Two-stage chance-constrained programming for system optimization under uncertainty

This study focuses on the two-stage stochastic program (SP) with chance constraints for decision-making in system optimization under normally-distributed uncertainties. At stage-I, the integer decision variables are determined such that the expected objective function is optimized and operational constraints can be satisfied with high chance. Once the uncertainty is realized, the optimal stage-II decision is made accordingly to adjust recourse operations. The introduction of chance constraints in comparison with traditional SP helps mitigation of system conservativeness because the worst-scenario less likely occurs and override operations can be employed to prevent catastrophic outcomes. The resulting chance-constrained two-stage SP (CC-SP) is solved through the linear decision-rule in which stage-II variables are parameterized by uncertainties. Such an optimization problem can be reformulated as a mixed-integer second-order cone program that is solved efficiently. Furthermore, the posterior evaluation together with the Balas cut is integrated with the CC-SP to improve the solution quality. A refinery optimization problem is solved through the proposed scheme to verify the computational efficiency and probabilistic feasibility.