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| Quy hoạch nguyên hỗn hợp× | Lập trình động× | |
|---|---|---|
| Lĩnh vực≠ | Mô phỏng | Tối ưu hóa |
| Họ | Process / pipeline | Process / pipeline |
| Năm ra đời≠ | 1958–1960 | 1957 |
| Người khởi xướng≠ | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) | Richard Bellman |
| Loại≠ | Mathematical optimization | Exact combinatorial optimization via recursive decomposition |
| Công trình gốc≠ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 | Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6 |
| Tên gọi khác | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming | DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama |
| Liên quan≠ | 6 | 3 |
| Tóm tắt≠ | Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally. | 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. |
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