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| Lập trình nguyên (Integer Programming× | Lập trình động× | Lập trình mục tiêu× | |
|---|---|---|---|
| Lĩnh vực≠ | Tối ưu hóa | Tối ưu hóa | Ra quyết định |
| Họ≠ | Process / pipeline | Process / pipeline | MCDM |
| Năm ra đời≠ | 1958 | 1957 | 1955 |
| Người khởi xướng≠ | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) | Richard Bellman | Charnes, A., Cooper, W. W. |
| Loại≠ | Mathematical optimisation — exact combinatorial method | Exact combinatorial optimization via recursive decomposition | Multi-objective optimisation — weighted/lexicographic goal deviation minimisation |
| Công trình gốc≠ | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 | 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 DOI ↗ |
| Tên gọi khác≠ | IP, MIP, mixed-integer programming, mixed-integer linear programming | DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama | — |
| Liên quan≠ | 4 | 3 | 8 |
| Tóm tắt≠ | 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. | 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. |
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