An Algorithm for the Joint Replenishment Problem with Multiple Resource Constraints

The deterministic joint replenishment problem with multiple resource constraints is presented and its mathematic model is set up. On the basis of that, a full analysis is given of the relationship between decision variables T (basic cycle time) and k_j (replenishment frequency of item j), then bounds on T and k_j are obtained. A modified simulated annealing algorithm is proposed to search the optimal value within a much tighter range and the problem is effectively solved. The results of the example indicate that the algorithm can get a good solution and is applicable to larger problems.