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Customer Scheduling with Incomplete Information

Published online by Cambridge University Press:  27 July 2009

Ulrich Rieder  and
Jürgen Weishaupt
Ulrich Rieder
Affiliation:
Department of Mathematics, University of Ulm, 89069 Ulm, Germany
Jürgen Weishaupt
Affiliation:
Department of Mathematics, University of Ulm, 89069 Ulm, Germany
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Abstract

A stochastic scheduling model with linear waiting costs and unknown routing probabilities is considered. Using a Bayesian approach and methods of Bayesian dynamic programming, we investigate the finite-horizon stochastic scheduling problem with incomplete information. In particular, we study an equivalent nonstationary bandit model and show the monotonicity of the total expected reward and of the Gittins index. We derive the monotonicity and well-known structural properties of the (greatest) maximizers, the so-called stay-on-a-winnerproperty and the stopping-property. The monotonicity results are based on a special partial ordering on .

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 269 - 284
Copyright
Copyright © Cambridge University Press 1995

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