قارن الطرق

	البرمجة الصحيحة المختلطة	البرمجة الخطية
المجال	المحاكاة	التحسين
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1958–1960	1947
صاحب الطريقة	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)	George B. Dantzig
النوع	Mathematical optimization	Mathematical programming / continuous optimization
المصدر التأسيسي	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
الأسماء البديلة	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming	LP, linear optimization, Doğrusal Programlama (LP)
ذات صلة	6	4
الملخص	Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally.	Linear programming (LP), pioneered by George B. Dantzig in 1947, is a mathematical method for finding the best value of a linear objective function — such as minimum cost or maximum profit — subject to a set of linear inequality and equality constraints. It is the foundational technique in operations research and underlies production planning, resource allocation, logistics, diet problems, and countless other decision-making scenarios across engineering, economics, and the natural sciences.