A simple improvement on Silver's heuristic for the joint replenishment problem

In this paper, we revisit the well–known joint replenishment problem. There is a family of items with a major fixed cost associated with any replenishment of the family and a minor, (item–dependent) setup cost for each item that is included in the replenishment. In contrast with optimization methods and sophisticated (iterative) heuristics that have been presented in the literature, we present a simple (including ease of understanding) improvement routine to be used in conjunction with the original, simple approach advocated by one of the authors 30 years ago. Tests on 48,000 examples reveal that the improvement routine does, indeed, substantially improve performance and with relatively little extra computational effort. Thus, it should be of particular interest to practitioners and for teaching materials.