Introduction to Stochastic Programming, 2011

Part 1: Models

1 Introduction and Examples

Shows the applications of SP in different areas, in different forms.

\( Q(x,\xi) = \min\{ q^\top y \mid Wy = h - T x , y \geq 0 \} \)

• Farming example: decide the distribution of acres -> random yield is realized -> decide the amount to purchase; random technology matrix;
• Financial planning: make investment -> random return -> make investment -> …; random technology matrix & multi-stage
• Electricity capacity: random demand; random RHS & multi-stage 具体不懂
• Manufacturing Quality:
• Routing: random demand; random RHS

2 Uncertainty and Modeling Issues

介绍SP的框架，从概率论基础到SP的基本概念（recourse, risk）。此外，

• 2.6: Implicit representation of the second stage

Part 2: Basic Properties

4 The Value of Information and the Stochastic Solution

Quantities of interest:

• RP (recourse problem): optimal SP solution
• WS (wait-and-see): prophet solution
• EEV (expectation of the expected value)
• EVPI (expected value of perfect information) = RP - WS
• VSS (value of stochastic solution) = EEV - RP

Part 3: Solution Methods

Solving methods:

• L-shaped method: 2-stage problems
• MC