Optimal production–inventory model with a limited time for backordering at zero-cost

This paper deals with a new production–inventory model with the same limited time of free backorder for each client, under the conditions of constant demand rate and finite production rate. It looks into the factors such as costs of stockout, loss of sale opportunity and etc. in each cycle, if they arise when the backorder time is longer than the client's limited time of free backorder. The method of finding the corresponding optimal schedule (including the optimal production time and cycle length) is proposed. Numerical examples worked out with the help of the Matlab software are given to illustrate the proposed solution procedure. The method and results provide theoretical principles for the management to make decisions in the inventory system.