Optimal control of a finite dam using PMλΤ policies and penalty cost: total discounted and long run average cases

Abstract

Zuckermann [10] considers the problem of optimal control of a finite dam using policies, assuming that the input process is Wiener with drift term μ ≧ 0. Lam Yeh and Lou Jiann Hua [7] treat the case where the input is a Wiener process with a reflecting boundary at zero, with drift term μ ≧ 0, using the long-run average cost and total discounted cost criteria. Attia [1] obtains results similar to those of Lam Yeh and Lou Jiann Hua for the long-run average case and extends them to include μ < 0. In this paper we look further into the results of Zuckerman [10], simplify some of the work of Attia [1], [2], offering corrections to some of his formulae and extend the results of Lam Yeh and Lou Jiann Hua [7].