## Analysis Under High Uncertainty

bility distribution was constructed (see Figure 2-5) to help identify the lowest-cost alternative and also the alternative with the lowest risk of a high cost, alternatives that are often not the same. As seen in the illustration, alternative 3 has the lowest expected cost (of 9) but also has the highest likelihood for a cost of 20 or more.

Figure 2-46: Risk analysis.
Figure 2-4c: Decision analysis. Source: |28|
Figure 2-5: Probability density for three alternatives. Noie: Alternative 3 has the lowest mean, but alternative 1 has a smaller variance and thus less risk.

A public utility faced with deciding between several R&D projects |21| used four separate cost-related distributions in a risk analysis simulation (Figure 2-6). (Total wage costs required two separate distributions, as shown in the figure.) The distributions were then combined to generate the distribution of a cost overrun for each potential project. In addition, sensitivity analysis was conducted to determine the effect of court rulings and specific task failures on project costs. High-risk projects were identified in this way, and tasks that posed high risk could then be moni-

Materials Salvage

Figure 2-6: Probability distributions for elements of project cost for a utility.

tored with tight managerial controls. Following the cost analysis, project schedules were analyzed in the same way. Finally, time and cost analyses were combined to determine interactions and overall project effects.

### General Simulation Analysis

Simulation combined with sensitivity analysis is also useful for evaluating R&D projects while they are still in the conceptual stage. Using the net present value approach, for example, we would support an R & D project if the net present value of the cash flows (including the initial cash investment) is positive and represents the best available alternative use of the funds. When these flows are estimated for purposes of the analyses, it is well to avoid the full-cost philosophy that is usually adopted. The full-cost approach to estimating cash flows forces the inclusion of arbitrarily determined overheads in the calculationâ€”overheads which, by definition, are not affected by the change in product or process and thus are not relevant to the decision. The only relevant costs are those that will be changed by the implementation of the new process or product.

The determination of such costs is not simple. If the concept being considered involves a new process, it is necessary to go to the detailed route sheet, or operations sequence sheet, describing the operation in which the new process would be used. Proceeding systematically through the operating sequence step by step, one asks whether the present time and cost required for this step are likely to be altered if the new process concept is installed. If and only if the answer is yes, three estimates (optimistic, most likely, and pessimistic) are made of the size of the expected change. These individual estimated changes in the production cost and time, together with upstream or downstream time and cost changes that might also result (e.g., a production method change on a part might also alter the cost of inspecting the final product), are used to generate the required cash flow informationâ€”presuming that the time savings have been properly costed. This estimation process will be explained in detail in Chapter 8.

The analysis gives a picture of the proposed change in terms of the costs and times that will be affected. The uncertainty associated with each individual element of the process is included. Simulation runs will then indicate the likelihood of achieving various levels of savings. Note also that investigation of the simulation model will expose the major sources of uncertainty in the final cost distributions. If the project itself is near the margin of acceptability, the uncertainty may be reduced by doing some preliminary research aimed at reducing uncertainty in the areas of project cost estimation where it was highest. This preliminary research can be subjected to a cost-benefit analysis when the benefit is reduced uncertainty. For an example of such an approach see j 411.