隨機規劃
Stochastic Programming
| 節 | 週四 |
|---|---|
2 09:00–09:50 | 隨機規劃 MB506（光復） 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
Stochastic programming is to find an optimal decision for problems involved uncertain data. The development of this field has contributed to broad applications in operations management, finances, engineers, and etc. This class is mainly designed for graduate students majored in operations research, industrial engineering or related disciplines. The objective is to prepare students with knowledge on modeling uncertainty into mathematical programs, and learn to utilize sophisticated solvers and develop approaches for solving stochastic programs.
1. Students must have solid knowledge in linear programming and integer programming, or have taken similar courses before. 2. Familiar with IBM CPLEX callable library using MS C# programming language.
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In-class performance (25%) Assignments (25%) Midterm project (25%) Final project (25%)
Introduction
1. Introduction 2. Purposes of stochastic programming 3. Examples 4. Formulations
- 講授：
- 6
- 示範：
- 3
Short Reviews and Preliminaries
1. Linear programming 2. Integer programming 3. Convex analysis 4. Probability and measure theory
- 講授：
- 6
Modeling Uncertain Problems
1. Two-stage stochastic LP with fixed resources 2. Probabilistic constraints 3. Stochastic integer programs (SIP) 4. Two-stage stochastic nonlinear programs with recourse 5. Multistage stochastic programs with recourse
- 講授：
- 9
- 示範：
- 6
The Value of Stochastic Solution
1. The expected value solution 2. The expected value of perfect information (EVPI) 3. The value of stochastic solution (VSS) 4. Bounds of EVPI and VSS
- 講授：
- 6
Solution Approaches
1. Decomposition methods for solving two-stage stochastic program 2. Valid inequalities and theorem for solving SIPs 3. Approximation algorithms for solving stochastic programs with continuous random variable
- 講授：
- 9
- 示範：
- 9
- 實作：
- 9
| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction |
| 第 2 週 | Examples of stochastic program / Applications |
| 第 3 週 | Short reviews and preliminaries |
| 第 4 週 | Short reviews and preliminaries |
| 第 5 週 | Modeling uncertain problems / Types of stochastic program |
| 第 6 週 | Basic property and theorem of stochastic programming |
| 第 7 週 | Basic property and theorem of stochastic programming |
| 第 8 週 | Comparison between deterministic and stochastic solutions (EVPI, VSS, and etc.) |
| 第 9 週 | Midterm |
| 第 10 週 | L-Shaped methods |
| 第 11 週 | Implementation issues |
| 第 12 週 | Lagrangian based methods / Scenario decomposition methods |
| 第 13 週 | Implementation of progressive hedging approach |
| 第 14 週 | Stochastic integer programs: Theorem and Methods for solving the problem with first-stage integer variables |
| 第 15 週 | Stochastic integer programs: Theorem and Methods for solving the problem with second-stage integer variables |
| 第 16 週 | Evaluating and approximating methods (Revisit newsvendor problem with stochastic demand / Direct methods / Bounds for stochastic programs with continuous random variables / etc.) |
| 第 17 週 | Monte Carlo methods (SAA / Important sampling / Sequential sampling/ etc.) |
| 第 18 週 | Final |
Introduction to Stochastic Programming, Second Edition, by John R. Birge and Francois Louveaux
- 地點
- MB513
- 時間
- TBD
- 聯絡方式
- sichen@nctu.edu.tw