Project Scheduling: Networks, Duration Estimation, and Critical Path Chapter 9

Learning Goals Understand and apply key scheduling terminology. Apply the logic used to create activity networks, including predecessor and successor tasks. Develop an activity network using Activity-on-Node (AON) techniques. Perform activity duration estimation based on the use of probabilistic estimating techniques. Construct the critical path for a project schedule network using forward and backward passes. Identify activity float and the manner in which it is determined. Understand the steps that can be employed to reduce the critical path.

Project Scheduling Project scheduling requires us to follow some carefully laid-out steps, in order, for the schedule to take shape. Project planning, as it relates to the scheduling process, has been defined by the PMBoK as: “The identification of the project objectives and the ordered activity necessary to complete the project including the identification of resource types and quantities required to carry out each activity or task.”

Project Scheduling Represents the conversion of project goals into an achievable methodology. Creates a timetable and reveals the network logic that relates project activities to each other. A graphical set of sequential relationships between project task which, when performed, result in the completion of the project goals. Vitally important to obtaining project goals, being on time and on budget.

Project Network Diagrams (PND) Allows project teams to use a method for planning and scheduling There are several advantages when project networks and scheduling are done well Show interdependence Help schedule resources Facilitate communication Show start & finish dates for task Identify critical activities Determine project completion See slide 26 for an example

Project Scheduling Terms Successors Predecessors Network diagram Serial activities Concurrent activities Merge activities Burst activities Node Path Critical Path E D C B A F

Most Common Methods for Constructing Activity Networks AOA vs. AON The same mini-project is shown with activities on arrow… E C D B F …and activities on node. E D B F C

Rules for Developing Activity Networks Some determination of activity precedence ordering must be done prior to creating the network. Network diagrams usually flow from left to right. An activity cannot begin until all preceding connected activities have been completed. Arrows on networks indicate precedence and logical flow. Arrows can cross over each other, although it is helpful for clarity’s sake to limit this effect when possible. Each activity should have a unique identifier associated with it (number, letter, code, etc.). Looping, or recycling through activities, is not permitted. Although not required, it is common to start a project on a single node. A single node point also is typically used as a project end indicator.

Example of Creating a Project Activity Network Information for Network Construction Name: Project Delta Activity Description Predecessors A Contract signing None B Questionnaire design A   C Target market ID A D Survey sample B, C E Develop presentation B F Analyze results D G Demographic analysis C H Presentation to client E, F, G Construct a Network Diagram

Activity Network Example Dev. Present. B Design A Contract D Survey F Analysis H Present C Market ID G Demog.

Project Activities Linked In Series/Parallel (Concurrent) College research paper example

Merge/Burst Activities Activity A Activity B Activity B Activity D Activity A Activity C Activity D Activity C

Node Labels Early Start Activity Float Activity Descriptor Late Start ID Number Activity Duration Late Finish Early Finish ES ID EF Slack Task Name LS Duration LF 11 D 24 0 Survey 11 13 24

Duration Estimation Assumptions Methods Based on normal working methods during normal hours Durations are always somewhat uncertain Timeframes can be from minutes to weeks Methods Past experience Expert opinion Mathematical derivation based on Beta Distribution Most optimistic (a) time – better then planned Most likely (m) time – realistic expectation Most pessimistic (b) time – Murphy’s Law kicks in There are only two types of estimates…lucky and wrong.

Variability in Activity Times Critical Path Method (CPM) assumes we know a fixed time estimate for each activity and there is no variability in activity times Program Evaluation and Review Technique (PERT) uses a probability distribution for activity times to allow for variability

Activity Duration Estimation – Beta Distribution   Where:  a = Most optimistic time  m = Most likely time  b = Most pessimistic time

Probability of Project Completion Project variance is computed by summing the variances of activities on the critical path Project variance = (variances of activities on critical path) Project standard deviation = Project Variance

Network Example Task Predecessor a m b mean variance Z -- 7 8 15 9.00 1.78 Y 13 16 19 16.00 1.00 X 14 18 22 18.00 W Y, X 12 14.00 0.44 V 1 4 5.00 4.00 T 6 10 10.00 S T, V 11 14.33 Task a m b Mean Variance Z 7 8 15 9.00 1.78 Y 13 16 19 16.00 1.00 X 14 18 22 18.00 1.78 W 12 14 16 14.00 0.44 V 1 4 13 5.00 4.00 T 6 8 14 8.67 1.78 S 11 14 19 14.33 1.78 Task Early Start Early Finish Late Start Late Finish Slack Z 0 9 0 9 0 Y 9 25 11 27 2 X 9 27 9 27 0 W 27 41 27 41 0 V 41 46 44.67 49.67 3.67 T 41 49.67 41 49.67 0 S 49.67 64 49.67 64 0 Project Length 64 Project Variance 7.555556 Project Std.dev 2.748737 Determine the expected duration and variance of each activity. Sketch the network described in the table. Determine the expected project time and standard deviation.

Constructing the Network Paths Forward pass – an additive move through the network from start to finish Backward pass – a subtractive move through the network from finish to start Critical path – the longest path from end to end which determines the shortest project length

Constructing the Critical Path Example Activity Description Predecessors Estimated Duration A Contract signing None 5 B Questionnaire design A 5 C Target market ID A 6 D Survey sample B, C 13 E Develop presentation B 6 F Analyze results D 4 G Demographic analysis C 9 H Presentation to client E, F, G 2 Construct the critical path.

Activity Network with Task Durations and Critical Path B Design 5 E Dev. Present 6 A Contract 5 D Survey 13 F Analysis 4 H Present 2 C Market ID 6 G Demog. 9 Critical Path is indicated in bold

Rules for Forward/Backward Pass Forward Pass Rules (ES & EF) ES + Duration = EF EF of predecessor = ES of successor Largest preceding EF at a merge point becomes ES for successor Backward Pass Rules (LS & LF) LF – Duration = LS LS of successor = LF of predecessor Smallest succeeding LS at a burst point becomes LF for predecessor ES ID EF Slack Task Name LS Duration LF Calculate the forward/backwards pass.

Activity Network with Forward Pass Added 5 B 10 Design 5 10 E 16 Dev. Present 6 0 A 5 Contract 5 11 D 24 Survey 13 24 F 28 Analysis 4 28 H 30 Presentation 2 5 C 11 Market ID 6 11 G 20 Demograph. 9 ES ID EF Slack Task Name LS Duration LF

Activity Network With Backward Pass Added Design 6 5 11 10 E 16 Dev. Present 22 6 28 0 A 5 Contract 0 5 5 11 D 24 Survey 11 13 24 24 F 28 Analysis 24 4 28 28 H 30 Presentation 28 2 30 5 C 11 Market ID 5 6 11 11 G 20 Demograph. 19 9 28 ES ID EF Slack Task Name LS Duration LF

Activity Float - Slack Time Informs us of the amount an activity can be delayed without delaying the overall project. It is determined as a result of performing the forward and backward pass through the network. Calculated either by LF-EF = Slack LS-ES = Slack The critical path is the network path with “0” slack.* *This assumes a deadline has not been set for LF that is within our calculated project time. *Negative float is a result of the project time being longer than a set project end time. Calculate the slack time and determine critical path.

Critical Path is indicated in bold Completed Activity Network With Critical Path And Activity Slack Times Identified 5 B 10 1 Design 6 5 11 10 E 16 12 Dev. Present 22 6 28 0 A 5 0 Contract 0 5 5 11 D 24 0 Survey 11 13 24 24 F 28 0 Analysis 24 4 28 28 H 30 0 Presentation 28 2 30 Critical Path is indicated in bold 5 C 11 0 Market ID 5 6 11 11 G 20 8 Demograph. 19 9 28 ES ID EF Slack Task Name LS Duration LF

Example Sketch the network described in the table. Determine the ES, LS, EF, LF, and slack of each activity. Determine the critical path. Task Predecessor Time A -- 4 B 9 C 11 D 5 E 3 F 7 G D, F H E, G 2 K 1 Task ES EF LS LF Slack A 0 4 0 4 0 B 4 13 8 17 4 C 4 15 4 15 0 D 13 18 17 22 4 E 13 16 22 25 9 F 15 22 15 22 0 G 22 25 22 25 0 H 25 27 25 27 0 K 27 28 27 28 0

Laddering Activities ABC=18 days Laddered ABC=12 days A(3) B(6) C(9) Project ABC can be completed more efficiently if subtasks are used. Example: A does not need to be completely finished before work on B starts. ABC=18 days A(3) B(6) C(9) A1(1) A2(1) A3(1) B1(2) B2(2) B3(2) C1(3) C2(3) C3(3) Laddered ABC=12 days

Hammock Activities Used as a summary for subsets of activities 0 A 5 0 5 5 B 15 5 10 15 15 C 18 15 3 18 0 Hammock 18 0 18 18 Useful with a complex project or one that has a shared budget

Reducing the Critical Path Eliminate tasks on the critical path remove task with no value Convert serial paths to parallel when possible Overlap sequential tasks use laddering when possible Shorten the duration on critical path tasks Shorten early tasks (have you read “The Goal”) longest tasks easiest tasks tasks that cost the least to speed up – “crashing”

Discussion Questions Define the following terms: Path, Activity, Early start, Early finish, Late start, Late finish, Forward pass, Backward pass, Node, AON, Float, Critical Path, PERT Distinguish between serial activities and concurrent activities. Why do we seek to use concurrent activities as a way to shorten a project’s length? List three methods for deriving duration estimates for project activities. What are the strengths and weaknesses associated with each method?

Discussion Questions In your opinion, what are the chief benefits and drawbacks of using beta distribution calculations (based on PERT techniques) to derive activity duration estimates? “The shortest total length of a project is determined by the longest path through the network.” Explain the concept behind this statement. Why does the longest path determine the shortest project length? The float associated with each project task can only be derived following the completion of the forward and backward passes. Explain why this is true.

Case Study 5 Now that Joe has agreed to your WBS, he wants to review a schedule and present it to the president. She is a “big picture” thinker and does not usually get involved with the details, so Joe wants to limit the content of the diagram you show her to the basics that concern her. You have also worked with your team on estimating the durations of each of the work packages in the WBS. Note that in this case, the work packages are the scheduled activities. Here is your current plan for the briefing to the president:

Case Study 5

Case Study 5 Build a network diagram Calculate forward pass, backward pass, float, and critical path Be ready to address— How long will the project take? When should you begin installing new furniture, communications equipment, and computers if you want to be in the new office by July 31? What items are on the critical path?