PERT/cost which is an extension of PERT to include economic considerations brings cost factors into project control decisions. However, PERT/cost is usually developed by project managers without enough experience. In calculating the critical path of crisp PERT/cost network, the authors usually suppose that all activity durations follow beta distribution of three time parameters (ai,mi,bi), i.e., the mean and variance of an activity duration are (ai+4mi+bi)/6, (bi-ai)2/36, respectively. Basically, the activity durations and their distributions are subjectively determined, so the beta distribution is not always applicable. Therefore, the authors propose a fuzzy PERT/cost that can be applied to a variety of fuzzy distributions of activity durations. Intuitively, the higher the risk level, the more uncertainty in time/cost is involved in the project. From fuzzy set theory, it corresponds to lower confident level (α-cut) or larger interval value. The authors will use such interval of confidence to represent fuzzy activity durations so that α-cut can be interpreted as a risk level and the attitude of the decision makers can be expressed by another index of optimism, λ. Thus, the relationships between project time and cost under different risk levels and different degrees of optimism can be obtained. The solution procedure will be described in detail in conjunction with an example to illustrate the analysis, algorithm and computation of the proposed method. The authors have verified two of the empirical philosophy that for the higher risk level, the shorter project time for the optimist (λ=1) have verified two of the empirical philosophy that for the higher risk level, the shorter project time for the optimist (λ=1) could be obtained; on the other hand, for the lower risk level, the shorter project time was obtained for the pessimist (λ=0). They have observed that no matter whatever the risk level is, the results of the project time and cost of fuzzy PERT/cost at λ=0.5 (neither optimistic nor pessimistic) are equal to those of the crisp PERT/cost.
