A genetic algorithm approach to solving a multiple inventory loading problem

In this paper we consider a multiple-inventory loading problem involving a set of commodities that must be transported from a distributor to a retailer. The vehicle carrying out this distribution is divided into several compartments, in which only one type of commodity may be loaded. The problem becomes one of determining optimal assignments of vehicle compartments to commodities in order to minimize a mix of transportation and inventory costs. We first demonstrate the weakness of the underlying linear relaxation of a traditional mixed-integer programming approach that must be solved in a branch-and-bound framework. Instead of pursuing the development of an exact algorithm, we instead recommend the use of a genetic algorithm to quickly provide good quality solutions. Next, we introduce an additional strategy for defeating symmetry complications arising in certain specially structured problems. Finally, the effectiveness of each of the proposed techniques is demonstrated on a test bed of problems.