Application of a goal programming algorithm to incorporate environmental requirements in a multi-objective Columbia River Treaty Reservoir optimization model

Abstract

Due to large variability in streamflows and a lack of adequate reservoir storage capability in US territories, a treaty for the Columbia River was established between Canada and the USA in 1964. However, the treaty only considers power generation and flood control, and to address environmental issues, supplemental operating agreements have been signed each year since the 1990s. In this paper, we present a goal programming (GP) optimization algorithm to model the terms and conditions of the Supplemental Operating Agreements of the Columbia River Treaty (CRT) between BC Hydro and “United States Entities”. The GP technique is a multi-objective programming method that has been used in many different fields including reservoir optimization. After its introduction in 1961, it has been used extensively and is considered a robust modeling technique. The GP algorithm we have developed models the multi-objective problem using a combination of lexicographic and weighted goal-programming techniques. Case studies using four scenarios were performed to assess the satisfaction of environmental requirements for different target flow requirements at the US–Canadian border of the Columbia River. The GP algorithm we have developed allows for the constraints to deviate from a target value. This in turn provides modeling flexibility to handle infeasibility, typically encountered when hard constraints are included in the formulation of the optimization problem. GP can be used to investigate the trade-offs between multiple objectives by minimizing the deviation from user-specified target levels. In addition, the goal-programming formulation can represent more realistic real-time operational situations of a complex multi-reservoir system like the BC Hydro system.