Natural Gas Planning:
An Application of Stochastic Linear Programming

Overview of the planning problem

"Forecasting is difficult . . . especially about the future." -- Bob Fourer, Northwestern University

The Natural Gas Planning problem presents users with the problem common to all who do long-term planning:
How do you plan for an uncertain future?

A common approach for tackling this problem is to generate a set of possible outcomes for the future. These are commonly called scenarios. Each scenario has some probability of occurrence, and the decision-maker is responsible to use the scenarios to make a wise decision in the current period to be ready for the future.

This case study allows users to create data for scenarios to use in planning the natural gas storage and purchase decisions for a fictitious natural gas company. The challenge is to use this information to devise an optimal strategy. The user's plan will be compared with two other competing approaches.

The planning problem can be simply stated as a linear program, but the complexity arises in that we are optimizing over an uncertain future. The data to pick for the future periods are not known. Being too conservative on our purchases for this year may leave us vulnerable if there is great demand for gas in the following period. On the other hand, buying and storing too much gas now may be wasteful if demand and costs are low in the future.

We will see that the stochastic programming approach optimizes over all of the scenarios at once by minimizing the expected cost over all the scenarios. The stochastic solution is, in some sense, the best "hedge" against future uncertainties.

The Problem description.

Formulating a "one-scenario" version:

• The Verbal formulation
• The Mathematical formulation
• The AMPL code

Formulation of the stochastic linear program

• The Verbal formulation
• The Mathematical formulation
• The AMPL code

Read more about stochastic linear programming in the NEOS Guide.

Try your hand at optimal planning

• Choose the number of scenarios.
• Choose the price and demand for the future (perhaps based on weather predictions).
• You will get solutions for each individual scenario and the "average" scenario.
• Choose a first-stage policy and compare your solution to the stochastic programming solution.

Give it a try!

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