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Tutorial 2 Project Management Activity Charts (PERT Charts)

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Activity Charts The Activity Network is sometimes called an Arrow Diagram or PERT Chart, where PERT stands for Programmed Evaluation Review Technique. It’s a Project Management software, which performs the critical path calculation, along with other tasks such as leveling and cost calculations.

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Activity Network: How to understand it A project is composed of a set of actions or tasks. The Activity Network diagram displays interdependencies between tasks through the use of boxes and arrows. Arrows pointing into a task box come from its predecessor tasks. Arrows pointing out of a task box go to its successor tasks.

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The Activity Network Diagram

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Slack time & Critical path Slack time: The amount of time that a task can be delayed without affecting the completion time of the overall project is known as the slack time or float. Critical Path: The critical path through the diagram is the sequence of tasks which have zero slack time. Thus, if any task on the critical path finishes late, then the whole project will also finish late

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How can it PERT charts Help you? Finding minimum completion times Determining maximum completion times Value of time for each step in the project Assigning specified times for parts of the project Creates a realistic schedule for the company

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The Critical Path and Slack

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Network analysis example 1996 MBA exam A project consists of 8 activities. The activity completion times and the precedence relationships are as follows: Activity Completion time Immediate predecessor (days) activities A 5 - B 7 - C 6 - D 3 A E 4 B,C F 2 C G 6 A,D H 5 E,F Draw the network diagram. Calculate the minimum overall project completion time and identify which activities are critical. If activity E is delayed by 3 days how is the project completion time affected? If activity F is delayed by 3 days how is the project completion time affected?

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Network Diagram 1

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Calculate the minimum overall project completion time Let E i represent the earliest start time for activity i such that all its preceding activities have been finished. We calculate the values of the E i (i=A,B,...,I) by going forward, from left to right, in the network diagram. To ease the notation let T i be the activity completion time associated with activity i (e.g. T B = 7). Then the E i are given by: E A = 0 (assuming we start at time zero) E B = 0 (assuming we start at time zero) E C = 0 (assuming we start at time zero) E D = E A + T A = 0 + 5 = 5 E G = max[E A + T A, E D + T D ] = max[0 + 5, 5 + 3] = 8 E E = max[E B + T B, E C + T C ] = max[0 + 7, 0 + 6] = 7 E F = E C + T C = 0 + 6 = 6 E H = max[E E + T E, E F + T F ] = max[7 + 4, 6 + 2] = 11 E I = max[E G + T G, E H + T H ] = max[8 + 6, 11 + 5] = 16 Hence the minimum possible completion time for the entire project is 16 days, i.e. 16 days is the minimum time needed to complete all the activities.

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Calculate the latest times for each activity Let L i represent the latest start time we can start activity i and still complete the project in the minimum overall completion time. We calculate the values of the L i (i=A,B,...,I) by going backward, from right to left, in the network diagram. Hence: L I = 16 L G = L I - T G = 16 - 6 = 10 L H = L I - T H = 16 - 5 = 11 L D = L G - T D = 10 - 3 = 7 L A = min[L D - T A, L G - T A ] = min[7 - 5, 10 - 5] = 2 L E = L H - T E = 11 - 4 = 7 L F = L H - T F = 11 - 2 = 9 L C = min[L E - T C, L F - T C ] = min[7 - 6, 9 - 6] = 1 L B = L E - T B = 7 - 7 = 0 Note that as a check all latest times are >=0 at least one activity has a latest start time value of zero.

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Calculate The Slack time slack or float time F i available is given by F i = L i - E i Activity L i E i Float F i A 2 0 2 B 0 0 0 C 1 0 1 D 7 5 2 E 7 7 0 F 9 6 3 G 10 8 2 H 11 11 0 Any activity with a float of zero is critical. Note here that, as a check, all float values should be >= 0. Hence the critical activities are B, E and H and the floats for the non-critical activities are given in the table above.

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Solution If activity E is delayed by 3 days then as E is critical the project completion time increases by exactly 3 days. If activity F is delayed by 3 days then as F has a float of 3 days the project completion time is unaffected.

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Example 2 The project consists of 8 activities. ActivityPreceding ActivityExpected Time(in days) 1. Requirements Collection _______ 5 2. Screen Design 1 6 3. Report Design 16 4. Data Base Design 2,32 5. User Documentation 45.5 6. Programming 45 7. Testing 63 8. Installation 5,71

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Network Diagram Activities as numbered in the table 1 2 3 4 5 6 7 8

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