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| Lập trình tuyến tính× | Lập trình nguyên (Integer Programming× | |
|---|---|---|
| Lĩnh vực | Tối ưu hóa | Tối ưu hóa |
| Họ | Process / pipeline | Process / pipeline |
| Năm ra đời≠ | 1947 | 1958 |
| Người khởi xướng≠ | George B. Dantzig | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) |
| Loại≠ | Mathematical programming / continuous optimization | Mathematical optimisation — exact combinatorial method |
| Công trình gốc≠ | Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136 | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 |
| Tên gọi khác≠ | LP, linear optimization, Doğrusal Programlama (LP) | IP, MIP, mixed-integer programming, mixed-integer linear programming |
| Liên quan | 4 | 4 |
| Tóm tắt≠ | 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. | 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. |
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