Notes:

A convenient way to lay out the steps of a capacity problem is through the use of decision trees. The tree format helps not only in understanding the problem but also in finding a solution. A decision tree is a schematic model of the sequence of steps in a problem and the conditions and consequences of each step.

Decision trees are composed of decision nodes with branches to and from them. By convention, squares represent decision points and circles represent chance events. Branches from decision points show the choices available to the decision maker; branches from chance events show the probabilities for their occurrence.

In solving decision tree problems, we work from the end of the tree backward to the start of the tree. As we work back, we calculate the expected values at each step.

Once the calculations are made, we prune the tree by eliminating from each decision point all branches except for the one with the highest payoff. This process continues to the first decision problem, and the decision problem is thereby solved.