The joint replenishment problem with quantity discounts under constant demand

In many practical situations quantity discounts on basic purchase price exist, and taking advantage of these can result in substantial savings. Quantity discounts have been considered in many production and inventory models. But unlike other research areas, there have been no studies to quantity discounts in the joint replenishment problem. The purpose of this paper is to develop efficient algorithms for solving this problem. Firstly, we suggest useful propositions to develop efficient heuristic algorithms. Secondly, we develop two algorithms using these propositions. Numerical examples are shown to illustrate the procedures of these algorithms. Extensive computational experiments are performed to analyze the effectiveness of the heuristics.