A simple parametric method to generate all optimal solutions of fuzzy solid transportation problem


Kocken H. , Sivri M.

APPLIED MATHEMATICAL MODELLING, vol.40, pp.4612-4624, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40
  • Publication Date: 2016
  • Doi Number: 10.1016/j.apm.2015.10.053
  • Title of Journal : APPLIED MATHEMATICAL MODELLING
  • Page Numbers: pp.4612-4624
  • Keywords: Solid transportation problem, Fuzzy mathematical programming, Parametric Programming, COST

Abstract

This paper deals with the fuzzy solid transportation problem (FSTP) that has fuzzy cost coefficients, fuzzy supplies, fuzzy demands and fuzzy conveyances. All these fuzzy quantities of FSTP are assumed to be triangular fuzzy numbers. For this problem, we propose an approach to generate all optimal solutions parametrically. The first stage of our approach is to determine the feasibility range based on fuzzy supply–demand–conveyance quantities. In the second stage, the breaking points of fuzzy costs are found by intersecting the membership functions of the fuzzy costs. The last stage constructs the optimal solutions of FSTP by means of some proposed auxiliary programs. Also a numerical example has been provided to illustrate our solution procedure.

This paper deals with the fuzzy solid transportation problem (FSTP) that has fuzzy cost coefficients, fuzzy supplies, fuzzy demands and fuzzy conveyances. All these fuzzy quantities of FSTP are assumed to be triangular fuzzy numbers. For this problem, we propose an approach to generate all optimal solutions parametrically. The first stage of our approach is to determine the feasibility range based on fuzzy supply-demand-conveyance quantities. In the second stage, the breaking points of fuzzy costs are found by intersecting the membership functions of the fuzzy costs. The last stage constructs the optimal solutions of FSTP by means of some proposed auxiliary programs. Also a numerical example has been provided to illustrate our solution procedure. (C) 2015 Elsevier Inc. All rights reserved.