Department of Industrial Engineering, University of Kharazmi, Tehran, Iran.
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.