An optimal ordering inventory policy when the purchase price follows a discrete-time Markov chain

Most of the time retailers are offered discount prices that are occurring at random points in time. One such scenario is the supplier offering discounts to the retailers to increase market share, cash flow, and to reduce the inventory of specific items. Surprisingly no models exist in the literature survey to model the randomly occurring discount price under discrete time. The primary objective of this article is to develop an optimal inventory policy for a retailer when the discount price arrives randomly and the time variable is discrete. Under such a scenario, the optimal inventory policy can be obtained by considering the variations in the purchase price as a discrete-time Markov chain. The renewal reward theorem is used to derive the expected profit per unit of time. To illustrate the application of the developed model a real case study is considered. The optimal solution of the developed model is compared with the EOQ policy and found that the developed model solution provides better profit. This justifies the significance of the developed model. The inventory manager can use the developed model as a tool to obtain the optimal solution for any two price problems that repeat randomly.