An interval-fuzzy two-stage stochastic programming model for filter management of hydraulic system under uncertainties is proposed in this paper. The interval-fuzzy two-stage stochastic programming model integrates the two-stage stochastic programming, fuzzy programming, and interval parameter nonlinear programming into an optimization model of contamination control in hydraulic system. For a typical hydraulic system, it can be used for expressing the uncertainties existed in the purchase cost of filters, contamination ingression and generation rates, and contamination-holding capacity as probability functions, interval numbers, and fuzzy sets. The developed method is applied to examining the decisions on the adoption of bypass filter and selection of filters within multi-segments, multi-period, and multi-option context. All potential scenarios of filters management policy associated with different economic penalties, objectives, and reliability of system are analyzed. The results of the illustrative example show that the reasonable solutions are generated, including binary and continuous variables which help the decision maker identify optimal strategies for filter allocation and selection, planning the adoption of bypass filter under different working conditions.
A two-stage stochastic programming model for production lot-sizing and scheduling under demand and raw material quality uncertainties
