Low price guarantee in inventory systems coordinated with pricing strategy

We analyze a finite horizon, single-product, periodic review model in which pricing and inventory decisions should be made simultaneously at the beginning of each period. Besides the traditional cost such as order cost, inventory cost, there is a new introduced cost called the reimbursement cost. Customers are ensured to be reimbursed the difference between the current purchase price and any lower price within a fixed future time limit. The price has a direct impact on the distribution of the demand and the expected demand is a non-increase function of the price. The model is formulated as a discrete-time optimal control problem. Its objective is to maximize expected revenue over the planning horizon. The existence of its optimal solution has been proved based on the (s, S, p) policy.