قارن الطرق

	توليد الأعمدة (دانزيغ-وولف)	تفكيك بندر	الطريقة السيمبلكس
المجال	بحوث العمليات	بحوث العمليات	بحوث العمليات
العائلة	Machine learning	Machine learning	Machine learning
سنة النشأة	1960	1962	1947
صاحب الطريقة	George B. Dantzig and Philip Wolfe	Jacques F. Benders	George Dantzig
النوع	algorithm	algorithm	algorithm
المصدر التأسيسي	Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111.	Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252.	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
الأسماء البديلة	Dantzig-Wolfe decomposition, column generation method	cutting plane method, constraint generation	simplex algorithm
ذات صلة	3	3	4
الملخص	Column Generation, developed by George B. Dantzig and Philip Wolfe in 1960, is a powerful optimization technique for solving large-scale linear programming problems with special structure. Also known as Dantzig-Wolfe Decomposition, it decomposes the problem into a master problem (restricted to a subset of variables/columns) and a pricing subproblem (identifying new variables), iteratively improving the solution by introducing only relevant columns.	Benders Decomposition, introduced by Jacques F. Benders in 1962, is a powerful algorithmic framework for solving large-scale mixed-integer programming (MIP) problems. It decomposes the problem into a master problem (controlling complicating variables) and subproblems (handling remaining variables), using cutting planes generated from subproblem dual information to iteratively tighten the master problem.	The Simplex Method, developed by George Dantzig in 1947, is a foundational algorithm for solving linear programming problems. It systematically explores vertices of the feasible region to find the optimal solution where the objective function is maximized or minimized subject to linear constraints.