Simply structured policies for a dynamic pricing problem with constant price elasticity demand

Consider a retailer, stocking a seasonal item facing a stochastic demand. The retailer places orders before the start of the season and in-season reorders are impossible. A question frequently asked is: How should one set prices throughout the selling season to optimize profits? Applications include the production of fashion goods, hotel rooms, airline seats, and car rentals. The objective function is typically non-concave, so finding an optimal solution is computationally challenging and heuristic approaches are often employed. For a T period dynamic pricing model with the expected profit objective, it was shown in the literature that the problem reduces to solving T single variable optimization problems. We extend the result by incorporating holding costs. We obtain similar simple solutions for the special cases of deterministic demands and nonnegative holding costs proportional to selling prices. For the general case, we introduce heuristics using simply structured policies.