手法を比較

	整数計画法	動的計画法	線形計画法
分野	最適化	最適化	最適化
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1958	1957	1947
提唱者	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Richard Bellman	George B. Dantzig
種類	Mathematical optimisation — exact combinatorial method	Exact combinatorial optimization via recursive decomposition	Mathematical programming / continuous optimization
原典	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
別名	IP, MIP, mixed-integer programming, mixed-integer linear programming	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	LP, linear optimization, Doğrusal Programlama (LP)
関連	4	3	4
概要	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.	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.	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.