CHARACTERIZATION OF THE OPTIMAL CLASS OF OUTPUT POLICIES IN A CONTROL MODEL OF A FINITE DAM.

The optimal class of output policies in a control model of a dam having a finite capacity is characterized. The input of water into the dam is determined by a Wiener process with positive drift. Water may be released at either of two possible rates 0 or M. At any time the output rate can be increased from 0 to M with a cost of K, (K greater than equivalent to 0) or decreased from M to 0 with zero cost, any such changes taking effect instantaneously. There is a reward of A monetary units for each unit of output, (A greater than equivalent to 0). The problem is to formulate an optimal output policy which maximizes the long-run average net reward per unit time.