A Partial Backlogging Mathematical Model under Variable Inflation and Demand with Considering Deterioration Cost

The practical experiences reveal that the inflation is non-deterministic and variable. Therefore, a mathematical model for the optimal production for an inventory control system of deteriorating items is formulated under time-varying and stochastic inflation environment. The demand rate is a function of inflation and the time horizon is finite. In the real situation, some but not all customers will wait for backlogged items during a shortage period, such as for fashionable commodities or high-tech 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 cost consists of the 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 and some special cases of the model are discussed.