পদ্ধতির তুলনা করুন
নির্বাচিত পদ্ধতিগুলো পাশাপাশি পর্যালোচনা করুন; যে সারিগুলোয় পার্থক্য আছে সেগুলো চিহ্নিত করা হয়।
| মিশ্র-পূর্ণসংখ্যা প্রোগ্রামিং× | রৈখিক প্রোগ্রামিং× | |
|---|---|---|
| ক্ষেত্র≠ | অনুকরণ | অনুকূলকরণ |
| পরিবার | Process / pipeline | Process / pipeline |
| উদ্ভবের বছর≠ | 1958–1960 | 1947 |
| প্রবর্তক≠ | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) | George B. Dantzig |
| ধরন≠ | Mathematical optimization | Mathematical programming / continuous optimization |
| মৌলিক উৎস≠ | 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 |
| অপর নাম≠ | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming | LP, linear optimization, Doğrusal Programlama (LP) |
| সম্পর্কিত≠ | 6 | 4 |
| সারসংক্ষেপ≠ | 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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