Introduction

Many linear programs have the property that some aspects of the problem are not knowable with certainty. The clearest example is when the linear program attempts to model the (unknown) future. If there are many possible futures, then it is likely that no decision made today will be optimal for every possible future. The decision must try to strike a balance between the various possibilities.

Many such models can be thought of as ``multiperiod decision models'', where a decision must be made at the beginning of each period. ``Nature'' then reveals a period of information, and we then make a decision to try to act on that decision. So, in a two period model, the order of the decisions is:

1. Make a first period decision.
2. Nature (or the market, or the business environment) make a random choice among its first period possibilities.
3. We make a second period decision to react to the new environment.

There are many examples of such decision making:

• Stockpiling of supplies of fuel and salt in preparation for street cleaning in the winter.
• Creating a financial portfolio in the face of uncertainty about such items as stock movement, interest rates, and political environment.
• Water release in a dam system.

In your introductory O.R. class and in your finance classes, you have seen some dynamic programming models for making such decisions. You may also remember one problem of those models: the state space may get very large, or unrealistic assumptions must be made on the underlying random process. The scenario approach to these problems is an effort to offset these problems.