(PROGRAM EVALUATION AND REVIE TECHNIQUE)
- 2. PERT A project management planning tool used to calculate the amount of time it will take to realistically finish a project. Quantitative analysis techniques that help managers plan, schedule, monitor, and control large and complex projects.
- 3. The first step in planning and scheduling a project is to develop the work breakdown structure. This involves identifying the activities that must be performed in the project. An activity is a job or task that is a part of a project. The beginning or end of an activity is called an event. There may be varying levels of detail, and each activity may be broken into its most basic components. The time, cost, resource requirements, predecessors, and person(s) responsible are identified for each activity. When this has been done, a schedule for the project can be developed.
- 4. Six Steps of PERT 1. Define the project and all of its significant activities or tasks. 2. Develop the relationships among the activities. Decide which activities must precede others. 3. Draw the network connecting all of the activities. 4. Assign time and/or cost estimates to each activity. 5. Compute the longest time path through the network; this is called the critical path. 6. Use the network to help plan, schedule, monitor, and control the project.
- 5. Questions answered by PERT. 1. When will the entire project be completed? 2. What are the critical activities or tasks in the project, that is, the ones that will delay the entire project if they are late? 3. Which are the noncritical activities, that is, the ones that can run late without delaying the entire project’s completion? 4. If there are three time estimates, what is the probability that the project will be completed by a specific date? 5. At any particular date, is the project on schedule, behind schedule, or ahead of schedule? 6. On any given date, is the money spent equal to, less than, or greater than the budgeted amount? 7. Are there enough resources available to finish the project on time?
- 6. General Foundry Example of PERT General Foundry, Inc., a metalworks plant in Milwaukee, has long been trying to avoid theexpense of installing air pollution control equipment. The local environmental protection grouphas recently given the foundry 16 weeks to install a complex air filter system on its main smokestack. General Foundry was warned that it will be forced to close unless the device is installed in the allotted period. Lester Harky, the managing partner, wants to make sure that installation of the filtering system progresses smoothly and on time.When the project begins, the building of the internal components for the device (activity A) and the modifications that are necessary for the floor and roof (activity B) can be started. The first step is to define the project and all project activities
- 7. The construction of the collection stack (activity C) can begin once the internal components are completed, and pouring of the new concrete floor and installation of the frame (activity D) can be completed as soon as the roof and floor have been modified. After the collection stack has been constructed, the high-temperature burner can be built (activity E), and the installation of the pollution control system (activity F) can begin. The air pollution device can be installed (activity G)after the high-temperature burner has been built, the concrete floor has been poured, and the frame has been installed. Finally, after the control system and pollution device have been installed, the system can be inspected and tested (activity H).
- 8. All of these activities seem rather confusing and complex until they are placed in a network. First, all of the activities must be listed. This information is shown in Table 12.1. We see in the table that before the collection stack can be constructed (activity C), the internal components must be built (activity A). Thus, activity A is the immediate predecessor of activity C. Similarly, both activities D and E must be performed just prior to installation of the air pollution device (activity G) Immediate predecessors are determined in the second step.
- 10. Drawing the PERT Network Once the activities have all been specified (step 1 of the PERT procedure) and management has decided which activities must precede others (step 2), the network can be drawn (step 3). There are two common techniques for drawing PERT networks. The first is called activity on-node (AON) because the nodes represent the activities. The second is called activity-on-ar(AOA) because the arcs are used to represent the activities. In this book, we present the AON technique, as this is easier and is often used in commercial software. In constructing an AON network, there should be one node representing the start of the project and one node representing the finish of the project. There will be one node (represented as a rectangle in this chapter) for each activity. Figure 12.1 gives the entire network for General Foundry. The arcs (arrows) are used to show the predecessors for the activities. For example, the arrows leading into activity G indicate that both D and E are immediate predecessors for G. Activities and events are drawn and connected in the third step.
- 11. Activity Times The next step in both CPM and PERT is to assign estimates of the time required to complete each activity. For some projects, such as construction projects, the time to complete each activity may be known with certainty. The developers of CPM assigned just one time estimate to each activity. These times are then used to find the critical path, as described in the sections that follow. However, for one-of-a-kind projects or for new jobs, providing activity time estimates is not always an easy task. Without solid historical data, managers are often uncertain about the activity times. For this reason, the developers of PERT employed a probability distribution based on three time estimates for each activity. A weighted average of these times is used with PERT in place of the single time estimate used with CPM, and these averages are used to find the critical path. The time estimates in PERT are The fourth step is to assign activity times.
- 13. Optimistic time (a) time an activity will take if everything goes as well as possible. ,There should be only a small probability (say, ) of this occurring. Pessimistic time (b) time an activity would take assuming very unfavorable conditions. There should also be only a small probability that the activity will really take this long. Most likely time (m) most realistic time estimate to complete the activity.
- 14. Activity Times The next step in both CPM and PERT is to assign estimates of the time required to complete each activity. For some projects, such as construction projects, the time to complete each activity may be known with certainty. The developers of CPM assigned just one time estimate to each activity. These times are then used to find the critical path, as described in the sections that follow. However, for one-of-a-kind projects or for new jobs, providing activity time estimates is not always an easy task. Without solid historical data, managers are often uncertain about the activity times. For this reason, the developers of PERT employed a probability distribution based on three time estimates for each activity. A weighted average of these times is used with PERT in place of
- 15. The beta probability distribution is often used. PERT often assumes that time estimates follow the beta probability distribution (see Figure 12.2). This continuous distribution has been found to be appropriate, in many cases, for determining an expected value and variance for activity completion times. To find the expected activity time (t), the beta distribution weights the estimates as follows:
- 16. t = a + 4m + b 6 To compute the dispersion or variance of activity completion time, we use this formula:* Variance = (b−𝑎)² 6 Table 12.2 shows General Foundry’s optimistic, most likely, and pessimistic time estimates for each activity. It also reveals the expected time (t) and variance for each of the activities, as computed with Equations 12-1 and 12-2.
- 17. How to Find the Critical Path Once the expected completion time for each activity has been determined, we accept it as the actual time of that task. Variability in times will be considered later. Although Table 12.2 indicates that the total expected time for all eight of General Foundry’s activities is 25 weeks, it is obvious in Figure 12.3 that several of the tasks can be taking place simultaneously. To find out just how long the project will take, we perform the critical path analysis for the network.
- 19. The fifth step is to compute the longest path through the network—the critical path. The critical path is the longest time path route through the network. If Lester Harky wants to reduce the total project time for General Foundry, he will have to reduce the length of some activity on the critical path. Conversely, any delay of an activity on the critical path will delay completion of the entire project.
- 20. To find the critical path, we need to determine the following quantities for each activity in the network: 1. Earliest start time (ES): the earliest time an activity can begin without violation of immediate predecessor requirements 2. Earliest finish time (EF): the earliest time at which an activity can end 3. Latest start time (LS): the latest time an activity can begin without delaying the entire project 4. Latest finish time (LF): the latest time an activity can end without delaying the entire project
- 21. We first show how to determine the earliest times. When we find these, the latest times can be computed. EARLIEST TIMES There are two basic rules to follow when computing ES and EF times. The first rule is for the earliest finish time, which is computed as follows: Earliest finish time = Earliest start time + Expected activity time EF = ES + t Also, before any activity can be started, all of its predecessor activities must be completed. In other words, we search for the largest EF for all of the immediate predecessors in determining ES. The second rule is for the earliest start time, which is computed as follows:
- 22. Earliest start= Largest of the earliest finish times of immediate predecessors ES= Largest EF of immediate predecessors The start of the whole project will be set at time zero. Therefore, any activity that has no predecessors will have an earliest start time of zero. So for both A and B in the General Foundry problem, as seen here:
- 23. The earliest times are found by beginning at the start of the project and making a forward pass through the network The rest of the earliest times for General Foundry are shown in Figure 12.4. These are found using a forward pass through the network. At each step, and ES is the largest EF of the predecessors. Notice that activity G has an earliest start time of 8, since both D (with ) and E (with ) are immediate predecessors. Activity G cannot start until both predecessors are finished, and so we choose the larger of the earliest finish times for these. Thus, G has . The finish time for the project will be 15 weeks, which is the EF for activity H.
- 24. The latest times are found by beginning at the finish of the project and making a backward pass through the network. LATEST TIMES The next step in finding the critical path is to compute the latest start time (LS) and the latest finish time (LF) for each activity. We do this by making a backward pass through the network, that is, starting at the finish and working backward. There are two basic rules to follow when computing the latest times. The first rule involves the latest start time, which is computed as Latest start time = Latest finish time - Activity time LS = LF - t
- 25. Also, since all immediate predecessors must be finished before an activity can begin, the latest start time for an activity determines the latest finish time for its immediate predecessors. If an activity is the immediate predecessor for two or more activities, it must be finished so that all following activities can begin by their latest start times. Thus, the second rule involves the latest finish time, which is computed as Latest finish time = Smallest of latest start times for following activities, or LF = Smallest LS of following activities To compute the latest times, we start at the finish and work backwards. Since the finish time for the General Foundry project is 15, activity H has LF latest start for activity H is LS = LF - t = 15 - 2 = 13 weeks
- 26. Continuing to work backward, this latest start time of 13 becomes the latest finish time for immediate predecessors F and G. All of the latest times are shown in Figure 12.5. Notice that for activity C, which is the immediate predecessor for two activities (E and F), the latest finish time is the smaller of the latest start times (4 and 10) for activities E and F
- 27. CONCEPT OF SLACK IN CRITICAL PATH COMPUTATIONS When ES, LS, EF, and LF have been determined, it is a simple matter to find the amount of slack time, or free time, that each activity has. Slack is the length of time an activity can be delayed without delaying the whole project. Mathematically, Slack = LS - ES, or Slack = LF – EF Table 12.3 summarizes the ES, EF, LS, LF, and slack times for all of General Foundry’s activities. Activity B, for example, has 1 week of slack time since (or, similarly,). This means that it can be delayed up to 1 week without causing the project to run any longer than expected.
- 30. On the other hand, activities A, C, E, G, and H have no slack time; this means that none of them can be delayed without delaying the entire project. Because of this, they are called critical activities and are said to be on the critical path. Lester Harky’s critical path is shown in network form in Figure 12.6. The total project completion time (T), 15 weeks, is seen as the largest number in the EF or LF columns of Table 12.3. Industrial managers call this a boundary timetable.
- 31. Probability of Project Completion The critical path analysis helped us determine that the foundry’s expected project completion time is 15 weeks. Harky knows, however, that if the project is not completed in 16 weeks, General Foundry will be forced to close by environmental controllers. He is also aware that there is significant variation in the time estimates for several activities. Variation in activities that are on the critical path can affect overall project completion—possibly delaying it. This is one occurrence that worries Harky considerably
- 32. Computing project variance is done by summing activity variances along the critical path PERT uses the variance of critical path activities to help determine the variance of the overall project. If the activity times are statistically independent, the project variance is computed by summing the variances of the critical activities: Project variance = avariances of activities on the critical path From Table 12.2 we know that
- 35. PERT has two assumptions How can this information be used to help answer questions regarding the probability of finishing the project on time? In addition to assuming that the activity times are independent, we also assume that total project completion time follows a normal probability distribution. With these assumptions, the bell-shaped curve shown in Figure 12.7 can be used to represent project completion dates. It also means that there is a 50% chance that the entire project will be completed in less than the expected 15 weeks and a 50% chance that it will exceed 15 weeks.* For Harky to find the probability that his project will be finished on or before the 16-week deadline, he needs to determine the appropriate area under the normal curve. The standard normal equation can be applied as follows:
- 37. What PERT Was Able to Provide PERT has thus far been able to provide Lester Harky with several valuable pieces of management information: 1. The project’s expected completion date is 15 weeks. 2. There is a 71.6% chance that the equipment will be in place within the 16-week deadline. PERT can easily find the probability of finishing by any date Harky is interested in. 3. Five activities (A, C, E, G, H) are on the critical path. If any one of them is delayed for any reason, the entire project will be delayed. 4. Three activities (B, D, F) are not critical but have some slack time built in. This means that Harky can borrow from their resources, if needed, possibly to speed up the entire project. 5. A detailed schedule of activity starting and ending dates has been made available (see Table 12.3). The sixth and final step is to monitor and control the project using the information provided by PERT