Chapter 19 - Transportation problems

Abstract

This chapter focuses on the transportation problems. One of the earliest and most important applications of linear programming has been the formulation and solution of the transportation problem as a linear programming problem. The classical transportation problem can be described as follows: In 1939, Kantorovich had shown that a class of transportation type problems arise very frequently in practical situations but the method of solution given was not complete. The standard form of the problem was first formulated along with a constructive method of solution by Hitchcock in 1941 and later, the problem was discussed in detail by Koopmans. The classical transportation problem is often referred as the Hitchcock–Koopmans transportation problem. As per classical transportation problem, a certain commodity is available in fixed quantities at a number of origins (sources), in which a specified amount are sent to satisfy its demand at each of a number of destinations. It is assumed that the total demand is equal to the total supply and the transportation cost is proportional to the amount transported. The problem is to determine an optimal schedule of shipments.