# Network Calculations

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1 Network Calculations The concepts and graphical techniques described in this week s readings form the basis of the tools widely used today to manage large projects. There is no way of simplifying the tasks of work breakdown, determination of dependencies or project estimation, but computer programs can take over the routine calculations involved in evaluating Gantt charts and Critical Path networks.. Practice Exercises with Network Diagrams Table represents the breakdown structure for a typical software development project. The task Ids and Descriptions are in columns and, respectively. The predecessors (dependencies) have been identified and are given in column. From estimates of the most likely time, the most optimistic time and the most pessimistic time for each activity, a best estimate has been calculated and is given in column. Durations are in weeks. Table. Task Id. Description. Immediate. Optimistic Time. Most Likely Time. Pessimistic Time. Expected Time Collect requirements -- Analyse processes Analyse data Design processes Design data Design screens, Design reports, Program, Test and Document 0 Install, Use the data of Table to complete the following exercises.. Confirm that expected times (Column ) are calculated according to the PERT network formula: Expected Time, e = (Optimistic Time + x Most Likely Time + Pessimistic Time) /. On a blank sheet of paper construct a network diagram (similar to Figure in Section. of this week s reading Project Management Tools and Techniques ) representing the activities listed in Table and the relationships between them. Can you draw a network diagram given any set of activities and predecessors? Is the network unique? Can you always draw the network diagram without having any lines crossing? Write the estimated duration for each task on the arrow leading from that task (as in Figure of Section.). Can you get any sense as to how long the project will take?. Complete the Gantt chart for the project defined in Table on the grid in Figure. Now what is the estimated duration of the project? Figure Week of the project Task Figure illustrates an alternate form of the network specified in Table. Draw arrows on the diagram to represent dependencies between activities and write the Expected Time for each in the duration box (D). Network Exercises

2 Now complete the evaluation of network diagram in Figure as explained in this week s readings. Identify the critical path by connecting those tasks for which Slack is zero. Note that the critical path is the longest path through the network and hence identifies the minimum duration for the project. Tasks on the critical path cannot be delayed without increasing the overall time for the project. Figure 0 ID D ES LS EF LF. Use the figures obtained from the network in Figure to complete Table. Table Id Task/Activity Immediate Duration Collect requirements -- Analyse processes Analyse data Design processes Design data Design screens, Design reports, Program, Test and Document 0 Install, Earliest Finish Latest Finish Slack On Critical Path? (Y,N). Making further use of your network diagram. Explore possible changes to the network. Revisit the original work breakdown and see if you can find some of the dependencies between tasks that could be changed. Try to make reasonable assumptions about predecessors. For example, see if you can find two apparently dependent tasks that could reasonable start at the same time, say, by reorganising project teams. This may allow you to revise the dependencies.. Explore the effect on the project plan if the dependencies are altered in this way.. Suppose that the project is only in its second week and it is discovered that already some of the estimates of task duration need revising. What sort of factors (apart from incompetence) might have led to a situation like this? Is there any simple way of revising the network diagram?. Suppose the client demands that the project be completed two weeks earlier that indicated by the original plan. What strategies could be invoked to accomplish this? Consider the following strategies: (i) (ii) Try reducing the duration of some tasks, for example by adding more people to the project team. Are there limits to how far you could pursue this strategy? What are they? Should you consider reducing the duration of tasks which lie on the critical path or those not on the critical path? Why is this important? What other strategies could help reduce the overall duration and hence satisfy the client s request? Network Exercises

3 . If activity turned out to take weeks instead of week as originally estimated, what effect would this have on the duration of the project? Would it affect the tasks that constitute the critical path?. The project is now under way and Task has been completed in weeks as estimated. You now find that Task can now be completed in weeks instead of. Revised estimates suggest that Tasks and will each take three times the figures given in Table and technical reasons it is considered likely that all other activities will take twice as long as originally estimated. Lastly, new activity, Id= Consult with council, is found to be necessary and expected to take week to complete. Activities and 0 both have to be completed before this consultation can begin. Fill in these new dependencies and revised expected times in Table. Table Id Task/Activity Immediate Collect requirements -- Analyse processes Analyse data Design processes Design data Design screens, Design reports, Program, Test and Document 0 Install, Consult with council Duration Earliest Finish Latest Finish Slack On Critical Path? (Y,N). Evaluate the resulting network in Figure and determine the revised project duration and critical path.. Fill in the remaining columns of Table with the values you obtain from Figure Figure 0 ID D ES LS EF LF. Crashing a project means adding resources to the project until a particular target duration is achieved. However, it has been observed that there is a limit to this process. Adding more personnel invariably increases problems of communication and management, and eventually can actually lead to an increase in the time taken for a particular activity. Moreover, unless you can find people with the necessary skill sets it is not always possible to add to a project team. In every cases, there will be additional costs associated with attempting to reduce the duration of a project by crashing. Table shows the minimum durations that can reasonably be achieved by crashing and the incremental cost per day of adding the resources. Determine the normal duration for the project. Network Exercises

4 Systematically crash the project as far as possible. Draw up a succession of tables showing the cost and duration at each step. Naturally you will try to reduce the duration of the most critical activity first. Table Project with Normal and Crash durations and costs Task Normal time (days) Crash time (days) Normal cost Incremental cost per day -- \$00 \$00 \$00 \$00 \$,000 \$00, \$00 \$00 0. Resource levelling is the process of planning so that resources are used as uniformly as possible throughout the project. Complete the Gantt chart in Figure for the data given in Table. Arrange the tasks so that the resource usage is a smooth as possible. Assume that all resources are interchangeable (i.e. all personnel have identical skill sets). Table Project with durations and resources Task Duration (weeks) Resources -- --,, Figure Task 0 0 Res ce Total. Further Practice Exercises Consolidate your understanding of Gantt charts and the Critical Path Method (CPM) by completing the following exercises. Table (over page) represents the work breakdown for an engineering project.. On a piece of paper, construct a simple network diagram representing the relationships between activities in Table (similar to Figure of Section. in this week s reading Project Management Tools & Techniques ). Can you avoid having lines crossing?. Using Figure construct a Gantt chart based on the data in Table. Consider whether resource levelling is necessary or not.. Using Figure complete the network diagram based on the data in Table. Network Exercises

5 Table Task Id Description Time Estimate (wks) Recruit project team -- R & D product design Plan market research Routing design Build prototype Prepare sales brochure, Prepare cost estimates Product testing Market survey, 0 Pricing and demand forecast Final report,,0 Figure Week of the project Task Res ce Figure ID D ES LS EF LF 0. Team task : Project Design due this week At this week s lab class the team is required to submit a summary, not exceeding two pages, outlining the team s proposed design for the solution to the problem to be solved. It must be attached to a completed Team Work Compliance Form, which may be downloaded from the course website (Doc_TeamWorkComplianceForm.docx). Network Exercises

6 . Suggested answers Gantt chart Figure I 0 0 d 0 Critical path network Figure ID D 0 0 ES LS EF LF Table Task/Activity Immediate Earliest Latest On Critical Duration Finish Finish Slack Path? (Y,N) Collect requirements -- 0 Y Analyse processes 0 Y Analyse data 0 N Design processes 0 Y Design data N Design screens, N Design reports, 0 Y Program, N Test and Document 0 Y Install, 0 Y Network Exercises

7 Table Id Task/Activity Immediate Duration Earliest Latest Slack On Critical Finish Finish Path? (Y,N) Collect requirements -- 0 Y Analyse processes 0 Y Analyse data 0 N Design processes 0 Y Design data N Design screens, N Design reports, Y Program, N Test and Document 0 Y 0 Install, Y Consult with council,0 0 Y Figure ID D 0 0 ES LS EF LF Resource allocation Figure a: Showing total resource usage Task 0 0 Res ce Total 0 It is possible to obtain a better pattern of resource usage by taking advantage of the slack in Tasks and. Typically, the resource usage builds up after the start and tapers off towards the end of the project. Spare resources can then be allocated elsewhere. Figure b: With resource levelling Task 0 0 Res ce Total Network Exercises

8 One possible form for network 0 Figure Week of the project Task Res ce Figure ID D ES LS 0 EF LF Network Exercises

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