an uncertain time horizon inventory management model with partial backlogging considering deterioration cost

a new mathematical model for the optimal production isformulated for the inventory management system under time-varyingand stochastic inflation environment for deteriorating items. the timehorizon is finite and demand rate is dependent to the inflation. in thereal situation, some but not all customers will wait for backlogged itemsduring a shortage period, such as for fashionable commodities or hightechproducts with the short product life cycle. the longer the waitingtime is, the smaller the backlogging rate would be. according tosuch phenomenon, taking the backlogging rate into account is necessary.thus, the model incorporates partial backlogging. the total systemcost including deterioration cost, production cost, inventory holdingcost, backordering cost, lost sale cost and ordering cost is formulated asan optimal control problem. the numerical example has been providedfor evaluation and validation of the theoretical results.