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Journal of Optimization
Volume 2013, Article ID 706176, 13 pages
Research Article

Optimal Multiplicative Generalized Linear Search Plan for a Discrete Random Walker

Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

Received 18 February 2013; Accepted 14 June 2013

Academic Editor: Bijaya Panigrahi

Copyright © 2013 Abd-Elmoneim Anwar Mohamed and Mohamed Abd Allah El-Hadidy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper formulates a search model that gives the optimal search plan for the problem of finding a discrete random walk target in minimum time. The target moves through one of n-disjoint real lines in : we have n-searchers starting the searching process for the target from any point rather than the origin. We find the conditions that make the expected value of the first meeting time between one of the searchers and the target finite. Furthermore, we show the existence of the optimal search plan that minimizes the expected value of the first meeting time and find it. The effectiveness of this model is illustrated using numerical example.