Project Management in Practice Fifth Edition

Introduction Project schedule is the project plan in an altered format It is a convenient form for monitoring and controlling project activities Can be prepared in several formats Gantt charts PERT network CPM network 5-2

PERT and CPM Networks PERT and CPM developed independently in 1950 s Program Evaluation and Review Technique (PERT) U.S. Navy, Booz-Allen Hamilton, and Lockheed Aircraft Probabilistic activity durations Critical Path Method (CPM) Dupont De Nemours Inc. Deterministic activity durations 5-3

The Language of PERT/CPM Activity A task or set of tasks Uses resources and time Event An identifiable state resulting from completion of one or more activities Consumes no resources or time Predecessor activities must be completed Milestones Identifiable and noteworthy events that mark significant progress 5-4

The Language of PERT/CPM Continued Network A diagram of nodes (activities or events) and arrows (directional arcs) that illustrate the technological relationships of activities Path A series of connected activities between two events Critical path The set of activities on a path that, if delayed, will delay the completion date of the project Critical Time The time required to complete all activities on the critical path 5-5

Building the Network There are two ways of displaying a project network 1. Activities on arrows (AOA) network The activities are shown as arrows and events as nodes Generally more difficult to draw but depicts the technical relationships of the activities well 2. Activities on nodes (AON) network Each task is shown as a node and the technological relationship is shown by the arrows AON network usually associated with CPM AOA network usually associated with PERT 5-6

Sample AON Network Table 5-1 Figure 5-3 5-7

Sample AOA Network Table 5-1 Figure 5-6 (a) 5-8

Which to Use? Mostly AON used throughout this textbook AON used by most of the popular software AON networks are easier to draw by hand Large (20+ activities) AOA networks are difficult to draw Software to draw AOA networks is expensive 5-9

Finding the Critical Path and Critical Time ES: Earliest start time EF: Earliest finish time LS: Latest start time LF: Latest finish time Displayed on node as shown ES + completion = EF LS + completion = LF Figure 5-9 5-10

A Sample Problem for Finding the Critical Path and Critical Time Table 5-2 5-11

The Complete Network Table 5-2 and Figure 5-8 5-12

The Critical Path and Completion Time for Sample Project Figure 5-10 5-13

Notes on Sample Project All activities, and thus all paths, must be completed to finish the project The shortest time for completion of the network is equal to the longest path through the network In this case a-e-h-j If any activity on this path is even slightly delayed, the project will be delayed 5-14

Calculating Activity Slack ES: Earliest start time EF: Earliest finish time LS: Latest start time LF: Latest finish time Slack = LS ES Slack = LF EF Either method of calculating slack gives the same results 5-15

Managerial Implications The primary attention of the project manager must be to activities on the critical path If anything delays one of these activities, the project will be late Projects are easier to manage when there is project slack 5-16

Doing It the Easy Way Microsoft Project (MSP) Data is entered using a tab entry table Shown on next slide MSP automatically numbers each activity MSP has numerous options for viewing the data MSP automatically draws an AON network Shown on later slide 5-17

A Microsoft Project Version of Data in Table 5-2 Table 5-3 5-18

A Microsoft Project Version of the PERT/CPM Network from Table 5-3 Figure 5-11 5-19

Calculating Probabilistic Activity Times Figure below shows distribution of all possible durations for some task Estimate a is such that the actual duration of the task will be a or lower less than 1 percent of the time Estimate b is such that the actual finish time will be b or greater less than 1 percent of the time Estimate m is the most likely time Figure 5-13 5-20

Activity Expected Time and Variance T E ( a 4m 6 b) Var 2 ( b 6 a) 2 5-21

95 Percent Level Task will be a or lower 5 percent of the time Task will be b or greater 5 percent of the time ( b a) 3.3 5-22

90 Percent Level Task will be a or lower 10 percent of the time Task will be b or greater 10 percent of the time ( b a) 2.6 5-23

The Probabilistic Network Expected time (T E ) for each activity is calculated Variance (σ 2 ) for each activity is calculated T E for each activity is used to find the critical path and critical time for the network Slack is calculated in the usual fashion The variance (σ 2 ) of a path is the sum of the activity variances for that path Standard deviation (σ) is the square of the variance 5-24

The Probabilistic Network, an Example Table 5-4 5-25

Is it Really the Critical path Given uncertainty, cannot be sure that any specific path is the critical path Critical path may take less than expected while another path takes longer Only after the fact do we know which path was actually critical Managerial implication is the project manager must carefully manage all paths that have a reasonable probability of becoming critical 5-26

Once More the Easy Way Microsoft Project can easily handle the probabilistic network However, it does not perform some of the calculations These can be done in Excel Microsoft Project calculates using a calendar rather than days Uses a real-world calendar including weekends and holidays 5-27

The Probability of Completing the Project on Time Can the project be completed in X days? Can be answered with the information available concerning the level of uncertainty for the various project activities Assumes activities are statistically independent To complete a project by a specified time requires that all the paths in the network be completed by the specified time 5-28

The Probability of Completing the Project on Time Continued Determining the probability that a project is completed by a specified time requires calculating the probability that all paths are finished by the specified time We then calculate the probability that the entire project is completed within the specified time by multiplying these probabilities together This requires the assumption that the paths are statistically independent 5-29

Calculating Path Probability D = desired project completion time 50 in this example μ = the sum of the T E activities on the path being investigated 47 in this example σ 2 u = the variance of the path being considered A Z of 1.10 yields a probability of 0.8643 or 86 percent Z D 2 50 47 1.78 0.25 0.00 4.00 1.10 Table 5-4 5-30

The Statistical Distribution of the Completion Times for Example Figure 5-18 5-31

Selecting Risk and Finding D 5-32

Simulation Simulation is a different approach to managing risk Builds on the probabilistic functions already discussed Helps to understand the consequences of uncertainty Provides insight into the range and distribution of project completion times 5-33

Crystal Ball Chart for Project Completion Time Figure 5-19 5-34

Traditional Statistics vs. Simulation Both approaches assume that task times are statistically independent Both approaches assume the paths are independent A simulation can circumvent the assumption of statistical independence by including the activity or path dependencies as part of the model Simulation requires less computational effort 5-35

The Gantt Chart Henry Gantt developed the Gantt chart around 1917 It displays project activities as bars measured against a horizontal time scale Most popular way of exhibiting sets of related activities in the form of schedules 5-36

The Chart Gantt charts are easy to draw Problems arise when several tasks begin at the same time and have the same duration Can make it hard to find critical path Only a problem on hand-drawn charts Software shows critical path using some visual method Even with software, technical dependencies are harder to see on a Gantt chart 5-37

A Gantt Chart of a Sample Project Figure 5-21 5-38

A Gantt Chart Showing Critical Path, Path Connections, Other Data Figure 5-22 5-39

Extensions to PET/CPM Application of fuzzy set theory to aid in estimating activity durations Extensions to precedence diagramming Goldratt s Critical Chain 5-40

Precedence Diagramming Finish to start (F to S) Finish of Activity A to start of Activity B Start to start (S to S) Start of Activity A to start of Activity B Finish to finish (F to F) Finish of Activity A to finish of Activity B Start to finish (S to F) Start of Activity A to finish of Activity B 5-41

Precedence Diagramming Conventions Figure 5-25 5-42

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