Advances in Decision Sciences
Volume 2011 (2011), Article ID 617812, 11 pages
Research Article

Explicit Solution of the Average-Cost Optimality Equation for a Pest-Control Problem

Department of Statistics, Athens University of Economics and Business, Patission 76, 10434 Athens, Greece

Received 16 December 2010; Revised 18 March 2011; Accepted 29 March 2011

Academic Editor: Raymond Chan

Copyright © 2011 Epaminondas G. Kyriakidis. 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.


We introduce a Markov decision process in continuous time for the optimal control of a simple symmetrical immigration-emigration process by the introduction of total catastrophes. It is proved that a particular control-limit policy is average cost optimal within the class of all stationary policies by verifying that the relative values of this policy are the solution of the corresponding optimality equation.