手法を比較

	動的計画法	ゴールプログラミング	線形計画法
分野	最適化	意思決定	最適化
系統	Process / pipeline	MCDM	Process / pipeline
提唱年	1957	1955	1947
提唱者	Richard Bellman	Charnes, A., Cooper, W. W.	George B. Dantzig
種類	Exact combinatorial optimization via recursive decomposition	Multi-objective optimisation — weighted/lexicographic goal deviation minimisation	Mathematical programming / continuous optimization
原典	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Charnes, A., Cooper, W. W. (1955). Optimal estimation of executive compensation by linear programming. Management Science	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
別名	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	—	LP, linear optimization, Doğrusal Programlama (LP)
関連	3	8	4
概要	Dynamic Programming (DP) is an exact optimization technique introduced by Richard Bellman in 1957 for solving multi-stage decision problems. It decomposes a complex problem into simpler, overlapping subproblems, solves each subproblem once, and stores the results to avoid redundant computation. Grounded in the Principle of Optimality, DP guarantees globally optimal solutions whenever the problem exhibits overlapping subproblems and optimal substructure.	GOAL-PROGRAMMING (Goal Programming — Minimise deviations from multiple aspiration levels) is a ranking multi-criteria decision-making (MCDM) method introduced by Charnes, A., Cooper, W. W. in 1955. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.	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.