15.053 商业分析中的优化方法

MIT Course 15 · Operations Research/Statistics · 课号 15.053

TL;DR

• 优化建模是管理决策的核心，涵盖线性规划、整数规划、网络流与决策树分析。
• 单纯形算法、对偶理论与影子价格量化了资源约束变化对总体经济收益的边际影响。
• 分支定界与割平面法为离散变量组合优化提供了通用精确求解框架。

课程简介 / Description

This course introduces students to the theory, algorithms, and applications of optimization. The optimization methodologies include linear programming, network optimization, integer programming, and decision trees. Applications to logistics, manufacturing, transportation, marketing, project management, and finance. Includes a team project in which students select and solve a problem in practice.

讲义 / Lecture Notes

• L1
  • Introduction (PDF)
  • Number partition problem (XLS)
  • Note: This file requires a macro for generating new problems
• L2
  • Formulations of linear and non-linear programs (PDF)
  • Diet problem (XLS)
• L3
  • Geometry and visualizations of linear programs (PDF)
• L4
  • The simplex method 1 (PDF)
• L5
  • The simplex method 2 (PDF)
  • Simplex method spreadsheets (XLS)
• L6
  • Sensitivity analysis and shadow prices (PDF)
  • mc² problem (XLS)
  • Initial and final tableaus (XLS)
• L7
  • Game theory 1: 2-person 0-sum, or constant sum (PDF)
• L8
  • Game theory 2 (PDF)
• L9
  • Discussion of projects; slack variables vs. artificial variables (PDF)
• L10
  • Introduction to integer programming (PDF)
  • IP reference guide (PDF)
• L11
  • Integer programming formulations (PDF)
• L12
  • Integer programming techniques 1: branch and bound (PDF)
• L13
  • Integer programming techniques 2: cutting planes (PDF)
• L14
  • Integer programming formulations, again (PDF)
• L15
  • Networks 1: Shortest path problem (PDF)
• L16
  • Networks 2: Network flows (PDF - 1.4MB)
  • The assignment problem (XLS)
• L17
  • Networks 3: Traveling salesman problem (PDF)
• L18
  • Decision trees 1 (PDF)
  • Juan Lee's decision (XLS)
• L19
  • Decision trees 2: the value of information (PDF)
  • L20–21
  • Behavioral economics (PDF)

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