قارن الطرق

	خوارزمية فاغنر-ويتِن	تفكيك بندر	توليد الأعمدة (دانزيغ-وولف)	الطريقة السيمبلكس
المجال	بحوث العمليات	بحوث العمليات	بحوث العمليات	بحوث العمليات
العائلة	Machine learning	Machine learning	Machine learning	Machine learning
سنة النشأة	1958	1962	1960	1947
صاحب الطريقة	Harvey M. Wagner and Thomson M. Whitin	Jacques F. Benders	George B. Dantzig and Philip Wolfe	George Dantzig
النوع	algorithm	algorithm	algorithm	algorithm
المصدر التأسيسي	Wagner, H. M., & Whitin, T. M. (1958). Dynamic version of the economic lot size model. Management Science, 5(1), 89-96.	Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252.	Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111.	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
الأسماء البديلة	Wagner-Whitin lot-sizing, dynamic lot-sizing algorithm	cutting plane method, constraint generation	Dantzig-Wolfe decomposition, column generation method	simplex algorithm
ذات صلة	3	3	3	4
الملخص	The Wagner-Whitin Algorithm, introduced by Harvey M. Wagner and Thomson M. Whitin in 1958, is a dynamic programming solution to the capacitated lot-sizing problem. It determines optimal production quantities over multiple periods to minimize the total cost of production setup and inventory holding while meeting deterministic demand.	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.	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.	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.