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Project Scheduling Prof. Jiang Zhibin Dept. of IE, SJTU

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What ’ s a Project? Bringing about change is hard Many related activities Hard to plan production A project focuses on the outcome Regular teamwork focuses on the work process

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Examples of Projects Building construction New product introduction Software implementation Training seminar Research project

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Project Scheduling Establishing objectives Determining available resources Sequencing activities Identifying precedence relationships Determining activity times & costs Estimating material & worker requirements Determining critical activities

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Project Scheduling Techniques Gantt chart Critical Path Method (CPM) Program Evaluation & Review Technique (PERT)

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Gantt Chart

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PERT & CPM Network techniques Developed in 1950 ’ s CPM by DuPont for chemical plants PERT by U.S. Navy for Polaris missile Consider precedence relationships & interdependencies Each uses a different estimate of activity times

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Completion date? On schedule? Within budget? Probability of completing by...? Critical activities? Enough resources available? How can the project be finished early at the least cost? Questions Answered by PERT & CPM

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PERT & CPM Steps Identify activities Determine sequence Create network Determine activity times Find critical path Earliest & latest start times Earliest & latest finish times Slack

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Activity on Node (AoN) 2 4? Years Enroll Receive diploma Project: Obtain a college degree (B.S.) 1 month Attend class, study etc. 1 1 day 3

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Activity on Arc (AoA) 4,5 ? Years Enroll Receive diploma Project: Obtain a college degree (B.S.) 1 month Attend class, study, etc. 1 1 day 234

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AoA Nodes Have Meaning Graduating Senior Applicant Project: Obtain a college degree (B.S.) 1 Alum 234 Student

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Activity Relationships 1-2 must be done before 2-3 or 3-4 can start 2 3 4 1

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Activity Relationships 2-3 must be done before 3-4 or 3-5 can start 2 3 4 1 5

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Activity Relationships 2-4 and 3-4 must be done before 4-5 can start 2 3 4 1 5

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Activity Relationships When 5-6 is done, project is complete. 2 3 4 1 56

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Network Example You ’ re a project manager for Bechtel. Construct the network. ActivityPredecessors A-- BA CA DB EB FC GD HE, F

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Network Example - AON ACEFBDGHZ

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Network Example - AOA 2 4 5136879 A C F E B D H G

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AOA Diagrams 231 A C B D A precedes B and C, B and C precede D 241 A C B D 354 Add a phantom arc for clarity.

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Critical Path Analysis Provides activity information Earliest (ES) & latest (LS) start Earliest (EF) & latest (LF) finish Slack (S): Allowable delay Identifies critical path Longest path in network Shortest time project can be completed Any delay on activities delays project Activities have 0 slack

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Critical Path Analysis Example

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Network Solution A A E E D D B B C C F F G G 1 6 2 3 1 43

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Earliest Start & Finish Steps Begin at starting event & work forward ES = 0 for starting activities ES is earliest start EF = ES + Activity time EF is earliest finish ES = Maximum EF of all predecessors for non-starting activities

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Activity A Earliest Start Solution For starting activities, ES = 0. A A E E D D B B C C F F G G 1 6 2 3 1 43

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Earliest Start Solution A A E E D D B B C C F F G G 1 6 2 3 1 43

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Latest Start & Finish Steps Begin at ending event & work backward LF = Maximum EF for ending activities LF is latest finish; EF is earliest finish LS = LF - Activity time LS is latest start LF = Minimum LS of all successors for non-ending activities

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Earliest Start Solution A A E E D D B B C C F F G G 1 6 2 3 1 4 3

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Latest Finish Solution A A E E D D B B C C F F G G 1 6 2 3 1 43

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Compute Slack

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Critical Path A A E E D D B B C C F F G G 1 6 2 3 1 43

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New notation Compute ES, EF for each activity, Left to Right Compute, LF, LS, Right to Left C 7 LSLF ESEF

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PERT Activity Times 3 time estimates Optimistic times (a) Most-likely time (m) Pessimistic time (b) Follow beta distribution Expected time: t = (a + 4m + b)/6 Variance of times: v = (b - a) 2 /36

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Project Times Expected project time (T) Sum of critical path activity times, t Project variance (V) Sum of critical path activity variances, v

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PERT Probability Example You ’ re a project planner for Sun Microsystems. A software project has an expected completion time of 40 weeks, with a standard deviation of 5 weeks. What is the probability of finishing the project in 50 weeks or less?

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Converting to Standardized Variable From Normal Distribution Table, Probability = 0.5 + 0.4772 = 0.9772

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Time-Cost Models 1. Identify the critical path 2. Find cost per day to expedite each node on critical path. 3. For cheapest node to expedite, reduce it as much as possible, or until critical path changes. 4. Repeat 1-3 until no feasible savings exist.

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Benefits of PERT/CPM Useful at many stages of project management Mathematically simple Use graphical displays Give critical path & slack time Provide project documentation Useful in monitoring costs

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Limitations of PERT/CPM Clearly defined, independent, & stable activities Specified precedence relationships Activity times (PERT) follow beta distribution Subjective time estimates Over emphasis on critical path

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Conclusion Explained what a project is Summarized the 3 main project management activities Drew project networks Compared PERT & CPM Determined slack & critical path Computed project probabilities

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