Issue: 2021/Vol.31/No.3, Pages
FUZZY PROGRAMMING FOR MULTI-CHOICE BILEVEL TRANSPORTATION PROBLEM
Cite as: R. Arora, K. Gupta. Fuzzy programming for multi-choice bilevel transportation problem. Operations Research and Decisions 2021: 31(3), . DOI 10.37190/ord210301
Multi-choice programming problems arise due to diverse needs of people. In this paper, multi-choice optimisation is applied to bilevel transportation problem. This problem deals with transportation at both the levels, upper as well as lower. There are multiple choices for demand and supply parameters. The multi-choice parameters at the respective levels are converted into polynomials which transmute the defined problem into a mixed integer programming problem. The objective of the paper is to determine a solution methodology for the transformed problem. The significance of the formulated model is exhibited through an example by applying it to a hotel industry. The fuzzy programming approach is employed to obtain the satisfactory solution for the decision makers at the two levels. A comparative analysis is presented in the paper by solving bilevel multi-choice transportation problem with goal programming mode as well as by the linear transformation technique proposed in the paper by Khalil et al. The example is solved using computing software.
Keywords: bilevel programming, interpolating polynomials, membership function, fuzzy programming, tolerance limits, satisfactory solution.
Received: 13 February 2021 Accepted: 28 September 2021