Multi-objective two-stage grey transportation problem using utility function with goals


Roy S. K. , Maity G., Weber G.

CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH, vol.25, no.2, pp.417-439, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s10100-016-0464-5
  • Title of Journal : CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH
  • Page Numbers: pp.417-439
  • Keywords: Transportation problem, Multi-objective decision making, Goal programming, Grey number, Utility function, ALGORITHM, DEMAND, COST

Abstract

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.