قارن الطرق

	البرمجة الصحيحة المختلطة الحتمية	البرمجة الصحيحة المختلطة العشوائية
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1958–1960	1990s–2000s
صاحب الطريقة	Gomory, R. E.; Dantzig, G. B.; Land, A. H.; Doig, A. G.	Birge, J. R.; Louveaux, F.; Sen, S.
النوع	Mathematical programming / combinatorial optimization	Stochastic optimization model
المصدر التأسيسي	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. John Wiley & Sons, New York. ISBN: 9780471359432	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175
الأسماء البديلة	Deterministic MIP, Deterministic MILP/MIQP, Classical Mixed-Integer Programming, Deterministic MIP Optimization	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP
ذات صلة	6	5
الملخص	Deterministic Mixed-Integer Programming (MIP) is a mathematical optimization framework that finds the provably optimal solution to problems involving both continuous and integer decision variables under fully known, fixed coefficients and constraints. It is the foundational workhorse of operations research when all data are treated as certain.	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.