قارن الطرق

	البرمجة الصحيحة العشوائية	البرمجة الصحيحة المختلطة العشوائية
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1955	1990s–2000s
صاحب الطريقة	Dantzig, G. B.; Beale, E. M. L.	Birge, J. R.; Louveaux, F.; Sen, S.
النوع	Optimization under uncertainty with discrete decisions	Stochastic optimization model
المصدر التأسيسي	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer, New York. ISBN: 978-1-4614-0237-4	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175
الأسماء البديلة	SIP, Stochastic IP, Integer Stochastic Programming, Mixed-Integer Stochastic Programming	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP
ذات صلة	6	5
الملخص	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.	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.