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Optimal search for a randomly moving object

Published online by Cambridge University Press:  14 July 2016

R. R. Weber
R. R. Weber*
Affiliation:
University of Cambridge
*
∗Postal address: Engineering Department, Control and Management Systems Group, Mill Lane, Cambridge, CB2 1RX, UK.
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Abstract

It is desired to minimize the expected cost of finding an object which moves back and forth between two locations according to an unobservable Markov process. When the object is in location i (i = 1, 2) it resides there for a time which is exponentially distributed with parameter λ1 and then moves to the other location. The location of the object is not known and at each instant until it is found exactly one of the two locations must be searched. Searching location i for time δ costs ciδ and conditional on the object being in location i there is a probability αiδ + o(δ) that this search will find it. The probability that the object starts in location 1 is known to bé p1(0). The location to be searched at time t is to be chosen on the basis of the value of p1(t), the probability that the object is in location 1, given that it has not yet been discovered. We prove that there exists a threshold Π such that the optimal policy may be described as: search location 1 if and only if the probability that the object is in location 1 is greater than Π. Expressions for the threshold Π are given in terms of the parameters of the model.

Keywords

MARKOV PROCESSESOPTIMAL CONTROLSEARCH PROBLEMS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 708 - 717
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This research was conducted at the Department of Electrical Engineering and Computer Sciences and Electronics Research Laboratory, University of California, Berkeley and was supported by the Office of Naval Research Contract N00014-80-C-0507.

References

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