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Dynamic search for a moving target

Part of: Markov processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

David Assaf  and
Ariela Sharlin-Bilitzky
David Assaf
Affiliation:
The Hebrew University of Jerusalem
Ariela Sharlin-Bilitzky*
Affiliation:
The Hebrew University of Jerusalem
*
∗ Postal address for both authors: Department of Statistics, The Hebrew University, 91905 Jerusalem, Israel.
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Abstract

An object is hidden in one of two boxes and occasionally moves between the boxes in accordance with some specified continuous-time Markov process. The objective is to find the object with a minimal expected cost. In this paper it is assumed that search efforts are unlimited. In addition to the search costs, the ‘real time' until the object is found is also taken into account in the cost structure. Our main results are that the optimal policy may consist of five regions and that the controls applied should be of the extreme 0 or ∞ type. The resulting expected cost compares favorably with that of the expected cost with bounded controls studied previously in the search literature.

Keywords

OPTIMAL SEARCH POLICYDYNAMIC PROGRAMMINGOPTIMALITY EQUATIONMARKOV CHAINS WITH CONTINUOUS PARAMETER

MSC classification

Primary: 90B40: Search theory
Secondary: 90C39: Dynamic programming 90C40: Markov and semi-Markov decision processes 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 438 - 457
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Supported by a grant from the Israel Foundation Trustees.

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