Planning reservoir operations with imprecise objectives

Abstract

Inclusion of soft elements in the formulation of water resource system problems has always received attention by water resource researchers and planners. In the case of reservoir operation, its multipurpose characteristic has been approached through the formulation of a multiobjective optimization problem. However, the non-quantitative nature of some objectives, like environmental and recreational objectives, has always represented a complex issue to deal with either in simulation or optimization models. Imprecise objectives and constraints have not been easily incorporated into a classical crisp model. Fuzzy sets theory allows us to deal with information which is valuable but not precise. Systems analysis tools such as dynamic programming provide the way to find optimal operational policies of a multipurpose reservoir. Hence, a fuzzy dynamic programming technique should allow finding a set of optimal controls or releases when the problem is addressed as a multidecision problem with imprecise objectives. A methodology is developed based on Bellman and Zadeh's approach. The methodology is tested through its application in a case study. Two cases are considered: deterministic and implicit stochastic. Grey Mountain Reservoir, a proposed water resource project in the Cache La Poudre River basin, is considered as the case study. The fuzzy goal is represented by the stored volume that the reservoir may have at the end of its yearly operation, and the fuzzy constraints are represented by the water uses or objectives, like municipal and industrial water supply, flood control space, hydropower, rafting, kayaking, angling and fish habitat, embedded with a subjective linguistic term. Membership functions of the fuzzy goal and fuzzy constraints are developed. In the deterministic case, fuzzy dynamic programming results show monthly releases and storage levels behaved as expected for reservoir operation problems. The achievement of the fuzzy goal was acceptable and in case of the water uses or objectives, the most achievable were flood control, fish habitat and water supply, while the less achievable ones were rafting, kayaking, angling and hydropower, with a high relative variability in the degree of their achievement. In the stochastic case, the results show the expected degree of satisfaction for the fuzzy goal was higher than for the deterministic case. In case of the water uses or objectives, the level of the expected achievement was in general similar to the deterministic case results; the most achievable objectives were also flood control, water supply and fish habitat, and the less achievable ones were again rafting, kayaking, angling and hydropower, and the relative variability of the degree of satisfaction was also high in several cases. Monthly storage levels were fit to linear models to obtain operating rules and the estimated values were further used in a simulation model to obtain monthly storage levels and releases. The comparison of simulated and optimal results reveals a good fit. Thus, operating rules can be used to make decisions about monthly releases from the reservoir. Finally, the results reveal that with the fuzzy approach it is possible to incorporate imprecision and non-commensurate issues in the formulation of objectives and constraints of water resources problems. In addition, the form of the results directly indicates the expected values and the variability in the degree of achievement of those objectives and constraints, providing commensurable and easily-interpreted measures of comparison among diverse and difficult-to-quantify objectives.