: Sankar Kumar Roy, Sudipta MidyaAbstract:This paper analyzes multi-objective fixed-charge solid Transportation Problem with product blending in intuitionistic fuzzy environment. The parameters of multi-objective fixed-charge solid Transportation Problem may not be defined precisely because of globalization of the market and other unmanageable factors. So, we often hesitate in prediction of market demand and other parameters connected with transporting systems in a period. Based on these facts, the parameters of the formulated model are chosen as triangular intuitionistic fuzzy number. New ranking method is used to convert intuitionistic fuzzy multi-objective fixed-charge solid Transportation Problem with product blending to a deterministic form. New intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) is initiated to derive Pareto-optimal solution from the proposed model. Furthermore, we solve the formulated model using intuitionistic fuzzy programming; and a comparison is drawn between the obtained solutions extracted from the approaches. Finally, a practical (industrial) Problem is incorporated to illustrate the applicability and feasibility of the proposed study. Conclusions with future research based on the paper are described at last.
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New approach for solving intuitionistic fuzzy multi-objective Transportation Problem
Sādhanā, 2018Co-Authors: Sankar Kumar Roy, Ali Ebrahimnejad, JosÉ Luis Verdegay, Sukumar DasAbstract:Multi-objective Transportation Problem (MOTP) under intuitionistic fuzzy (IF) environment is analysed in this paper. Due to the fluctuation of market scenario, we assume that the Transportation cost, the supply and the demand parameters are not always precise. Hence, the parameters are imprecise, i.e., they are IF numbers. Considering the specific cut interval, the IF Transportation cost matrix is converted to interval cost matrix in our proposed Problem. Again, using the same concept, the IF supply and the IF demand of the MOTP are reduced to the interval form. Then the proposed MOTP is changed into the deterministic MOTP, which includes interval form of the objective functions. Two approaches, namely intuitionistic fuzzy programming and goal programming, are used to derive the optimal solutions of our proposed Problem, and then the optimal solutions are compared. A numerical example is included to illustrate the feasibility and the applicability of the proposed Problem. Finally, we present the conclusions with the future scopes of our study.
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Multi-objective two-stage grey Transportation Problem using utility function with goals
Central European Journal of Operations Research, 2017Co-Authors: Sankar Kumar Roy, Gurupada Maity, Gerhard-wilhelm WeberAbstract:Multi-Objective Goal Programming is applied to solve Problems in many application areas of real-life decision making Problems. We formulate the mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate grey parameters for supply and demands into the Two-Stage MOTP, and a procedure is applied to reduce the grey numbers into real numbers. Thereafter, we present a solution procedure to the proposed Problem by introducing an algorithm and using the approach of Revised Multi-Choice Goal Programming. In the proposed algorithm, we introduce a utility function for selecting the goals of the objective functions. A numerical example is encountered to justify the reality and feasibility of our proposed study. Finally, the paper ends with a conclusion and an outlook to future investigations of the study.
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conic scalarization approach to solve multi choice multi objective Transportation Problem with interval goal
Annals of Operations Research, 2017Co-Authors: Sankar Kumar Roy, Gurupada Maity, Gerhard-wilhelm Weber, Sirma Zeynep Alparslan GokAbstract:This paper explores the study of multi-choice multi-objective Transportation Problem (MCMTP) under the light of conic scalarizing function. MCMTP is a multi-objective Transportation Problem (MOTP) where the parameters such as cost, demand and supply are treated as multi-choice parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTPs are solved by goal programming (GP) approach, but the solution of MOTP may not be satisfied all times by the decision maker when the objective functions of the proposed Problem contains interval-valued aspiration levels. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP, and then we compare among the solutions. Two numerical examples are presented to show the feasibility and usefulness of our paper. The paper ends with a conclusion and an outlook on future studies.
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multi objective Transportation Problem with cost reliability under uncertain environment
International Journal of Computational Intelligence Systems, 2016Co-Authors: Gurupada Maity, Sankar Kumar Roy, Jose L VerdegayAbstract:AbstractThis paper analyzes the study of a Multi-Objective Transportation Problem (MOTP) under uncertain environment. Assuming the uncertainty in real-life decision making Problems, the concept of reliability is incorporated in the Transportation cost and the effectiveness is justified through the proposed MOTP. Again, considering the real phenomenon in the MOTP, we consider the Transportation parameters, like as supply and demand as uncertain variables. Also, we consider the fuzzy multi-choice goals to the objective functions of the MOTP; and Fuzzy Multi-Choice Goal Programming (FMCGP) is used to select the proper goals to the objective functions of the proposed MOTP. Here, the proposed study is not only confined to obtain the compromise solution but also to fix up the proper goals to the objective functions of the MOTP. A numerical example is presented to illustrate and justify the proposed study. Finally, the paper ends with the conclusion and future study.
Manoranjan Maiti - One of the best experts on this subject based on the ideXlab platform.
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defuzzification of trapezoidal type 2 fuzzy variables and its application to solid Transportation Problem
Journal of Intelligent and Fuzzy Systems, 2016Co-Authors: Amrit Das, Uttam Kumar Bera, Manoranjan MaitiAbstract:The main proposal of this paper is to derive two different reduction process for a trapezoidal type-2 fuzzy number. The first reduction method is based on critical values and the second method is based on α-cut of fuzzy number. As an application a multi-objective solid Transportation Problem, minimizing the cost and time has been developed using trapezoidal type-2 fuzzy number as system parameters and hereby solved. Finally after solving the proposed multi-objective Problem by intuitionistic fuzzy programming technique a comparison between the two proposed reduction methods are discussed briefly. The proposed models and techniques are finally illustrated by providing numerical examples at the end. Also this paper present a comparative study between the proposed method to the KM algorithm and NT method for type reduction.
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fully fuzzy fixed charge multi item solid Transportation Problem
Soft Computing, 2015Co-Authors: Pravash Kumar Giri, Manas Kumar Maiti, Manoranjan MaitiAbstract:Graphical abstractDisplay Omitted HighlightsFully fuzzy fixed charge multi-item solid Transportation Problem (FFFCMISTP) is considered.FFFCMISTP with the decision variable are taken as fuzzy.New defuzzification method, fuzzy slack and surplus variable is used for FFFCMISTP.Minimization of Transportation cost as well as fuzziness of the solution for FFFCMISTP is discussed. This paper presents fully fuzzy fixed charge multi-item solid Transportation Problems (FFFCMISTPs), in which direct costs, fixed charges, supplies, demands, conveyance capacities and transported quantities (decision variables) are fuzzy in nature. Objective is to minimize the total fuzzy cost under fuzzy decision variables. In this paper, some approaches are proposed to find the fully fuzzy transported amounts for a fuzzy solid Transportation Problem (FSTP). Proposed approaches are applicable for both balanced and unbalanced FFFCMISTPs. Another fuzzy fixed charge multi-item solid Transportation Problem (FFCMISTP) in which transported amounts (decision variables) are not fuzzy is also presented and solved by some other techniques. The models are illustrated with numerical examples and nature of the solutions is discussed.
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solution of multi item interval valued solid Transportation Problem with safety measure using different methods
Opsearch, 2014Co-Authors: Abhijit Baidya, Uttam Kumar Bera, Manoranjan MaitiAbstract:The goal of this work is to solve an interval valued multi-item solid Transportation Problem (MIIVSTP) with safety measure. In this paper we introduce a new concept “safety factor” in Transportation Problem. When items are transported from origins to destinations through different conveyances, there are some difficulties/risks to transport the items due to bad road, insurgency etc. in some routes specially in developing countries. Due to this reason desired total safety factor is being introduced and depending upon the nature of safety factor, we formulate five models without and with safety factor where this factor may be crisp, fuzzy, interval, stochastic in nature. Here the Transportation costs are intervals, the corresponding multi-objective Transportation Problem is formulated using “mean and width” technique. Then the Problem is converted to a single objective Transportation Problem taking convex combination of the objectives according to their weights. Finally all the models are solved by Generalized Reduced Gradient (GRG) method using LINGO software. Numerical examples are used to illustrate the model and methodologies.
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multi item interval valued solid Transportation Problem with safety measure under fuzzy stochastic environment
Journal of Transportation Security, 2013Co-Authors: Abhijit Baidya, Uttam Kumar Bera, Manoranjan MaitiAbstract:In this paper we introduce “safety factor” in Transportation Problem. Here we solve Multi Item Interval Valued Solid Transportation Problem (MIIVSTP) with safety factor under Desire Safety Measure (DSM) fuzzy-stochastic and stochastic. When items are transported from origins to destinations through different conveyances, there are some difficulties/risks to transport the items due to bad road, insurgency etc. in some routes specially in developing countries. Due to this reason desired total safety factor is being introduced. Also our goal is to evaluate the solution of MIIVSTP using Global Criteria Method. Here we developed five model with taking DSM as fuzzy-stochastic and stochastic and safety factor as crisp, fuzzy, interval, stochastic, fuzzy-stochastic. Here the Transportation costs are intervals, the corresponding multi-objective Transportation Problem is formulated using “mean and width” technique. Then the Problem is converted to a single objective Transportation Problem taking convex combination of the objectives according to their weights. Finally all the models are solved by Generalized Reduced Gradient (GRG) method using LINGO software. Numerical examples are used to illustrate the model and methodologies.
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multi objective multi item solid Transportation Problem in fuzzy environment
Applied Mathematical Modelling, 2013Co-Authors: Pradip Kundu, Samarjit Kar, Manoranjan MaitiAbstract:Abstract A multi-objective multi-item solid Transportation Problem with fuzzy coefficients for the objectives and constraints, is modeled and then solved by two different methods. A defuzzification method based on fuzzy linear programming is applied for fuzzy supplies, demands and conveyance capacities, including the condition that both total supply and conveyance capacity must not fall below the total demand. First, expected values of the fuzzy objective functions are considered to derive crisp values. Another method based on the concept of “minimum of fuzzy number” is applied for the objective functions that yields fuzzy values instead of particular crisp values for the fuzzy objectives. Fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives. A numerical example is solved using above mentioned methods and corresponding results are compared.
Mitsuo Gen - One of the best experts on this subject based on the ideXlab platform.
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nonlinear fixed charge Transportation Problem by spanning tree based genetic algorithm
Computers & Industrial Engineering, 2007Co-Authors: Mitsuo GenAbstract:Abstract Networks provide a useful way for modeling real world Problems and are extensively used in many different types of systems: communications, hydraulic, mechanical, electronic, and logistics. The Transportation Problem (TP) is known as one of the important network Problems. When the TP Problem is associated with additional fixed cost for establishing the facilities or fulfilling the demand of customers, then it is called fixed charge Transportation Problem (fcTP). This Problem is one of the NP-hard (IE/OR) Problems that are difficult to solve using traditional methods. This paper aims to show the application of spanning tree-based Genetic Algorithm (GA) approach for solving nonlinear fixed charge Transportation Problem. Our new idea lies on the GA representation that includes the feasibility criteria and repairing procedure for the chromosome. Several numerical experimental results are presented to show the effectiveness of the proposed method.
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spanning tree based genetic algorithm for the bicriteria fixed charge Transportation Problem
Congress on Evolutionary Computation, 1999Co-Authors: Mitsuo GenAbstract:In this paper, we present a genetic algorithm with a spanning tree representation for solving the bicriteria fixed charge Transportation Problem. First we consider the fixed charge Transportation Problem with a single objective function by the spanning tree-based genetic algorithm, and then extend this GA approach to solve the bicriteria Problem. Due to the bicriteria program, the fitness function is constructed by dynamic scaling which normalizes the different data from the bicriteria region. The proposed genetic algorithm can find Pareto optimal solutions in the bicriteria space. Computational results will show the performance of the spanning tree-based genetic algorithm.
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spanning tree based genetic algorithm for bicriteria Transportation Problem
Annual Conference on Computers, 1998Co-Authors: Mitsuo GenAbstract:In this paper, we present a new approach which is spanning tree-based genetic algorithm for bicriteria Transportation Problem. The Transportation Problem have the special data structure in solution characterized as a spanning tree. In encoding Transportation Problem, we introduce one of node encoding which is adopted as it is capable of equally and uniquely representing all possible basic solutions. The crossover and mutation was designed based on this encoding. And we designed the criterion that chromosome always feasibility converted to a Transportation tree. In the evolutionary process, the mixed strategy and roulette wheel selection is used. Numerical experiments will be shown the effectiveness and efficiency of the proposed algorithm.
Lixing Yang - One of the best experts on this subject based on the ideXlab platform.
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a solid Transportation Problem with type 2 fuzzy variables
Soft Computing, 2014Co-Authors: Pei Liu, Lixing Yang, Li WangAbstract:We give this figure to show the searching process in the tabu search algorithm. Clearly, for the initial several iterations, the best objective encountered decreases drastically. After iteration 6, the best objective changes with a fairly slow ratio, and at iteration 27, the optimal objective is found. This result shows the effectiveness of the proposed algorithm. Three new defuzzification methods are proposed for type-2 fuzzy variables.The solid Transportation Problem is formulated as a chance-constrained expected value model.Fuzzy simulation based on tabu search algorithm is designed to solve the proposed model.The effectiveness of the model and algorithm is verified by the numerical experiments. This paper focuses on generating the optimal solutions of the solid Transportation Problem under fuzzy environment, in which the supply capacities, demands and Transportation capacities are supposed to be type-2 fuzzy variables due to the instinctive imprecision. In order to model the Problem within the framework of the credibility optimization, three types of new defuzzification criteria, i.e., optimistic value criterion, pessimistic value criterion and expected value criterion, are proposed for type-2 fuzzy variables. Then, the multi-fold fuzzy solid Transportation Problem is reformulated as the chance-constrained programming model with the least expected Transportation cost. To solve the model, fuzzy simulation based tabu search algorithm is designed to seek approximate optimal solutions. Numerical experiments are implemented to illustrate the application and effectiveness of the proposed approaches.
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a bicriteria solid Transportation Problem with fixed charge under stochastic environment
Applied Mathematical Modelling, 2007Co-Authors: Lixing Yang, Yuan FengAbstract:In this paper, a bicriteria solid Transportation Problem with stochastic parameters is investigated. Three mathematical models are constructed for the Problem, including expected value goal programming model, chance-constrained goal programming model and dependent-chance goal programming model. A hybrid algorithm is also designed based on the random simulation algorithm and tabu search algorithm to solve the models. At last, some numerical experiments are presented to show the performance of models and algorithm.
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fuzzy fixed charge solid Transportation Problem and algorithm
Soft Computing, 2007Co-Authors: Lixing Yang, Linzhong LiuAbstract:This paper mainly investigates the fixed charge solid Transportation Problem under fuzzy environment, in which the direct costs, the fixed charges, the supplies, the demands and the conveyance capacities are supposed to be fuzzy variables. As a result, several new models, i.e., expected value model, chance-constrained programming model and dependent-chance programming model, are constructed on the basis of credibility theory. After that, the crisp equivalences are also discussed for different models. In order to solve the models, hybrid intelligent algorithm is designed based on the fuzzy simulation technique and tabu search algorithm. Finally, two application results are given to show the applications of the models and algorithm.
S S Alam - One of the best experts on this subject based on the ideXlab platform.
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multiobjective Transportation Problem with interval cost source and destination parameters
European Journal of Operational Research, 1999Co-Authors: S K Das, Adrijit Goswami, S S AlamAbstract:In this paper, we focus on the solution procedure of the multiobjective Transportation Problem (MOTP) where the cost coefficients of the objective functions, and the source and destination parameters have been expressed as interval values by the decision maker. This Problem has been transformed into a classical MOTP where to minimize the interval objective function, the order relations that represent the decision maker's preference between interval profits have been defined by the right limit, left limit, centre, and half-width of an interval. The constraints with interval source and destination parameters have been converted into deterministic ones. Finally, the equivalent transformed Problem has been solved by fuzzy programming technique. Numerical examples have been provided to illustrate the solution procedure for three possible cases of the original Problem.
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fuzzy programming approach to multiobjective solid Transportation Problem
Fuzzy Sets and Systems, 1993Co-Authors: A K Bit, M P Biswal, S S AlamAbstract:Abstract The linear multiobjective solid Transportation Problem is a special type of vector minimum Problem in which constraints are all equally type and the objectives are conflicting in nature. A generalization of the linear multiobjective solid Transportation Problem, in which the supply, demand, and capacity constraints are not only of equality type but also of inequality type, is considered. This paper presents an application of fuzzy linear programming to the linear multiobjective solid Transportation Problem. It gives efficient solutions as well as an optimal compromise. For this method, a Fortran program has been developed based on the fuzzy linear programming algorithm. This method is compared with some existing algorithms using numerical example.
