This paper deals with the problem of setting an optimal price for a product. The product is priced by maximizing the objective function, which accounts for both income from sales and operational costs. Since the price-sensitive demand is the common factor that determines the two components of the objective, it is used as an independent decision variable. We develop a closed-form solution for the discounted infinite-horizon variety of the problem. For a finite horizon, we suggest an approximate numerical procedure that sets the price dynamically as the horizon-length decreases, such as may occur, for example, towards the end of the sales period. When modeling the operational cost component, we consider a stochastic production-inventory problem and solve it using optimal control methods. In particular, we show that the optimal production policy is of a threshold type and we calculate the threshold value.
Bibliographical notePublisher Copyright:
- Optimal control
- Pricing policy
- Threshold policy
- Wiener process