This paper studies intertemporal pricing policies when selling seasonal products in retail stores. We first present a continuous time model where a seller faces a stochastic arrival of customers with different valuations of the product. For this model, we characterize the optimal pricing policies as functions of time and inventory. We use this model as a benchmark against which we compare more realistic models that consider periodic pricing reviews. We show that the structure of the optimal pricing policies in this case is consistent with the procedures observed in practice; retail stores successively discount the product during the season and promote a liquidation sale at the end of the planning horizon. We also show that the loss experienced when implementing periodic pricing reviews instead of continuous policies is small when the appropriate number of reviews is chosen. Several interesting economic insights emerge from our analysis. For example, uncertainty in the demand for new products leads to higher prices, larger discounts, and more unsold inventory. Finally, we study the effect of announced discount policies on prices and profits. We show that stores that have adopted this type of strategy usually set prices such that with high probability the merchandise is sold during the first periods and the largest discounts rarely take place.dynamic pricing, retailing, stochastic models, dynamic programming
Catalog sales are among the fastest growing businesses in the U.S. The most important asset a company in this industry has is its list of customers, called the house list. Building a house list is expensive, since the response rate of names from rental lists is low. Cash management therefore plays a central role in this capital intensive business. This paper studies optimal mailing policies in the catalog sales industry when there is limited access to capital. We consider a stochastic environment given by the random responses of customers and a dynamic evolution of the house list. Given the size of real problems, it is impossible to compute the optimal solutions. We therefore develop a heuristic based on the optimal solutions of simplified versions of the problem. The performance of this heuristic is evaluated by comparing its outcome with an upper bound derived for the original problem. Computational experiments show that it behaves satisfactorily. The methodology presented permits the evaluation of potential catalog ventures thus proving useful to entrepreneurs in this industry.catalog sales, direct marketing, stochastic models, dynamic programming
In this paper we study optimal strategies for renting hotel rooms when there is a stochastic and dynamic arrival of customers from different market segments. We formulate the problem as a stochastic and dynamic programming model and characterize the optimal policies as functions of the capacity and the time left until the end of the planning horizon. We consider three features that enrich the problem: we make no assumptions concerning the particular order between the arrivals of different classes of customers; we allow for multiple types of rooms and downgrading; and we consider requests for multiple nights. We also consider implementations of the optimal policy. The properties we derive for the optimal solution significantly reduce the computational effort needed to solve the problem, yet in the multiple product and/or multiple night case this is often not enough. Therefore, heuristics, based on the properties of the optimal solutions, are developed to find “good” solutions for the general problem. We also derive upper bounds which are useful when evaluating the performance of the heuristics. Computational experiments show a satisfactory performance of the heuristics in a variety of scenarios using real data from a medium size hotel.
In this paper we propose a methodology to set prices of perishable items in the context of a retail chain with coordinated prices among its stores and compare its performance with actual practice in a real case study. We formulate a stochastic dynamic programming problem and develop heuristic solutions that approximate optimal solutions satisfactorily. To compare this methodology with current practices in the industry, we conducted two sets of experiments using the expertise of a product manager of a large retail company in Chile. In the first case, we contrast the performance of the proposed methodology with the revenues obtained during the 1995 autumn-winter season. In the second case, we compare it with the performance of the experienced product manager in a “simulation-game” setting. In both cases, our methodology provides significantly better results than those obtained by current practices.
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