Bi-criteria transportation problem with multiple parameters

This paper introduces a bi-criteria transportation problem with multiple parameters which brings together the concept of price discrimination from the area of marketing management to the world of multi objective transportation problems. The problem deals with two objectives, the overall shipment cost and the bottleneck time of shipment. Both the objectives are of minimization type and have multi-choice coefficients pertaining to differential marketing strategies or different modes of transportation available. First, the problem with minimum availability and demand of goods is solved and then the problem is extended to the case of interval demand and supply. By iteratively solving multi-choice variants of a cost minimizing transportation problem/minimum cost flow problem, all Pareto optimal time–cost pairs are obtained. The proposed algorithm for both the variants is successfully implemented and solved using the CPLEX optimization package.