A genetic algorithm for joint replenishment based on the exact inventory cost

Given the order cycles of items in joint replenishment, no closed-form formula or efficient method is known to compute the exact inventory cost. Previous studies avoid the difficulty by restricting the replenishment policy to the cases where the order cycle of each item is a multiple of the cycle of the most frequently ordered item. This simplifies the computation but may entail sub-optimality of a solution. To cope with this, we devise an unbiased estimator of the exact cost which is computable in time polynomial of the problem input size and 1/ε1/ε, where εε is a pre-specified relative error of estimation. We then develop a genetic algorithm based on this new cost evaluation, report the experimental results in comparison to the “RAND” [Kaspi M, Rosenblatt MJ. An improvement of Silver's algorithm for the joint replenishment problem. IIE Transactions 1983; 15: 264–9] which has been known as a state-of-the-art method for joint replenishment, and discuss their implications.