Dynamic Pricing Strategies for Multiproduct Revenue Management Problems

Abstract

C onsider a firm that owns a fixed capacity of a resource that is consumed in the production or delivery of multiple products. The firm strives to maximize its total expected revenues over a finite horizon, either by choosing a dynamic pricing strategy for each product or, if prices are fixed, by selecting a dynamic rule that controls the allocation of capacity to requests for the different products. This paper shows how these wellstudied revenue management problems can be reduced to a common formulation in which the firm controls the aggregate rate at which all products jointly consume resource capacity, highlighting their common structure, and in some cases leading to algorithmic simplifications through the reduction in the control dimension of the associated optimization problems. In the context of their associated deterministic (fluid) formulations, this reduction leads to a closed-form characterization of the optimal controls, and suggests several natural static and dynamic pricing heuristics. These are analyzed asymptotically and through an extensive numerical study. In the context of the former, we show that "resolving" the fluid heuristic achieves asymptotically optimal performance under fluid scaling.

A Dynamic Near-Optimal Algorithm for Online Linear Programming

“…On the other hand, in the management science community, a dynamic and optimal pricing strategy for various online resource allocation problems has always been an important research topic, some literatures include [10,11,12,19,15,7,4]. In [12,11,4], the arrival process are assumed to be price sensitive.…”

“…The organizer needs to allocate the network capacity online to those bidders to maximize social welfare. A similar format also appears in online auctions [2], online keyword matching problems [9,13,16], online packing problems [5], and various other online revenue management and resource allocation problems [15,7,4].…”

List pricing versus dynamic pricing: Impact on the revenue risk

“…They conclude that for large sized problems with known demand functions and no constraint on price setting, there were no great benefits when using dynamic pricing. Cooper (2002) and Maglaras and Meissner (2006) present results of contrasting static and resolving pricing policies. Cooper (2002) provides an example showing that resolving policies does not necessarily lead to a better result, whereas the numerical results of Maglaras and Meissner (2006) show that its expected revenue is superior to static pricing in non-asymptotically settings.…”

“…Maglaras and Meissner (2006) demonstrate that resolving the deterministic problem at each time step and implementing the resulting prices often offers better results than a static policy. Given the choice between dynamic and static pricing with capacity control, Gallego and van Ryzin (1994); Talluri and van Ryzin (2005) show that dynamic pricing should be preferred, as price flexibility allows for reducing simultaneously demand and increasing revenue.…”

“…We approach this question by comparing results from numerical experiments conducted with these two different pricing policies. In particular, we use the dynamic pricing policy and the list price capacity control policy proposed by Maglaras and Meissner (2006). The dynamic pricing policy resolves the revenue management problem at each time step and updates the prices.…”