Capacity expansion for water resource facilities: a control theoretic algorithm for nonstationary uncertain demands

Abstract

Municipal water and waste water investments represent a large and important segment of the expenditures made by local governments. The response of designers to the problem of sizing increments to capacity has been to overbuild in order to assure safe and adequate supplies. A growing body of evidence suggests that the magnitude of overbuilding has been excessive. Earlier research has neglected to model demand growth as uncertain with the possibility of both nonstationary mean and variance. Also, failure to recognize the problem as one of closed loop control has resulted in erroneous modeling efforts. The basic approach in this research is to model using stochastic dynamic programming. The criterion was minimization of expected cost. Excess capacity, the state of the system, increases due to investment decisions. Negative excess capacity implies shortage. As time progresses known, but possibly uncertain demands impinge upon the system. Overall, several highly flexible capacity planning models for nonstationary demands can be formulated, are computationally feasible, and produce excellent approximations to known solutions. However, these models should only be used after sensitivity testing in conjunction with simpler approaches.