Fuzzy programming for multi-choice bilevel transportation problem

Abstract

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 programing 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.

Branch-and-Cut Method for Solving the Integer Linear Multiplicative Bilevel Problem

“…As a result, many researchers have conducted in-depth research in this field. The formal formulation of BLPP was proposed in Candler & Townsley (1982); Fortuny-Amat & McCarl (1981); Arora & Gupta (2021; Neves et al (2023). In Golpîra (2017), the Karush-Kuhn-Tucker (KKT) conditions are employed to transform the BLPP problem into a single-level, mixedinteger linear programming problem by considering some relaxations.…”

“…In Golpîra (2017), the Karush-Kuhn-Tucker (KKT) conditions are employed to transform the BLPP problem into a single-level, mixedinteger linear programming problem by considering some relaxations. Multichoice optimization has been applied to the bilevel transportation problem in Arora & Gupta (2021), the fuzzy programming approach is employed in order to obtain a satisfactory solution for the decision-makers at the two levels. In Neves et al (2023), the Dynamic Vehicle Allocation problem is presented and solved using the bilevel programming where the shipper's objective is to minimize shipping delays, while the carrier's objective is to maximize profits.…”