隨機規劃
Stochastic Programming
| 節 | 週一 |
|---|---|
2 09:00–09:50 | 隨機規劃 MB414（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 the 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 who interest in learning how to model uncertainties in mathematical programs, and solution approaches for solving large-scale problems.
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.
無備註
English lecture
Homework will be assigned in every three weeks, and each of them will include 2 to 3 problem sets.
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：
- 6
- 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 programs 2. Valid inequalities and theorem for solving SIPs 3. Approximation algorithms for solving stochastic programs with continuous random variable
- 講授：
- 6
- 示範：
- 6
- 實作：
- 6
Introduction
1. Purposes of stochastic programming 2. Examples 3. Types of stochastic programs
- 講授：
- 6
- 示範：
- 3
| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction 2026-02-23(一) |
| 第 2 週 | Examples of stochastic program / Applications 2026-03-02(一) |
| 第 3 週 | Short reviews and preliminaries 2026-03-09(一) |
| 第 4 週 | Modeling uncertain problems / Types of stochastic program 2026-03-16(一) |
| 第 5 週 | Basic property and theorem of stochastic programming 2026-03-23(一) |
| 第 6 週 | Basic property and theorem of stochastic programming 2026-03-30(一) |
| 第 7 週 | Comparison between deterministic and stochastic solutions (EVPI, VSS, and etc.) 2026-04-06(一) |
| 第 8 週 | Midterm 2026-04-13(一) |
| 第 9 週 | L-Shaped methods 2026-04-20(一) |
| 第 10 週 | Implementation issues 2026-04-27(一) |
| 第 11 週 | Lagrangian based methods / Scenario decomposition methods 2026-05-04(一) |
| 第 12 週 | Implementation of progressive hedging approach 2026-05-11(一) |
| 第 13 週 | Stochastic integer programs: Theorem and Methods for solving the problem with first-stage integer variables 2026-05-18(一) |
| 第 14 週 | Evaluating and approximating methods (Revisit newsvendor problem with stochastic demand / Direct methods / Bounds for stochastic programs with continuous random variables / etc.) 2026-05-25(一) |
| 第 15 週 | Monte Carlo methods (SAA / Important sampling / Sequential sampling/ etc.) 2026-06-01(一) |
| 第 16 週 | Final 2026-06-08(一) |
Introduction to Stochastic Programming, Second Edition, by John R. Birge and Francois Louveaux
- 地點
- T.B.D.
- 時間
- By appointment
- 聯絡方式
- sichen@nycu.edu.tw