Engineering Economic Analysis

316 UNCERTAINTY IN FUTURE EVENTS

Then the EUAC of the first cost and the expected annual flood damage are added together to

find the total EUAC for each height. The 30 ft dam is somewhat cheaper than the 40 ft dam.

Economic Decision Trees

Some engineering projects are more complex, and evaluatingthem properly is correspond-

ingly more complex. For example, consider a new product with potential sales.volumes

ranging from low to high. If the sales volume is low, then the product may be discontinued

early in its potential life. On the other hand, if sales volume is high, additional capacity

may be added to the assembly line and new product variations may be added. This can be

modeled with a decision tree.

The following symbols are used to model decisions with decision trees:

Dl

/

Decision nodeD -- D2:Decision maker chooses 1 of the available paths.

'\

Dx

;;;:C 1

Chance node 0~C2: Represents a probabilistic (chance) event. Each possible

~.

Cy

outcome (CI, Cz, ..., Cy)has a probability(PI, pz,..., py)associated with it.

Outcome node--0: Shows result for a partic~lar path through the decision tree.

Pruned branch---H--: The double hash mark indicates that a branch has been pruned

because another branch has been chosen. This can happen only at decision nodes,

not at chance nodes. The term "pruned" is chosen to correspond with the gardener's

practice of trimming or pruning off branches to make a tree or bush healthier.

Figure 10-3 illustrates how decision nodesD, chance nodes0, and outcome nodes

o can be used to describe the problem's structure. Details such as the probabilities and

costs can be added on the branches that link the nodes. With the branches from decision

and chance nodes the model becomes a decision tree.

Dam EUAC of Expected Annual Total

Height (ft) First Cost Flood Damages Expected EUAC

No dam $ (^0) $200,000 $200,000
(^20) 38,344 25,000 63,344
(^30) 43,821 (^3000) 46,821
(^40) 49,299 (^400) 49,699