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| Programació entera× | Programació Lineal× | |
|---|---|---|
| Camp | Optimització | Optimització |
| Família | Process / pipeline | Process / pipeline |
| Any d'origen≠ | 1958 | 1947 |
| Autor original≠ | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) | George B. Dantzig |
| Tipus≠ | Mathematical optimisation — exact combinatorial method | Mathematical programming / continuous optimization |
| Font seminal≠ | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 | Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136 |
| Àlies≠ | IP, MIP, mixed-integer programming, mixed-integer linear programming | LP, linear optimization, Doğrusal Programlama (LP) |
| Relacionats | 4 | 4 |
| Resum≠ | 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. | 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. |
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