Order and exit decisions under non-increasing price curves for products with short life cycles

We consider a supplier selling a product with a relatively short life cycle and following a non-increasing price curve. Because of the short cycle, there is a single procurement opportunity at the beginning of the cycle. The objective of the supplier is to determine the initial order quantity and the time to remove the product from the market in order to maximize her profits. We study this problem in a continuous-time framework where the demand is modeled with a non-homogeneous Poisson process having a general intensity function and the pricing strategy is given by an arbitrary non-increasing function. We give a rigorous mathematical analysis for the problem and show how it can be solved in two stages. We also consider the special case with piecewise constant intensity and price functions. For this case, we show that the optimal exit time is included in the set of break points of these functions. This brings a fast method to obtain the optimal solution for this special case.