So sánh phương pháp

	Lập trình động	Lập trình nguyên (Integer Programming
Lĩnh vực	Tối ưu hóa	Tối ưu hóa
Họ	Process / pipeline	Process / pipeline
Năm ra đời	1957	1958
Người khởi xướng	Richard Bellman	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
Loại	Exact combinatorial optimization via recursive decomposition	Mathematical optimisation — exact combinatorial method
Công trình gốc	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
Tên gọi khác	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	IP, MIP, mixed-integer programming, mixed-integer linear programming
Liên quan	3	4
Tóm tắt	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.	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.