A CRITICAL STUDY ON AN UNBALANCED TRANSPORTATION PROBLEM

An unbalanced version of a Transportation Problem (TP) is one which occurs due to either supply or demand imbalance. Its fundamental objective is to minimize the cost of shipment while distributing goods or products from several origins (factories) to various destinations (warehouses). However, this objective is to be achieved by transforming the problem in to a balanced type. For supply imbalance problem i.e. the problem with total supply greater than total demand, we usually add a fictitious sink in order to receive excess of supply. In case when total demand is greater than total supply, i.e. for demand imbalance problem, a fictitious source is usually introduced so as to satisfy the unfilled demand. Moreover, the cost of transportation to or from fictitious sink/fictitious source is assumed to be zero as units are not really transported. Unlike this approach, some other techniques have also come in to being to balance the problem without the need to have fictitious sinks or sources. Once it is balanced, the problem can be solved by simplex method-a well- known but tedious technique for dealing with any linear programming. A special procedure for solving a transportation problem is the so called “transportation method” which requires much less effort than the simplex algorithm. In this thesis work, solution approaches of an unbalanced transportation problem have been reviewed and a New Alternate Method (NAM) for unbalanced transportation problems is proposed. Our approach has shown an efficient performance over the existing methods.