Solving fuzzy transportation problem using multi-choice goal programming

This paper explores the study of fuzzy transportation problem (FTP) using multi-choice goal-programming approach. Generally, the decision variable in transportation problem (TP) is considered as real variable, but here the decision variable in each node is chosen from a set of multi-choice fuzzy numbers. Here, we formulate a mathematical model of FTP considering fuzzy goal to the objective function. Thereafter, the solution procedure of the proposed model is developed through multi-choice goal programming approach. The proposed approach is not only improved the applicability of goal programming in real world situations but also provided useful insight about the solution of a new class of TP. A real-life numerical experiment is incorporated to analyze the feasibility and usefulness of this paper. The conclusions about our proposed work including future studies are discussed last.

[1]  Sankar Kumar Roy,et al.  Minimizing cost and time through single objective function in multi-choice interval valued transportation problem , 2017, J. Intell. Fuzzy Syst..

[2]  Sankar Kumar Roy,et al.  Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal , 2017, Ann. Oper. Res..

[3]  R. Narasimhan.  GOAL PROGRAMMING IN A FUZZY ENVIRONMENT , 1980 .

[4]  Amarpreet Kaur,et al.  A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers , 2012, Appl. Soft Comput..

[5]  José L. Verdegay,et al.  Multi-objective Transportation Problem with Cost Reliability Under Uncertain Environment , 2016, Int. J. Comput. Intell. Syst..

[6]  Carlos Romero,et al.  A general structure of achievement function for a goal programming model , 2004, Eur. J. Oper. Res..

[7]  Amy H. I. Lee,et al.  An evaluation framework for product planning using FANP, QFD and multi-choice goal programming , 2010 .

[8]  Sankar Kumar Roy,et al.  Solving multi-choice multi-objective transportation problem: a utility function approach , 2014 .

[9]  Mehrdad Tamiz,et al.  Goal programming for decision making: An overview of the current state-of-the-art , 1998, Eur. J. Oper. Res..

[10]  Gerhard-Wilhelm Weber,et al.  Multi-objective two-stage grey transportation problem using utility function with goals , 2016, Central European Journal of Operations Research.

[11]  Chin-Nung Liao,et al.  Formulating the multi-segment goal programming , 2009, Comput. Ind. Eng..

[12]  F. L. Hitchcock.  The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[13]  Kamran Shahanaghi,et al.  Fuzzy multi-choice goal programming , 2012 .

[14]  Ching-Ter Chang.  Revised multi-choice goal programming , 2008 .

[15]  Sankar Kumar Roy,et al.  Analysis of interval programming in different environments and its application to fixed-charge transportation problem , 2017, Discret. Math. Algorithms Appl..

[16]  Sankar Kumar Roy,et al.  Multi-choice stochastic transportation problem involving extreme value distribution , 2013 .

[17]  T. Koopmans.  Optimum Utilization of the Transportation System , 1949 .

[18]  Ching-Ter Chang,et al.  Multi-choice goal programming , 2007 .

[19]  Ali Ebrahimnejad,et al.  An improved approach for solving fuzzy transportation problem with triangular fuzzy numbers , 2015, J. Intell. Fuzzy Syst..

[20]  Amit Kumar,et al.  A new method for solving fuzzy transportation problems using ranking function , 2011 .

[21]  Abraham Charnes,et al.  Optimal Estimation of Executive Compensation by Linear Programming , 1955 .

[22]  Sankar Kumar Roy,et al.  Multi-choice stochastic transportation problem involving Weibull distribution , 2014 .