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| 確率的混合整数計画法× | 混合整数計画法× | |
|---|---|---|
| 分野 | シミュレーション | シミュレーション |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1990s–2000s | 1958–1960 |
| 提唱者≠ | Birge, J. R.; Louveaux, F.; Sen, S. | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) |
| 種類≠ | Stochastic optimization model | Mathematical optimization |
| 原典≠ | Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175 | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 |
| 別名 | SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming |
| 関連≠ | 5 | 6 |
| 概要≠ | Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints. | 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. |
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