An Uncertain Time Horizon Inventory Management Model with Partial Backlogging Considering Deterioration Cost

A new mathematical model for the optimal production is formulated for the inventory management system under time-varying and stochastic inflation environment for deteriorating items. The time horizon is finite and demand rate is dependent to the inflation. In the real situation, some but not all customers will wait for backlogged items during a shortage period, such as for fashionable commodities or hightech products with the short product life cycle. The longer the waiting time is, the smaller the backlogging rate would be. According to such phenomenon, taking the backlogging rate into account is necessary. Thus, the model incorporates partial backlogging. The total system cost including deterioration cost, production cost, inventory holding cost, backordering cost, lost sale cost and ordering cost is formulated as an optimal control problem. The numerical example has been provided for evaluation and validation of the theoretical results.