Optimal search for a moving target with the option to wait

Optimal search for a moving target with the option to wait

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Article ID: iaor200970182
Country: United States
Volume: 56
Issue: 6
Start Page Number: 526
End Page Number: 539
Publication Date: Sep 2009
Journal: Naval Research Logistics
Authors: , ,
Keywords: markov processes
Abstract:

We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (1970). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Moreover, when the agent searches the location that contains the object, he finds it with probability 1 (i.e. there is no overlooking). Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber (1986)). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting.

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