Linganisha mbinu

	Algoriti ya Wagner-Whitin	Uharibifu wa Benders	Njia ya Simplex
Nyanja	Utafiti wa Operesheni	Utafiti wa Operesheni	Utafiti wa Operesheni
Familia	Machine learning	Machine learning	Machine learning
Mwaka wa asili	1958	1962	1947
Mwanzilishi	Harvey M. Wagner and Thomson M. Whitin	Jacques F. Benders	George Dantzig
Aina	algorithm	algorithm	algorithm
Chanzo asilia	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. (1963). Linear Programming and Extensions. Princeton University Press.
Majina mbadala	Wagner-Whitin lot-sizing, dynamic lot-sizing algorithm	cutting plane method, constraint generation	simplex algorithm
Zinazohusiana	3	3	4
Muhtasari	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.	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.