Uncertain Multi-objective Transportation Problems and Their Solution

Abstract

Nowadays, it is seen that the transportation of goods is a crucial part in each and every sector of our Indian economy. The parameters like transportation cost, supply and demand etc. involved in the Transportation problem (TP) cannot be always precisely defined and can vary due to certain reasons like weather conditions or incomplete information. This chapter focusses on studying the multi-objective TP (MOTP) in the uncertain domain area. To solve the uncertain MOTP model, Expected value and Dependent chance constraint models have been developed using the basic concepts of uncertainty theory which are further converted into their deterministic forms for computational work. The deterministic form of DCCM model is further converted into linear model with the help of Charnes and Cooper’s transformations. The deterministic models are then solved using the fuzzy programming technique and weighted sum methodology to obtain the compromise solution. At last, numerical illustration is also given to demonstrate the working of the proposed models.