Multi-Index Fixed Charge Bicriterion Transportation Problem

Abstract

The Fixed charge bi-criterion transportation problem which is an extension of the bi-criterion transportation problem has been studied in the present work. In this type of problem, a fixed cost called the setup cost is incurred for every origin. In the bi-criterion transportation problem the cost of transportation is directly proportional to the number of units transported, but on account of quantity discounts, price breaks etc., the transportation may not be linear. Thus in real world situations, when a commodity is transported, a fixed cost is incurred in the objective function. The Multi-index fixed charge bi-criterion transportation problem has also been studied in which there are three indices. The problem is an extension of the Multi-index bi-criterion transportation problem, in which a fixed cost is incurred in the objective function. The present thesis consists of three chapters. The first chapter is introductory in nature. In the second chapter the Fixed charge bi-criterion transportation problem given by Basu et al. (1994) is reviewed to find the cost-time trade-off pairs. Multi-index fixed charge bi-criterion transportation problem has been considered in chapter third which is an extension of the fixed charge bi-criterion transportation problem and may be thought of as a block in which the layers in all the directions form restricted transportation problem and an attempt has been made to find the cost-time trade-off pairs using an alternate approach of Ahuja and Arora (2001).