Fuzzy-stochastic linear programming in water resources engineering

Linear programming (LP) is a popular method for optimization of a wide range of applications because of its simplicity and availability. However, LP, in its classic form, is not equipped to handle information with fizzy uncertainty. This paper considers the situations that both stochastic as well as fuzzy information are available and therefore could be coupled for improved optimization. For this purpose, fuzzy linear programming is modified by considering the stochastic properties of variables; so the new problem, fuzzy-stochastic linear programming (FSLP), can be formulated. The proposed method can be used as a complement and/or replacement of linear programming when enough data is not available for crisp statistical optimization. FSLP is then applied to a classic problem in water resources engineering, in particular the storage-yield problem applied to numerical data from Saugatuck reservoir. Simulation results demonstrate that for the presented scenario, the FSLP presents a more realistic water management, and can be used for replacement and/or complement of crisp LP optimization.