This study performs theoretical analysis on the Joint Replenishment Problem (JRP) under General-Integer (GI) policy. The JRP models concern how to determine lot sizes and to schedule replenishment times for products so as to minimize the total costs per unit time. GI policy requires replenishment frequency of each product, denoted by ki, to be a general integer, i.e., ki = 1, 2, 3, …. In this study, we utilize a 10-product example to graphically present the curve of the optimal total cost with respect to the values of basic period. Under GI policy, we discover an interesting property on the optimal curve for the JRP, and we prove that the optimality structure of the JRP is piece-wise convex. By making use of the junction points in the optimality structure, we derive an effective (polynomial-time) search algorithm to secure a global solution for the JRP under GI policy. Evidently, we provide a numerical example to demonstrate the efficiency of the proposed algorithm.
