More efficient optimization of long‐term water supply portfolios

Abstract

[1] The use of temporary transfers, such as options and 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 comprising firm capacity and transfers, using decision rules that determine the timing and volume of transfers. However, such work has only focused on the short-term (e.g., 1-year scenarios), which limits the utility of these planning efforts. Developing multiyear portfolios can lead to the exploration of a wider range of alternatives but also increases the computational burden. This work utilizes a coupled hydrologic-economic model to simulate the long-term performance of a city's water supply portfolio. This stochastic model is linked with an optimization search algorithm that is designed to handle the high-frequency, low-amplitude noise inherent in many simulations, particularly those involving expected values. This noise is detrimental to the accuracy and precision of the optimized solution and has traditionally been controlled by investing greater computational effort in the simulation. However, the increased computational effort can be substantial. This work describes the integration of a variance reduction technique (control variate method) within the simulation/optimization as a means of more efficiently identifying minimum cost portfolios. 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 computing time by 50% or more. Using these efficiency gains, water supply portfolios are evaluated over a 10-year period in order to assess their ability to reduce costs and adapt to demand growth, while still meeting reliability goals. As a part of the evaluation, several multiyear option contract structures are explored and compared.

Managing population and drought risks using many‐objective water portfolio planning under uncertainty

“…Leasing and adaptive options supply instruments can significantly lower water supply costs and improve reliability while enhancing the overall efficiency of alternatives (both logistically and volumetrically). The work confirmed the cost savings at high reliability suggested in prior studies [ Characklis et al , 2006; Kirsch et al , 2009]. Our “many‐objective” analysis shows that cost savings appeared even in portfolios that followed a more conservative water supply approach by using leases and options sparingly as a supplement to the city's permanent rights.…”

“…Table 2 shows that Case B adds the dropped transfers objective f dropped and the cost variability objective f costvar with an additional constraint on cost variability, c costvar . Prior work has shown that adding temporary transfers such as options and leases can reduce the city's supply cost while maintaining high reliability [ Characklis et al , 2006; Kirsch et al , 2009]. The purpose of this section is to provide a broader understanding of the cost effectiveness and efficiencies provided by the adaptive options contract.…”

“…The objective function calculations are strongly representative of their expected values. A smaller sample size, though, could also generate useful results, especially when coupled with variance reduction techniques as in work by Kirsch et al [2009]. We were highly conservative in this study with the number of Monte Carlo samples used per portfolio evaluation because we had sufficient parallel computational resources to do so.…”

“…Monthly draws are performed that simulate 10 years of water supply decisions, such that a reservoir mass balance, municipal demand, lease pricing distribution, and portfolio performance is tracked for each of the 120 simulation months. In a given month t , the city's supply is denoted by S t and the city's expected supply, based on historical averages for permanent rights allocation, is denoted by The initial condition in the model specifies a starting reservoir volume and volume of water for the city's supply, In this study, the initial condition for the water supply was set to 0.3 times the city's permanent rights, consistent with Kirsch et al [2009]. For the multiyear planning scenario, also represents the water that the city has on hand in the beginning of each subsequent simulation year.…”

“…Beyond price volatility, options also provide the added benefit of allowing planners to delay transfer purchase decisions until they have more up‐to‐date information on the state of their water supply systems. Several studies have shown that water portfolio planning with both options and leases can reduce the costs associated with maintaining reliable urban water supplies [ Lund , 1995; Wilchfort and Lund , 1997; Watkins and McKinney , 1999; Jenkins and Lund , 2000; Characklis et al , 2006; Kirsch et al , 2009]. These prior studies have used a range of deterministic and stochastic single‐objective planning formulations to minimize the expected costs of reliably meeting urban water demand.…”