Management of Uncertain Information for Environmental Systems Using a Multistage Fuzzy-Stochastic Programming Model with Soft Constraints

In this study, a multistage fuzzy-stochastic programming model with soft constraints (FSPM-SC) is developed for managing environmental systems associated with uncertain information. The developed model can deal with uncertainties expressed as probability distributions and fuzzy sets; it can also reflect the dynamics in terms of decisions for waste-flow allocation and capacity expansion, through transactions at discrete points of a complete scenario set over a multistage context. The results indicate that solutions have been generated for binary and continuous decision variables under fuzzy and random information. They can be used for generating waste-flow-allocation pattern and facility-capacity-expansion scheme with a cost-effective manner. Sensitivity analyses are also conducted to demonstrate that the violation of waste-disposal-demand constraint has significant effect on reducing system cost.