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Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis

Columbia Business School, Columbia University, 409 Uris Hall, 3022 Broadway, New York, New York 10027
c.maglaras{at}gsb.columbia.edu

Motivated by the recent adoption of tactical pricing strategies in manufacturing settings, this paper studies a problem of dynamic pricing for a multiproduct make-to-order system. Specifically, for a multiclass M_n/M/1 queue with controllable arrival rates, general demand curves, and linear holding costs, we study the problem of maximizing the expected revenues minus holding costs by selecting a pair of dynamic pricing and sequencing policies. Using a deterministic and continuous (fluid model) relaxation of this problem, which can be justified asymptotically as the capacity and the potential demand grow large, we show the following: (i) greedy sequencing (i.e., the cµ-rule) is optimal, (ii) the optimal pricing and sequencing decisions decouple in finite time, after which (iii) the system evolution and thus the optimal prices depend only on the total workload. Building on (i)–(iii), we propose a one-dimensional workload relaxation to the fluid pricing problem that is simpler to analyze, and leads to intuitive and implementable pricing heuristics. Numerical results illustrate the near-optimal performance of the fluid heuristics and the benefits from dynamic pricing.

Subject classifications: revenue management; yield management; dynamic pricing; queuing; sequencing; fluid models.
History: Received November 2003; revision received August 2005; accepted September 2005.

This article has been cited by other articles:

				S. Celik and C. Maglaras Dynamic Pricing and Lead-Time Quotation for a Multiclass Make-to-Order Queue Management Science, June 1, 2008; 54(6): 1132 - 1146. [Abstract] [PDF]