Multi-Index Fixed Charge Bi-Criterion Transportation Problem with Restricted Flow

Abstract

The Fixed charge bi-criterion transportation problem with restricted flow which is an extension of the fixed charge bi-criterion transportation problem has been studied in the present thesis. In this type of problem, there is a restriction on the total flow. In the fixed charge bi-criterion transportation 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 fixed-charge transportation problem (FCTP) is an extension of the classical transportation problem in which a fixed cost is incurred, independent of the amount transported, along with a variable cost that is proportional to the amount shipped. The introduction of fixed costs in addition to variable costs results in the objective function being a step function. Therefore, fixed-charge problems are usually solved using sophisticated analytical or computer software. This thesis deviates from that approach. It presents a simple algorithm for the solution of small fixed-charge problems with restricted flow. We present numerical example to illustrate applications of the proposed method. The present thesis consists of two chapters. The first chapter is introductory in nature. In the second chapter the Fixed charge bi-criterion transportation problem with restricted flow given by Deepa Thirwani et al. (1997) is reviewed to find the cost-time trade-off pair