The pricing strategy of complete pre-ordered merchandise under discounted profit for maximizing

When a customer steps into a complete pre-ordered store, he will review the merchandise and consider his demands based on the merchandise price levels and price variability at that point in time. However, after declaring his intention to purchase said merchandise, the store assistant informs him that the merchandise will not be available for a period of time. This is a typical stock-out merchandise scenario in which customers may only place an order for delivery at a later point in time. Therefore, whether or not customer purchases merchandise does not just depend on the price at that moment. It is also influenced by the expected future increase or decrease of the price of the merchandise and the length of time before the store can supply the merchandise. In this study, we will explore how to set price levels at each point in time during the stock-out period in order to maximize the discounted profit after considering the influence of the price level, price variability, and waiting time on customer demand. The main assumption in this study is that customers' potential demand rate function at a given point during the stock-out period is a linear function of the price level and price variability at that point. Also, the ratio function of customers willing to wait for the merchandise is an exponential function of the length of time before the merchandise will be delivered. Constructing a mathematical model that is concrete to discuss the above problem, to derive the optimal price function of the merchandise at each point in time, and to discuss the characteristics of this function are the main parts of this study.