In many industries, managers face the problem of selling a given stock of items by a deadline. We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm's objective is to maximize expected revenues. Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, and rooms in hotels that become worthless if not sold by a specific time. We formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity (resp., price) as a function of the stock level and the length of the horizon. For a particular exponential family of demand functions, we find the optimal pricing policy in closed form. For general demand functions, we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple, fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity. Finally, we extend our results to the case where demand is compound Poisson; only a finite number of prices is allowed; the demand rate is time varying; holding costs are incurred and cash flows are discounted; the initial stock is a decision variable; and reordering, overbooking, and random cancellations are allowed.dynamic pricing, inventory, yield management, intensity control, stochastic demand, optimal policies, heuristics, finite horizon, stopping times

Customer choice behavior, such as "buy-up" and "buy-down", is an important phenomenon in a wide range of revenue management contexts. Yet most revenue management methodologies ignore this phenomenon -or at best approximate it in a heuristic way. In this paper, we provide an exact and quite general analysis of this problem. Specifically, we analyze a single-leg yield management problem in which the buyers' choice behavior is modeled explicitly. The choice model is perfectly general and simply specifies the probability of purchasing each fare product as function of the set of fare products offered. The control problem is to decide which subset of fare products to offer at each point in time. We show that the optimal policy is of a simple form. Namely, it consists of 1) identifying the ordered family of "nondominated" subsets S 1 , ..., S m , and 2) at each point in time opening one of these sets S k , where the optimal index k is increasing in the remaining capacity x. That is, the more capacity we have available, the further the optimal set is along this sequence. Moreover, we show that the optimal policy is nested if and only if the ordered sets are increasing, that is S 1 ⊆ S 2 ⊆ ... ⊆ S n , and we give a complete characterization of when nesting by fare order is optimal. We then show that two important models, the independent demand model and the multinomial logit model (MNL), satisfy this later condition and hence nested-by-fare-order policies are optimal in these cases. We also develop an estimation procedure for this setting based on the expectation-maximization (EM) method that jointly estimates arrival rates and choice model parameters when no-purchase outcomes are unobservable. Numerical results are given to illustrate both the model and estimation procedure.

Gallego et al. [Gallego, G., G. Iyengar, R. Phillips, A. Dubey. 2004. Managing flexible products on a network. CORC Technical Report TR-2004-01, Department of Industrial Engineering and Operations Research, Columbia University, New York.] recently proposed a choice-based deterministic linear programming model (CDLP) for network revenue management (RM) that parallels the widely used deterministic linear programming (DLP) model. While they focused on analyzing "flexible products"--a situation in which the provider has the flexibility of using a collection of products (e.g., different flight times and/or itineraries) to serve the same market demand (e.g., an origin-destination connection)--their approach has broader implications for understanding choice-based RM on a network. In this paper, we explore the implications in detail. Specifically, we characterize optimal offer sets (sets of available network products) by extending to the network case a notion of "efficiency" developed by Talluri and van Ryzin [Talluri, K. T., G. J. van Ryzin. 2004. Revenue management under a general discrete choice model of consumer behavior. Management Sci. 50 15-33.] for the single-leg, choice-based RM problem. We show that, asymptotically, as demand and capacity are scaled up, only these efficient sets are used in an optimal policy. This analysis suggests that efficiency is a potentially useful approach for identifying "good" offer sets on networks, as it is in the case of single-leg problems. Second, we propose a practical decomposition heuristic for converting the static CDLP solution into a dynamic control policy. The heuristic is quite similar to the familiar displacement-adjusted virtual nesting (DAVN) approximation used in traditional network RM, and it significantly improves on the performance of the static LP solution. We illustrate the heuristic on several numerical examples.network revenue management, choice behavior, multinomial logit choice model, dynamic programming, linear programming

A firm has inventories of a set of components that are used to produce a set of products. There is a finite horizon over which the firm can sell its products. Demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered. The problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon. An upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem. The solution to the deterministic problem suggests two heuristics for the stochastic problem that are shown to be asymptotically optimal as the expected sales volume tends to infinity. Several applications of the model to network yield management are given. Numerical examples illustrate both the range of problems that can be modeled under this framework and the effectiveness of the proposed heuristics. The results provide several fundamental insights into the performance of yield management systems.

Consider a category of product variants distinguished by some attribute such as color or flavor. A retailer must construct an assortment for the category, i.e., select a subset variants to stock and determine purchase quantities for each offered variant. We analyze this problem using a multinomial logit model to describe the consumer choice process and a newsboy model to represent the retailer's inventory cost. We show that the optimal assortment has a simple structure and provide insights on how various factors affect the optimal level of assortment variety. We also develop a formal definition of the level of fashion in a category using the theory of majorization and examine its implications for category profits.variety, inventory, retailing, consumer choice, assortment, optimization, newsboy, fashion, majorization, multinomial logit