On inventory replenishment with non-linear increasing demand

We present a consecutive improvement approach to solve the problem of determining the timing and size of replenishments in order to minimize the total inventory costs in the case of a non-linear increasing demand pattern. The proposed procedure is computationally simple compared to other methods. It considers the replenishment in reverse time sequence with the time horizon being exactly the ending point and it thus guarantees to meet the demand over the preestablished time frame. The concept of inventory correspondence is introduced. Numerical examples are also presented and compared with other heuristics using an analytic procedure for replenishment with non-linear increasing demand.