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Bounds for discounted stochastic scheduling problems

Published online by Cambridge University Press:  14 July 2016

K. D. Glazebrook
K. D. Glazebrook*
Affiliation:
University of Newcastle upon Tyne
*
∗ Postal address: Department of Mathematics and Statistics, The University, Newcastle upon Tyne NE1 7RU, UK.
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Abstract

Suppose that π is a policy for resource allocation in a stochastic environment and π ∗ is an optimal policy. Two existing procedures for policy evaluation are described and compared. Both of these evaluate π by means of upper bounds on R(π ∗) – R(π), the total reward lost when making resource allocations according to π rather than π∗. The bounds developed by these two methods are called Type 1 and Type 2. We demonstrate by example that neither of these procedures dominates the other in the sense of always yielding tighter bounds. A modification to Type 2 bounds is proposed resulting in an improved procedure which always dominates the Type 1 approach.

Keywords

GITTINS INDEXSTRATEGY EVALUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 791 - 801
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

During the course of this research the author was supported by the National Research Council as a Senior Research Associate at the Department of Operations Research, Naval Postgraduate School, Monterey, CA 93943–5000, USA.

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