Algorithms for an ammunition loading problem with mixed loading constraints

Abstract

We consider a loading planning problem in a military ammunition unit with variable sized vehicles. The problem is to assign the ammunitions to the available vehicles with the objective of minimizing the number of vehicles required for loading the ammunitions. In this research, we introduce the novel packing constraints, called the mixed-loading constraints that ammunitions of the same type can be loaded on the same vehicle except for certain sets of ammunition types, which can be loaded together. In other words, we cannot load a vehicle with different types of ammunitions, even though there is available space for loading ammunitions. We develop heuristic for our problems based on the column generation method. For the evaluation of the performance of the heuristics, the suggested heuristic is compared with heuristics that are modified from well-known bin-packing algorithms, the first-fit decreasing and best-fit decreasing algorithms. Results of tests on a number of randomly-generated instances show that the proposed heuristic is better than existing methods.