विधियों की तुलना करें
चुनी हुई विधियों की आमने-सामने समीक्षा करें; भिन्नता वाली पंक्तियाँ रेखांकित हैं।
| मिश्रित-पूर्णांक प्रोग्रामिंग× | रैखिक प्रोग्रामन× | |
|---|---|---|
| क्षेत्र≠ | अनुकरण | अनुकूलन |
| परिवार | Process / pipeline | Process / pipeline |
| उद्भव वर्ष≠ | 1958–1960 | 1947 |
| प्रवर्तक≠ | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) | George B. Dantzig |
| प्रकार≠ | Mathematical optimization | Mathematical programming / continuous optimization |
| मौलिक स्रोत≠ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 | Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136 |
| उपनाम≠ | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming | LP, linear optimization, Doğrusal Programlama (LP) |
| संबंधित≠ | 6 | 4 |
| सारांश≠ | 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. | 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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