Multi-index fixed charge bi-criterion transshipment problem

Abstract

The multi index fixed charge transshipment problem is an extension of the classical transshipment problem in which a fixed cost is incurred for every origin. In the transshipment problem all the sources and destinations can function in any direction, thus it is very useful to reduce the transportation cost. In this paper we present an algorithm to find out the efficient cost-time trade-off pairs for the three-dimensional fixed charge bi-criterion transshipment problem having the same priority to cost as well as time. To find out the efficient cost-time trade off pairs for the given problem, we form a related fixed charge bi-criterion three dimensional transportation problem and the efficient cost-time trade-off pairs for the given problem are derivable from this related problem. Also, we find out an optimum trade-off pair among all the efficient cost-time trade-off pairs, which has the minimum distance from the ideal pair. The algorithm involves finite number of iterations and is easy to understand and apply. It can serve the managers by providing the solution to a variety of production distribution problem where heterogeneous amount of commodities are to be transshipped. Numerical examples are also included to support the theory.