项目管理之路3(doc121)英文版!-项目管理(编辑修改稿)

项目管理之路3(doc121)英文版!-项目管理(编辑修改稿)内容摘要：

some problems, then assembling them on both occasions might take longer than expected. This is an example of a positive correlation in activity times. In application, such correlations are monly ignored, leading to errors in results. As a final problem and discouragement, easy to use software systems for Monte Carlo simulation of project schedules are not generally available. This is particularly the case when correlations between activity durations are desired. Another approach to the simulation of different activity durations is to develop specific scenarios of events and determine the effect on the overall project schedule. This is a type of whatif problem solving in which a manager simulates events that might occur and sees the result. For example, the effects of different weather patterns on activity durations could be estimated and the resulting schedules for the different weather patterns pared. One method of obtaining information about the range of possible schedules is to apply the scheduling procedure using all optimistic, all most likely, and then all pessimistic activity durations. The result is three project schedules representing a range of possible outes. This process of whatif analysis is similar to that undertaken during the process of construction planning or during analysis of project crashing. Example 111: Scheduling activities with uncertain time durations. Suppose that the nine activity example project shown in Table 102 and Figure 104 of Chapter 10 was thought to have very uncertain activity time durations. As a result, project scheduling considering this uncertainty is desired. All three methods (PERT, Monte Carlo simulation, and Whatif simulation) will be applied. Table 111 shows the estimated optimistic, most likely and pessimistic durations for the nine activities. From these estimates, the mean, variance and standard deviation are calculated. In this calculation, niyfifth percentile estimates of optimistic and pessimistic duration times are assumed, so that Equation () is applied. The critical path for this project ignoring uncertainty in activity durations consists of activities A, C, F and I as found in Table 103 (Section ). Applying the PERT analysis procedure suggests that the duration of the project would be approximately normally distributed. The sum of the means for the critical activities is + + + = days, and the sum of the variances is + + + = leading to a standard deviation of days. With a normally distributed project duration, the probability of meeting a project deadline is equal to the probability that the standard normal distribution is less than or equal to (PD D)| D where PD is the project deadline, D is the expected duration and D is the standard deviation of project duration. For example, the probability of project pletion within 35 days is: where z is the standard normal distribution tabulated value of the cumulative standard distribution appears in Table of Appendix B. Monte Carlo simulation results provide slightly different estimates of the project duration characteristics. Assuming that activity durations are independent and approximately normally distributed random variables with the mean and variances shown in Table 111, a simulation can be performed by obtaining simulated duration realization for each of the nine activities and applying critical path scheduling to the resulting work. Applying this procedure 500 times, the average project duration is found to be days with a standard deviation of days. The PERT result is less than this estimate by days or three percent. Also, the critical path considered in the PERT procedure (consisting of activities A, C, F and I) is found to be the critical path in the simulated works less than half the time. TABLE 111 Activity Duration Estimates for a Nine Activity Project Activity Optimistic Duration Most Likely Duration Pessimistic Duration Mean Variance A B C D E F G H I 3 2 6 5 6 10 2 4 4 4 3 8 7 9 12 2 5 6 5 5 10 8 14 14 4 8 8 If there are correlations among the activity durations, then significantly different results can be obtained. For example, suppose that activities C, E, G and H are all positively correlated random variables with a correlation of for each pair of variables. Applying Monte Carlo simulation using 500 activity work simulations results in an average project duration of days and a standard deviation of days. This estimated average duration is days or 20 percent longer than the PERT estimate or the estimate obtained ignoring uncertainty in durations. If correlations like this exist, these methods can seriously underestimate the actual project duration. Finally, the project durations obtained by assuming all optimistic and all pessimistic activity durations are 23 and 41 days respectively. Other whatif simulations might be conducted for cases in which peculiar soil characteristics might make excavation difficult。 these soil peculiarities might be responsible for the correlations of excavation activity durations described above. Results from the different methods are summarized in Table 112. Note that positive correlations among some activity durations results in relatively large increases in the expected project duration and variability. TABLE 112 Project Duration Results from Various Techniques and Assumptions for an Example Procedure and Assumptions Project Duration (days) Standard Deviation of Project Duration (days) Critical Path Method PERT Method Monte Carlo Simulation No Duration Correlations Positive Duration Correlations Whatif Simulations Optimistic Most Likely Pessi。