Chapter 1. Introduction and Examples

Objective

• Build intuition on how to model uncertainty.
• Simple models can lead to significant savings.

Outline

1st Section - Farmer problem / News vendor (Two-stage stochastic linear programs with recourse)
2nd Section - Finance planning (Discrete-time control problem)
3rd Section - Power system capacity expansion (Dynamic problem - block separable recourse - Probabilistic or chance-constrained programming)
4th Section - Simple axle design (Fundamental non-linearities)
5th Section - Simple routing problem (Integer decision)
Final Section - Modeling techniques

1st Section

The top line gives the planting areas, which must be determined before realizing the weather and crop yields.

- This decision is called the first stage.

The other lines describe the three scenarios' yields, sales, and purchases.

- They are called the second stage.

Such decisions can appear in a stochastic model because decisions have to be 'balanced or hedged' against the various scenarios.

Assume that yields vary over years, but on a random basis - the farmer, unfortunately, does not get prior information on the yields.

Terminology
- The expected value of perfect information (EVPI).
- Value of the stochastic solution (VSS).

EVPI measures the value of knowing the future with certainty

while VSS assesses the value of knowing and using distributions on future outcomes.