A diffusion model for the control of a multipurpose reservoir system

This paper develops a methodology for optimizing operation of a multipurpose reservoir with a finite capacity V. The input of water into the reservoir is a Wiener process with positive drift. There are n purposes for which water is demanded. Water may be released from the reservoir at any rate, and the release rate can be increased or decreased instantaneously with zero cost. In addition to the reservoir, a supplementary source of water can supply an unlimited amount of water demanded during any period of time. There is a cost of C_i dollars per unit of demand supplied by the supplementary source to the i^th purpose (i = 1, 2, …, n). At any time, the demand rate R_i associated with the i^th purpose (i = 1, 2, …, n) must be supplied. A controller must continually decide the amount of water to be supplied by the reservoir for each purpose, while the remaining demand will be supplied through the supplementary source with the appropriate costs. We consider the problem of specifying an output policy which minimizes the long run average cost per unit time.