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Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Graduate School of Business, Columbia University, New York, New York 10027
obesbes{at}wharton.upenn.edu
c.maglaras{at}gsb.columbia.edu

We consider a revenue-maximizing make-to-order manufacturer that serves a market of price- and delay-sensitive customers and operates in an environment in which the market size varies stochastically over time. A key feature of our analysis is that no model is assumed for the evolution of the market size. We analyze two main settings: (i) the size of the market is observable at any point in time; and (ii) the size of the market is not observable and hence cannot be used for decision making. We focus on high-volume systems that are characterized by large processing capacities and market sizes, and where the latter fluctuate on a slower timescale than that of the underlying production system dynamics. We develop an approach to tackle such problems that is based on an asymptotic analysis and that yields near-optimal policy recommendations for the original system via the solution of a stochastic fluid model.

Subject classifications: revenue management; dynamic pricing; market uncertainty; queueing; state-dependent queues; asymptotic analysis.
History: Received August 2007; revision received February 2008; accepted April 2008.