Optimal control of dams using Pλ, τM policies and penalty cost

Abstract

We discuss recent results on optimal control of dams using P λ, τ M policies and penalty cost. Specifically, we assume that the water is released at one of two rates, zero or M, per a unit of time. The release rate is zero until the water reaches level λ, and then the water is released at rate M, until it reaches level τ(τ < λ). Once the water reaches level T again the release rate remains zero until level λ is reached again and the cycle is repeated. At any time, the release rate can be switched from zero to M, with a starting cost of MK 1, or switched from M to zero at a closing cost of MK 2. For each unit of output, a reward A is received. Moreover, there is a penalty cost that accrues at rate g, where g is a bounded measurable function defined on the state space of the content process. We determine the optimal control policy according to the total discounted cost and the long-run average cost criteria.