قارن الطرق

	البرمجة الخطية	البرمجة الصحيحة
المجال	التحسين	التحسين
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1947	1958
صاحب الطريقة	George B. Dantzig	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
النوع	Mathematical programming / continuous optimization	Mathematical optimisation — exact combinatorial method
المصدر التأسيسي	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
الأسماء البديلة	LP, linear optimization, Doğrusal Programlama (LP)	IP, MIP, mixed-integer programming, mixed-integer linear programming
ذات صلة	4	4
الملخص	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.	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.