A project network is a tool for graphically depicting a schedule. This # discusses the use of project networks and the critical path method to evaluate options for developing a system in crash mode.
CPM (Critical Path Method) is used to help plan and monitor a project schedule when the activity times are known with reasonable precision. Only by shortening the critical path can the project completion time be improved. Consequently, the critical path defines those activities into which additional resources might be poured to accelerate the schedule.
Creating a project network and performing crash mode analysis are complex undertakings. The computations are straightforward but non-trivial. Errors in computing earliest event times, latest event times, and slack times are not always apparent, so all computations should be checked carefully. Finally, the accuracy of the project network is no better than the activity duration estimates, and the accuracy of the cost computations is no better than the cost estimates.
This # assumes that the reader understands the concepts and techniques introduced in #s 20 (Gantt charts) and 21 (project networks). Before preparing a project network, the tasks or activities to be performed must be identified and each activitys duration (the time required to complete the activity) and cost must be estimated. Additionally, the precedence relationships between activities must be known. The necessary information is typically collected during the problem definition and information gathering stage of the system development life cycle (Part II).
This # discusses the use of project networks and the critical path method to evaluate options for developing a system in crash mode. Often, it is possible to expedite a project by pouring additional resources (personnel, computing power, etc.) into one or more critical path activities, essentially trading cost for time. Crash mode analysis is a technique for studying the cost/time tradeoff by manipulating the project network (# 21).
Table 22.1 lists the activities associated with a generic system development project. The initial project network is shown as Figure 22.1. The time to complete each activity is shown above the activity arrow. The earliest event time and latest event time for each event are noted to the right of the event circle. Note that there are two critical paths, 1-2-3-7-8 and 1-2-3-4-7-8.
Table 22.2 provides additional information about the completion times and costs for each of the activities. For example, the normal completion time for activity 1-2 is 2 weeks, but the crash mode time (the shortest possible time for completing the activity) is only 1 week. Saving that week is expensive, however. Normally, activity 1-2 is expected to cost $5000, but operating in crash mode will increase the cost by $3000 to $8000. Thus, the cost per week saved (the cost increase divided by the number of weeks saved) is $3000.
|Table 22.1 The Activities Associated with the # Example|
|1-2||Study the old system||2|
|2-4||Determine user needs||4|
|2-5||Examine old system requirements||2|
|3-7||Analyze interview results||4|
|4-7||Define new system objectives||5|
|7-8||Determine new systems specifications||2|
Figure 22.1 The initial project network for the # example.
Read through Table 22.2. The time and cost columns are estimates. Cost per week is computed by dividing the extra cost for crash mode by the number of time periods (in this example, weeks) saved.
Given the data in Table 22.2, the project network can be modified (Figure 22.2) to show crash time (next to the normal time, in parentheses) and the cost per week (below the activity line) for each activity. The next step is to investigate the impact of performing one or more of the activities on the critical path in crash mode. Generally, those activities with a smaller cost per week saved promise a greater return (time saved per dollar spent). Obviously, those activities with the greatest difference between normal and crash mode time have the greatest potential for shortening the schedule.
|Table 22.2 Normal and Crash Mode Activity Times and Costs|
|Time (weeks)||Cost ($)||Cost||Cost|
Figure 22.2 The project network with crash times and crash costs per week saved.
For example, suppose the system designer decides to crash those activities that promise to save the greatest amount of time (2-3 and 4-7). Figure 22.3 shows the new project network; note that activities 2-3 and 4-7 use the crash mode time estimates while the other activities use the normal time estimate. Changing some of the activity times changes the computed earliest and latest event times which, in turn, (potentially) changes the critical path. The new project network has a single critical path (1-2-3-7-12). The total elapsed time is 12 weeks, a saving of 3 weeks. From Table 22.2, the extra cost associated with activity 2-3 is $6,000, and the extra cost associated with 4-7 is $6,000, so the total project cost is $64,000, an increase of $12,000 over performing all activities in normal mode.
Additional alternatives can be considered. For example, Figure 22.4 shows the project network for performing only activity 2-3 in crash mode. Once again there are two critical paths. The total elapsed time is 13 weeks and the total system cost is $58,000, an increase of $6,000 over performing all activities in normal mode.
Table 22.3 summarizes the elapsed times and total system costs for several alternatives, including performing all activities on the critical path in crash mode. Clearly, the option of crashing 4-7 (14 weeks, $58,000) can be eliminated because crashing 2-3 (13 weeks, $58,000) saves an extra week for the same cost. Note that crashing activity 7-8 (14 weeks, $53,000) saves one week at a cost of only $1,000, an outcome consistent with the cost per week saved computations in Table 22.2. Although the optimal solution is not obvious, the cost/time tradeoff is clearly defined, giving the responsible managers the information they need to make a decision.
Figure 22.3 The project network with activities 2-3 and 4-7 performed in crash mode.
Figure 22.4 The project network with only activity 2-3 performed in crash mode.
|Table 22.3 Several Alternatives|
|Crash||Total Time||Total Cost|
|2-3, 4-7||12 weeks||$64,000|
Such project management software products as Microsoft Project, Primavera Suretrack Project Manager, SuperProject from Computer Associates, Harvard Project Manager from Software Publishing Company, and Project Management Workbench from Applied Business Technology support project networks, PERT, CPM, and related techniques. Such charting or drawing tools as Visio and Flowcharter by Micrografx can be used to create a project network, although the project management tools are much more effective.