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

We discuss recent results on optimal control of dams using Pλ,τM 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 MK1, or switched from M to zero at a closing cost of MK2. 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.