Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal


Roy S. K. , Maity G., Weber G. W. , ALPARSLAN GÖK S. Z.

ANNALS OF OPERATIONS RESEARCH, vol.253, no.1, pp.599-620, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 253 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1007/s10479-016-2283-4
  • Title of Journal : ANNALS OF OPERATIONS RESEARCH
  • Page Numbers: pp.599-620
  • Keywords: Transportation problem, Multi-objective decision making, Multi-choice programming, Goal programming, Conic scalarization, Interval uncertainty, PROPER EFFICIENCY, OPTIMIZATION

Abstract

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.