手法を比較

	ロバスト混合整数計画法	確率的混合整数計画法
分野	シミュレーション	シミュレーション
系統	Process / pipeline	Process / pipeline
提唱年	1998–2004	1990s–2000s
提唱者	Ben-Tal & Nemirovski; Bertsimas & Sim	Birge, J. R.; Louveaux, F.; Sen, S.
種類	Deterministic robust reformulation of MIP under uncertainty	Stochastic optimization model
原典	Bertsimas, D., Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53.	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175
別名	RMIP, Robust MIP, Uncertain MIP, Robust MILP/MIQP	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP
関連	4	5
概要	Robust Mixed-Integer Programming (RMIP) combines mixed-integer programming with robust optimization to find solutions that remain feasible and near-optimal despite uncertain parameters. Instead of assuming fixed data, it protects decisions against adversarial or worst-case realizations of uncertain inputs, using an explicit uncertainty set to control the degree of conservatism while preserving the combinatorial structure of integer decisions.	Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints.