## Decisions with Independent Conditions

Let us first discuss the project situation of a decision to be made conditioned on the prior or prer package or some other external event. However, let us say that the alternatives we are deciding prerequisite; just our ability to make decisions about the alternatives is affected.

For illustrating decision making in the context of independent conditions, we will continue with the developing in this chapter. The matter before the project team for decision is whether or not to n us impose a condition that is independent of the performance of the in-house manufacturing or selected:

■ The make or buy decision is conditioned on whether or not the project sponsor exercises an project deliverables. That is to say, the WBS item in question is optional with the sponsor. It is to be delivered.

■ The sponsor's decision is a random variable, S, with values 1 or 0. S = 1 means the item wil = 0 means it will not be included. Once this prerequisite is satisfied, then the project team c

■ The performance, D, of the subsequent make or buy is independent of the sponsor's decisi exercise the option for the item. In that case, there would be no subsequent make or buy.

■ Our account manager dealing with the sponsor estimates that there is a 75% chance the sp option for the item. Probability of S = 1 is 0.75. In the "1-p" space there is a 25% chance the item: probability of S = 0 is 0.25.

Under these new circumstances, what is the decision of the project team, what is the expected v downside considerations? We proceed as follows: We must add columns to the decision table to the sponsor's decision, S, about adding the item to the project deliverables. We then recalculate account for all events in the "1-p" spaces. Table 4-3 illustrates the results.

Table 4-3: Decision with Independent Conditions

 EV De (p Op of Face Ov Value of \$F Alternative Sponsor Exercises Sponsor's Decision Probability of 20-Day Schedule Delay, D, @ \$10,000 Va Sp De ID Description Option Value, S Overrun per Day Va A MAKE 0.75 Yes 1 0.6 Yes \$200,000 \$9 0.75 Yes 1 0.4 No Yes \$0 No 0.7 \$2 A MAKE 0.25 No 0 0.6 Yes \$200,000 \$0 0.25 No 0 0.4 No Yes \$0 No B BUY 0.75 Yes 1 0.2 Yes \$200,000 \$3' 0.75 Yes 1 0.8 No Yes \$0 No 0.7 \$2 B BUY 0.25 No 0 0.2 Yes \$200,000 \$0 0.25 No 0 0.8 No Yes \$0 No

Following the mathematics through the table row by row, you can see that the probability of the ( probability of a subsequent delay and weights the acquisition cost. By this we mean that there ci decides favorably to go forward and include the item in the project deliverables. Overall, the prol sponsor makes the decision favorably times the probability of delay given that the decision is fav unfavorably, S = 0, so that there is to be no item in the project deliverables, and there is no chan

Summing the buy and the make from Table 4-3:

Expected value (buy) = \$0 + \$180,000 = \$180,000 Expected value (make) = \$0 + \$183,750 = \$183,750

Under the conditions of the scenario in Tables 4-2 and 4-3, we see that the decision is not chan expected value of the final decision, \$180,000, has a higher unbudgeted downside risk compare

Downside risk (make) = \$183,750 - (\$125,000 acquisition + \$200,000 delay) = -\$141,250 Upside (make) = \$125,000, the acquisition cost without delay

Downside risk (buy) = \$180,000 - (\$200,000 acquisition + \$200,000 delay) = -\$220,000 Upside (buy) = \$200,000, the acquisition cost without delay

The decision tree or table provides the project manager with the expected value of the decision-previous discussion, expected value is the best single-number representation of a range of unce could fall anywhere in the range. Understanding the range is the purpose of the upside and dow

Furthermore, the acquisition cost of either alternative (\$125,000 for "make" or \$200,000 for "buy deterministic to random by the dependency acquired from the effect of the sponsor's decision. Ir acquire the item is the random variable, S, with discrete density function So = 0, p = 0.25 and Si acquisition cost, AC:

ACi = 1 * make or buy cost, p = 0.75, acquire the item

Therefore, for decision-making purposes the decision maker would look first to the expected val expected value. Then the decision maker would look to the risks and opportunities, downside an of possible effects on the business. The decision policy elements for both risk consideration and the decision process.

Figure 4-8 shows the "make" part of the scenario we have been discussing. It is evident that dec of conditions. Thus, the project team should understand and use tables to simplify matters, espe setup, computation, and maintenance in spreadsheets.

Figure 4-8: Decision Tree with Independent Conditions.