A Comparison between Scatter Search and the RAND Method for Solving the Joint Replenishment Problem

The purpose of the present paper is to compare the performance of scatter search (SS) against one of the best heuristics, known as the RAND algorithm (Kaspi and Rosenblatt [7]), in order to solve a popular and useful multi-product inventory problem referred to in the literature as the joint replenishment problem (JRP). The JRP is a classical problem of great utility for many real problems. This paper applies the SS method to a set of randomly generated examples, and shows that the solutions obtained, when compared to RAND, are, when not better, at least identical in the majority of cases for up to 50 items. An important observation is that the average number of iterations employed by SS to find the best solutions on the set of examples, had a linear behavior with respect to the number of items.