Efficient Optimization of Long - term Water Supply Portfolios

The use of temporary transfers, such as options and spot market leases, has grown as utilities attempt to meet increases in demand while reducing dependence on the expansion of costly infrastructure capacity (e.g. reservoirs). Earlier work has been done to construct optimal portfolios comprised of firm capacity, transfers, and the decision rules that determine the timing and volume of such transfers. However, such work has only focused on the short term (e.g. one year scenarios). Long term modeling efforts allow for the investigation of multi-year portfolios, but can greatly increase the computational burden. This work utilizes a coupled hydrologic-economic model to stochastically simulate the long-term performance of a city’s water supply portfolio. The model is linked with an optimization search algorithm that is designed to handle the high-frequency, low-amplitude noise inherent in stochastic simulations. This noise is a detriment to the accuracy and precision of the optimized solution, and has traditionally been controlled through investing greater computational effort in the simulation. However, given the complexity of some simulations and the computational effort required to manage this noise, a variance reduction technique known as the control variate method is applied within the simulation/optimization approach in order to more efficiently arrive at an accurate optimum. Random variation in model output (i.e. noise) is moderated using knowledge of random variations in stochastic input variables (e.g. reservoir inflows, demand), thereby reducing the computational burden by approximately 50%. Using these gains in efficiency, different scenarios and option contract structures are evaluated for their ability to reduce costs and adapt to growth in demand while continuing to meet reliability goals. INTRODUCTION Increased scarcity of water is leading many utilities to consider the integrated management of multiple water supply alternatives, as rising costs, environmental regulations, and public opposition provide growing disincentives to large-scale water supply projects (NRC 2001). Among these water supply alternatives are temporary water transfers, many of the uses and advantages of which having been documented (Michelsen and Young 1993; Lund and Israel 1995a; Characklis, Griffin et al. 1999; Knapp, Weinberg et al. 2003; Brown 2006). Managing a range of water supply alternatives can be analogous to the approach power utilities use to manage a “portfolio” of production assets, delivering energy to consumers through a mix of infrastructure and market-based transfers. In both cases, diversifying the range of alternatives provides utilities with the flexibility to reduce the firm, or baseload, capacity that must be maintained in order to meet demand, an advantage that generally translates to lower costs. Some work has been done in simulating and optimizing water supply portfolios over short-term planning horizons (e.g. one-year) (Smith and Marin 1993; Lund and Israel 1995b; Watkins and McKinney 1997; Wilchfort and Lund 1997; Characklis, Kirsch et al. 2006). While these shortterm studies provide insights into portfolio development, utilities are likely to be interested in arrangements designed to accommodate longer planning horizons, and the composition and computational approaches involved in formulating multi-year portfolios remains largely unexplored. Most of the earlier work has involved linear (LP) or dynamic (DP) programming, but simulation-based Monte Carlo (MC) methods can be used as a means of representing the uncertainty inherent in many water resource systems, as well as the probabilistic nature of the decision making (e.g. when to purchase leases or exercise options). MC methods can be particularly useful if the objective is characterized in terms of an expected value (e.g., expected 5