方法对比

	Policy Scenario Integer Programming	鲁棒整数规划	随机整数规划
领域	仿真	仿真	仿真
方法族	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1950s–1960s (scenario extension: 1990s onwards)	2003	1955
提出者	Operations research community (Dantzig, Gomory, and others)	Bertsimas, D. and Sim, M.	Dantzig, G. B.; Beale, E. M. L.
类型	Discrete combinatorial optimization under scenario uncertainty	Deterministic robust optimization with integer variables	Optimization under uncertainty with discrete decisions
开创性文献	Birge, J. R., & Louveaux, F. (2011). Introduction to Stochastic Programming (2nd ed.). Springer. ISBN: 9781461402367	Bertsimas, D., Sim, M. (2003). Robust discrete optimization and network flows. Mathematical Programming, 98(1-3), 49-71.	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer, New York. ISBN: 978-1-4614-0237-4
别名	PSIP, scenario-based integer programming, policy-driven IP, scenario integer optimization	RIP, Robust IP, Robust Combinatorial Optimization, Integer Robust Optimization	SIP, Stochastic IP, Integer Stochastic Programming, Mixed-Integer Stochastic Programming
相关	2	6	6
摘要	Policy Scenario Integer Programming (PSIP) solves an integer programming model — where some or all decision variables must take whole-number values — separately under each of several distinct policy scenarios, then compares objective values, feasibility, and solution structures to identify which policy environment leads to the best discrete allocation or assignment outcome.	Robust Integer Programming (RIP) finds integer or binary solutions that remain feasible and near-optimal across all scenarios in a prescribed uncertainty set. Rather than assuming exact knowledge of data, RIP hedges against the worst-case realization of uncertain costs or constraint coefficients, delivering decisions that are guaranteed to perform well even when inputs deviate from their nominal values.	Stochastic Integer Programming (SIP) is an optimization framework that combines integer (discrete) decision variables with explicit probabilistic modeling of uncertainty. It seeks the best here-and-now decision that minimizes expected cost (or maximizes expected benefit) across a distribution of future scenarios, accounting for the fact that some decisions must be made before uncertainty is resolved.