A global optimum search algorithm for the joint replenishment problem under power-of-two policy

In this study, we perform theoretical analysis and derive a global optimum search algorithm for the joint replenishment problem (JRP) under power-of-two (PoT) 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. PoT policy requires replenishment frequency of each product, denoted by ki, to be a PoT integer, i.e., ki=2p where p=0,1,2,…. By utilizing a 10-product example, we graphically present the curve of the optimal total cost with respect to the values of basic period. Under PoT policy, 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 search algorithm to secure a global optimal solution for the JRP under PoT policy. Evidently, we provide a numerical example to demonstrate the efficiency of the proposed algorithm.