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Price-Directed Control of a Closed Logistics Queueing Network

Graduate School of Business, University of Chicago, Chicago, Illinois 60637
dan.adelman{at}gsb.chicagogsb.edu

Motivated by one of the leading intermodal logistics suppliers in the United States, we consider an internal pricing mechanism for managing a fleet of service units (shipping containers) flowing in a closed queueing network. Nodes represent geographic locations, and arcs represent travel between them. Customer requests for arcs arrive over time, and the problem is to find an accept/reject policy that maximizes the long-run time average reward rate from accepting requests.

We formulate the problem as a semi-Markov decision process and give a simple linear program that provides an upper bound on the optimal reward rate. Using Palm calculus, we derive a nonlinear program that approximately captures queueing and stockout effects on the network. Using its optimal Lagrange multipliers, we construct a simple functional approximation to the dynamic programming value function. The resulting policy is computationally efficient and produces superior economic performance as compared with other policies. Furthermore, it provides a methodologically grounded solution to the firm's internal pricing problem.

Subject classifications: dynamic programming/optimal control; semi-Markov; programming; nonlinear; queues; networks; industries; transportation/shipping.
History: Received May 2004; revision received September 2006; accepted September 2006.