Optimal Inventory Control Problem with Inflation-Dependent Demand Rate Under Stochastic Conditions

The practical experiences reveal that the Supply Chain Management (SCM) is under uncertain and variable conditions. One of the most important parts of SCM is inventory system management which is inherently in non-deterministic situation. The many departments of organization such as warehouse, marketing, sale, purchasing, financial, planning, production, maintenance and etc. are relevance to the inventory problem. Since 1975 a series of related papers appeared that considered the effects of inflation on the inventory system. There are a few works in the inflationary inventory researches under stochastic conditions, especially with multiple stochastic parameters. Therefore, a new mathematical model for the optimal production for an inventory control system is formulated under stochastic environment. The demand rate is a function of inflation and time value of money where the inflation and time horizon i.e., period of business, both are random in nature. 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. Thus, the model incorporates partial backlogging. A numerical method has been used and the numerical example has been provided for evaluation and validation of the theoretical results and some special cases of the model are discussed. The results show the importance of taking into account stochastic inflation, time horizon and demand.