   #### Estimate    Estimate - Risk There are many risks associated with the estimates regarding a project, but the add-in only considers the risks associated with the costs of the work packages. We model the risk by providing the probability distribution for each work package. Computations for the distributions are provided by the Random Variables add-in. This add-in must be installed for the risk feature to work. As we will see, the add-in allows computations of probabilities associated with the project cost. We can compute these using probability analysis or Monte Carlo simulation. To create a model with risk, fill in the dialog as below. To keep the illustration simple we use only the first level of detail for the project, but the analysis can be done for any level of detail. We have also chosen to not include time, but that option is available. We have chosen Distribution for the items amount option. Several distributions are available, and we have chosen to use the triangular distribution. In fact, using the General option allows any parametric distribution allowed by the Random Variables add-in. The list of the distributions is found on the distributions page of the add-in. The work breakdown structure is constructed as before, but now rather than a single value for the costs, the name of the distributions and their parameters are entered in columns E through H. Only the first three letters, Tri, are necessary to describe the distribution. The triangular distribution has three parameters, minimum, most likely, and maximum. Other distributions are entered in the same way, with perhaps different parameters. If the activities have different distributions, the separate distributions are described by name. We see in cell B8 the method by which the point estimates of the activity times are to be selected. In the present case we use the mean value of the distribution. The other options are shown later on this page. The percentile in B9 has no bearing on the mean value option. The figure below shows the computations for the moments of the activity costs. Column L shows point estimates of the costs, in this case the mean values. We show the contents of some of the cells in row 15. The functions used in columns I and J are evaluated by the Random Variables add-in, so that add-in must be installed. The point estimates in column L are the same as column I, the mean values. Summary Clicking the Summarize button at the top of the page summarizes the statistical parameters of the distributions of the activities at the first level of detail. The mean and variance values are sums over the parameters of the work package means and variances. The sum operation is appropriate when we assume that the work package costs are independent random variables. Column S shows point estimates for the activity costs and cell X14 shows the cost of the entire project. Unless we assume that all costs are Normally distributed, the distribution of the sum of the random values is not known. When there are many activities that together comprise the project, it is reasonable to assume that the project estimate is normally distributed. Then we can use the Normal distribution to compute probabilities regarding this cost. We also can simulate the project cost as described below. Percentile Option Clicking the Change button at the top of the page brings the Change Dialog shown below. The dialog allows the user to add or delete activities, but in this case we change the estimation method to the percentile method. The data table is the same except the equation used to select the point estimate in column L. Now we use the RV_Inverse function. This returns the value of the activity cost that will exceed the actual value 60% of the time. It is a conservative estimate since it is larger than the median value. A percentile of 50% returns the median, and a percentile less 50% returns a number that is less than the median. Cell B8 holds the percentile used and can be changed. B7 holds the word "Percent" indicating that this is a percentile estimation. Simulation The simulation estimation method replaces the formulas in column L by the RV_Sim function. This function simulates a value using the Monte Carlo method for the distribution defined by its argument. Every time the worksheet is computed new simulated values are obtained and the summary ranges that relate to the point estimate also change. The simulation option is not of much value by itself, but it allows the user to simulate the total project cost using the Simulation option of the Random Variables add-in. The dialog below is called by choosing the Simulate_RV item from the ORMM menu. The simulated cell is the X14. This cell holds the total cost of the project. The statistics to be computed are selected by checking the boxes on the dialog. We ask for a simulation of 500 observations. The worksheet is recomputed 500 times and statistics associated the value in cell X14, the project cost, are accumulated. They are shown on the worksheet starting in Y14. The simulated mean and variance are close to the theoretical mean and variance in cells U14 and V14. The histogram generated by the add-in is below. It is similar to a typical bell-shaped curve (the Normal distribution), but it is skewed to the right. This is not unexpected since all the triangular distributions were skewed to the right. Other measures related to the project cost can easily be computed using features of the Random Variables add-in. Time The time option is also available for the models with risk. In that case the summary will describe the statistics for the net present worth of the project.  Operations Management / Industrial Engineering
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by Paul A. Jensen    