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Quantitative Decision Techniques

Quantitative Decision Techniques. 30/03/2009 PROJECT MANAGEMENT. Project Planning, Scheduling, and Controlling. Project Planning 1. Setting goals 2. Defining the project 3. Tying needs into timed project activities 4. Organizing the team. Project Scheduling

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Quantitative Decision Techniques

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  1. Quantitative Decision Techniques 30/03/2009 PROJECT MANAGEMENT

  2. Project Planning, Scheduling, and Controlling Project Planning 1. Setting goals 2. Defining the project 3. Tying needs into timed project activities 4. Organizing the team Project Scheduling 1. Tying resources to specific activities 2. Relating activities to each other 3. Updating and revising on regular basis Project Controlling 1. Monitoring resources, costs, quality and budgets 2. Revising and changing plans 3. Shifting resources to meet demands Before Project During Project

  3. Project Management Models • PERT – Program Evaluation and Review Technique • CPM -Critical Path Method

  4. Six Steps Common toPERT and CPM • Define the project and all of its significant activities or tasks. • Develop relationships among the activities. Decide which activities must precede and which ones must follow others. • Draw the network connecting all of the activities. • Assign time and/or cost estimates to each activity • Compute the longest time path through the network. This is called the critical path. • Use the network to help plan, schedule, monitor, and control the project.

  5. Questions That May Be Addressed by PERT and CPM • When will the project be completed? • What are the critical activities or tasks in the project? • Which are the noncritical activities? • What is the probability that the project will be completed by a specific date? • Is the project on schedule, ahead of schedule, or behind schedule? • Is the project over or under the budgeted amount? • Are there enough resources available to finish the project on time? • If the project must be finished in less than the scheduled amount of time, what is the best way to accomplish this at least cost?

  6. Identifying Activities • Subdivides a large project into smaller units • Each activity should have a clearly defined starting point and ending point • Each activity is clearly distinguishable from every other activity • Each activity can be a project in itself

  7. Project: Design a garment • Refining your idea (including identifying the style and who will wear it)  • Sketching the design • Pattern making • Steps for draping • Choosing the fabric, color, trims, etc. • Making samples • Manufacturing garments

  8. General Foundry Inc. • Have 16 weeks to install a complex air filter system on its smokestack • May be forced to close if not completed w/in 16 weeks due to environmental regulations • Have identified 8 activities

  9. For Each Activity Identify: • Which other activities must be completed previously (predecessors) • Time required for completion • Resources required

  10. A - Activity on Arc A - Activity on Node Methods of Diagramming Projects AON – Activity on Node networks show each activity as a node and arcs show the immediate predecessor activities AOA – Activity on Arc networks show each activity as an arc, and the nodes represent the starting and ending points We’ll use AON

  11. AON Network for General Foundry

  12. Activity Times • Uses 3 time estimates for each activity Optimistic time (a) Pessimistic time (b) Most likely time (m) • These estimates are used to calculate an expected value and variance for each activity (based on the Beta distribution)

  13. TIME ESTIMATES for General Foundry

  14. Calculating Time Estimates • Expected activity time (t) t = (a + 4m + b) 6 • Variance = [ (b – a) / 6 ]2 • Standard deviation = SQRT(variance) = (b – a) 6

  15. Time Estimates for General Foundry

  16. Activity Time Estimates

  17. Determining the Project Schedule • Some activities can be done simultaneously so project duration should be less than 25 weeks • Critical path analysis is used to determine project duration • The critical path is the longest path through the network

  18. Critical Path Analysis Need to find the following for each activity: • Earliest Start Time (EST) • Earliest Finish Time (EFT) • Latest start time (LST) • Latest Finish Time (LFT)

  19. Node Notation:

  20. ForwardPass • Identifies earliest times (EST and EFT) • EFT Rule: EFT = EST + activity time • EST Rule: All immediate predecessors must be done before an activity can begin • If only 1 immediate predecessor, then EST = EFT of predecessor • If >1 immediate predecessors, then EST = Max {all predecessor EFT’s}

  21. Forward Pass: Earliest Start and Finish Times

  22. BackwardPass • Identifies latest times (LST an LFT) • LFT Rule: • If activity is the immediate predecessor to only 1 activity, then LFT = LST of immediate follower • If activity is the immediate predecessor to multiple activities, then LFT = Min {LST of all imm. followers} • LST Rule: LST = LFT – activity time

  23. Backward Pass: Latest Start and Finish Times

  24. Slack Time and Critical Path(s) • Slack is the length of time an activity can be delayed without delaying the project Slack = LST – EST • Activities with 0 slack are CriticalActivities • The Critical Path is a continuous path through the network from start to finish that include only critical activities

  25. Project Schedule and Slack Times

  26. Project Variance and Standard Deviation • Project variance (σp2) = ∑ (variances of all critical path activities) σp2 = 0.11 + 0.11 + 1.0 + 1.78 + 0.11 = 3.11 • Project standard deviation (σp) = SQRT (Project variance) σp = SQRT ( 3.11) = 1.76

  27. Probability of Project Completion • What is the probability of finishing the project within 16 weeks? • Assumptions: • Project duration is normally distributed • Activity times are independent • Normal distribution parameters: μp = expected completion time= 15 weeks σp = proj standard deviation = 1.76 weeks

  28. Normal Probability Calculations Z = (Target time – expected time) σp Z = (16 - 15) = 0.57 1.76 This means 16 weeks is 0.57 standard deviations above the mean of 15 weeks.

  29. Probability Based on Standard Normal Table Prob (proj completion < 16 weeks) = 0.7158

  30. Project Duration fora Given Probability • What project duration does General Foundry have a 99% chance of completing the project within? i.e. Prob (proj duration < ? ) = 0.99 • From Std. Normal Table, this corresponds to Z = 2.33

  31. Z = (? - 15) = 2.33 1.76 So ? = 15 + 2.33 x 1.76 = 19.1 weeks

  32. Scheduling Project Costs • Estimate total cost for each activity • Identify when cost will actually be spent (we will assume costs are spread evenly) • Use EST and LST for each activity to determine how costs are spread over project

  33. Monitoring and Controlling Project Costs • While the project is underway, costs are tracked and compared to the budget • What is the value of work completed? Value of work completed = (% of work completed) x (total activity budget) • Are there any cost overruns? Cost difference = (Actual cost) – (Value of work completed)

  34. Project Crashing • Reducing a project’s duration is called crashing • Some activities’ times can be shortened (by adding more resources, working overtime, etc.) • The crash time of an activity is the shortest possible duration, and has an associated crash cost

  35. Steps in Project Crashing • Compute the crash cost per time period • Find the current critical path (CP) • Find the lowest cost way to crash the CP by 1 time period • Update all activity times. If further crashing is needed, go to step 2.

  36. Crash and Normal Times and Costs Activity Cost Crash Crash Cost - Normal Cost $34,000 $33,000 $32,000 $31,000 $30,000 Crash Cost/Week = Normal Time - Crash Time Crash Cost $34,000 - $30,000 = 3 - 1 $4,000 = = $2,000/Week 2 Weeks Normal Normal Cost 1 2 3 Time (Weeks) Crash Time Normal Time PG 13.19

  37. Crashing UsingLinear Programming Decision: How many time periods to crash each activity? Objective: Minimize the total crash cost Decision Variables Ti = time at which activity i starts Ci = number of periods to crash activity i

  38. Advantages of PERT/CPM • useful at several stages of project management • straightforward in concept, and not mathematically complex • uses graphical displays employing networks to help user perceive relationships among project activities • critical path and slack time analyses help pinpoint activities that need to be closely watched • networks generated provide valuable project documentation and graphically point out who is responsible for various project activities • applicable to a wide variety of projects and industries • useful in monitoring not only schedules, but costs as well

  39. Limitations of PERT/CPM • project activities must be clearly defined, independent, and stable in their relationships • precedence relationships must be specified and networked together • time activities in PERT are assumed to follow the beta probability distribution -- this may be difficult to verify • time estimates tend to be subjective, and are subject to fudging by managers • there is inherent danger in too much emphasis being placed on the critical path

  40. REFERENCES • Quantitative Analysis for Management, 9th Edition, Barry Render, Ralph M. Stair, M. Hanna, Prentice Hall, New Jersey, 2006. ISBN: 0-13-153688-5, ITU Library Number: T56.R46 2006. • Introduction to Management Science, 9th Edition, Taylor B.W., Prentice Hall, New Jersey, 2007. ISBN: 0-13-1966133-0, ITU Library Number: T56.T39.1990/T56.T39 1986.

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