A Model for Uncertain Multi-objective Transportation Problem with Fractional Objectives

Abstract

Fractional programming problems take into account the situations where the decision maker is interested to maximize or minimize the ratios of some functions rather than a simple function. Fractional programming modeling approach has a lot of scope in dealing with the transportation planning decision problems. This paper presents a model for transportation problem with multiple fractional objectives involving uncertain parameters. In order to make the model more realistic, we have considered the case when there exists more than one fractional objective. All the parameters involved in the proposed model viz. objective function coefficients, availabilities and demands are assumed to be uncertain. Moreover, an equivalent deterministic model is also presented. Fuzzy goal programming approach is discussed as the solution approach for reaching the compromise solution. A numerical example is also given to illustrate the model more clearly.

Keywords

• Fractional programming problem
• Transportation problems
• Uncertain variables
• Uncertain programming
• Fuzzy goal programming
• Membership function