Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T01:19:30.478Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic search for a moving target

Part of: Operations research and management science Markov processes

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Supported by a grant from the Israel Foundation Trustees.

References

Assaf, D, and Zamir, S. (1985) Optimal sequential search: a Bayesian approach. Ann. Statist. 13, 1213–1221.Google Scholar
Assaf, D. and Zamir, S. (1987) Continuous and discrete search for one of many objects. Operat. Res. Lett. 6, 205–209.Google Scholar
Brown, S. S. (1980) Optimal search for moving target in discrete time and space. Operat. Res. 28, 1275–1289.Google Scholar
Dobbie, J. M. (1974) A two cell model of search for a moving target. Operat. Res. 22, 79–92.Google Scholar
Dobbie, J. M. (1975) Search for an avoiding target. SIAM J. Appl. Math. 28, 72–86.CrossRefGoogle Scholar
Eagle, J. N. (1984) The optimal search for moving target when the search path is constrained. Operat. Res. 32, 1107–1115.CrossRefGoogle Scholar
Fleming, W. H. and Rishel, R. W. (1975) Deterministic and Stochastic Optimal Control. Springer-Verlag, New York.Google Scholar
Gal, S. (1980) Search Games. Academic Press, San Francisco.Google Scholar
Pollock, S. M. (1970) A simple model of search for a moving target. Operat. Res. 18, 883–903.Google Scholar
Ross, S. M. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, San Francisco.Google Scholar
Schweitzer, P. J. (1971) Threshold probabilities when searching for moving targets. Operat. Res. 19, 707–709.CrossRefGoogle Scholar
Sharlin, A. (1987) Optimal search for one of many objects hidden in two boxes. European J. Operat. Res. 32, 251–259.CrossRefGoogle Scholar
Sharlin-Bilitzky, A. (1990) Optimal Search for Static and Moving Targets. , The Hebrew University, Jerusalem.Google Scholar
Stone, L. D. (1975) Theory of Optimal Search. Academic Press, San Francisco.Google Scholar
Stone, L. D. (1977) Search for targets with generalized conditionally deterministic motion. SIAM J. Appl. Math. 33, 456–468.Google Scholar
Stone, L. D. (1979) Necessary and sufficient conditions for optimal search plans for moving targets. Math. Operat. Res. 4, 431–440.Google Scholar
Stone, L. D. and Kadane, J. B. (1981) Optimal whereabouts search for a moving target. Operat. Res. 29, 1154–1166.Google Scholar
Stone, L. D. and Richardson, H. R. (1974) Search for targets with conditionally deterministic motion. SIAM J. Appl. Math. 27, 239–255.Google Scholar
Stromquist, W. R. and Stone, L. D. (1981) Constrained optimization of functionals with search theory applications. Math. Operat. Res. 6, 518–529.CrossRefGoogle Scholar
Varaiya, P. (1972) Notes on Optimization. Van Nostrand Reinhold, New York.Google Scholar
Washburn, A. R. (1980) A search for a moving target. Naval Res. Logist. Quart. 27, 315–321.Google Scholar
Weber, R. R. (1986) Optimal search for a randomly moving object. J. Appl. Prob. 23, 708–717.Google Scholar
Whittle, P. (1982) Optimization over Time 1. Wiley, New York.Google Scholar