OUTLINE

1. OUTLINE • Questions? • Major projects in the news? • Take roll • Budgeting – additional topics • Start Chapter 5

2. Adding up the costs (Second example) • Labor = 0.2 hours, material = $200 • Direct and indirect labor =0.2* $146.40=$29.28 • Material =$200.00 • Material Overhead= 0.057*200 =$11.40 • Total Cost =$240.68 • We can separate the direct and indirect labor into: • Direct labor = 0.2*30 =$6 • Indirect =$23.28 • And you can see why everyone attacks Material Costs • If you are independent, the profit would add another 10% or so. It is very dependent on the industry and level of investment

3. Cost Distribution (second example)

4. Learning curves • Most repetitive human activities tend to become more efficient at first and if repeated too many times, fatigue or boredom sets in and they become less efficient • Examples • Computer development project operating at 57 hours per week for more than 6 months • Daily manufacturing labor productivity per hour

5. Learning curves

6. Learning curves

7. Time series forecasting • Mean average deviation (MAD) = the average of the absolute differences between forecasts and actuals • Tracking Signal (TS) = Running sum of forecast errors divided by the number of forecasts

8. Scheduling • Background • Network Techniques • Terminology • Constructing the network • Gantt charts • Risk Analysis

9. Background • Not all project activities need to be scheduled at the same level of detail. In fact, there may be several schedules (e.g., the master schedule, the development and testing schedule, the assembly schedule). • These schedules are typically based on the previously determined action plan and/or work breakdown structure (WBS), and it is good practice to create a schedule for each major task level in the WBS that will cover the work packages. • It is rarely necessary, however, to list all work packages. One can focus mainly on those that need to be monitored for maintaining adequate control over the project. (Caution – easy to skip important tasks!)

10. Background – Basic approach • The basic approach of all scheduling techniques is to form a network of activity and event relationships that graphically portrays the sequential relations between the tasks in a project. • Tasks that must precede or follow other tasks are then clearly identified, in time as well as function. • Such a network is a powerful tool for planning and controlling a project.

11. Benefits of scheduling • It is a consistent framework for planning, scheduling, monitoring, and controlling the project. • It illustrates the interdependence of all tasks, work packages, and work elements. • It denotes the times when specific individuals and resources must be available for work on a given task. • It determines an expected project completion date. • It identifies so-called critical activities that, if delayed, will delay the project completion time.

12. Benefits of scheduling (cont) • It also identifies activities with slack that can be delayed for specified periods without penalty, or from which resources may be temporarily borrowed without harm. • It determines the dates on which tasks may be started-or must be started if the project is to stay on schedule. • It illustrates which tasks must be coordinated to avoid resource or timing conflicts. • It also illustrates which tasks may be run, or must be run, in parallel to achieve the predetermined project completion date. • It relieves some interpersonal conflict by clearly showing task dependencies. • It may, depending on the information used, allow an estimate of the probability of project completion by various dates, or the date corresponding to a particular a priori probability.

13. Project Scheduling • Analyze -- Plan -- Schedule -- represented as a network of activities • Most used: • PERT - Program Evaluation and Review Technique • CPM - Critical Path Method

14. Project Scheduling

15. My earliest venture into scheduling

16. Project Scheduling • Predecessor and successor relationships between activities • If there is no such relationship, the activity is independent • Durations are independent (necessary for statistical analysis)

17. Project Scheduling • Activity = Task = Job • Has a beginning and an end • Has a duration = elapsed time = process time • Uses resources

18. Project Scheduling • Planning and scheduling steps • Identify activities • Precedence constraints • Construct the network • Estimate durations • Assign starting times • Analyze resources • Once project starts, check progress against plan • Reschedule

19. Project Scheduling – Networks AOA – Activity On Arc • Network = directed graph • Finite number of nodes (n) i,j, ….. = N • subset of ordered pairs (i,j) = arcs = A • To draw a network: • from each i of N, draw arrow to j, if (i,j) is in A • where • arrow = (i,j) or name of activity (AOA) • i - starting event • j - ending event Activity i Start j end

20. Project Scheduling – Networks AON – Activity on Node • Network = directed graph • Finite number of nodes (n) i,j, ….. = N = Activities • To draw a network: • Create a starting point • Draw a box for each activity • Connect predecessors and dependents with single arrows

21. Project Scheduling - Networks (cont) • Rules: • The length of the arrow has no significance • At a node, the activity cannot start until all predecessor activities are complete

22. Project Scheduling - Networks (cont) • Rules (continued) • Only one initial node (no predecessors) and only one terminal node (no successors) • An activity is uniquely identified by start and end events • - no duplicate node numbers • - at most one arrow between nodes • No closed loops!

23. Project Scheduling - Networks (cont) • Multiple paths can be avoided with dummies Dummy

24. Project Scheduling - Network example

25. Project Scheduling - Example – AOA List • List activity only if its predecessor is complete – non-decreasing i or j numbers - topological order

26. Project Scheduling – an AOA example • B - E - F 3 + 2 + 2 = 7 • A - D - E - F 2 + 2 + 2 + 2 = 8 • A - C - F 2 + 5 + 2 = 9 Critical path, similar to bottleneck idea • We’ll generate all possible schedules to get the concepts C, 5 A, 2 2 F, 2 D,2 4 5 1 3 E, 2 B, 3 • 3

27. Comments • Does it matter if AOA or AON diagrams are used? While the book maps PERT to AOA and CPM to AON, is there any logic behind this decision? No it does not • Are Beta distributions always used? I’ve seen triangular distributions used in practice when those three parameters are estimated (process times involving people in manufacturing plants). Is there any benefit to using one over another if the data can be fit to what you estimate? • Triangular distributions are excellent approximations to the beta – that is why they are popular. • Beta distributions are continuous, triangular ones are not – so where mathematics requires continuity, beta are preferred. Another consideration is the audience – triangular is easier to explain, although all distributions are difficult to explain to people.

28. Project Scheduling - More definitions • Earliest start time ESij or ESA • delayed = start after earliest start time • Latest start time LSij or LSA • Delay without affecting start of successors = free slack = Fsij • Delay that affects start of successors - Total slack - TSij • Free slack <= Total slack • Critical activities have the least total slack, usually 0

29. Project Scheduling - More definitions(cont) • EF = Earliest finish • LF = Latest finish • Y = duration • Forward pass to determine ES • Topological order - a task is listed only if all its predecessors have been listed

30. Project Scheduling - Forward Pass

31. Project Scheduling - More definitions(cont) • Backward Pass • Reverse topological order • Free slack = scheduling flexibility with respect to its immediate successors

32. Project Scheduling - Backward Pass

33. Project Scheduling • Free slack - scheduling flexibility with respect to its immediate successors • FSij = min [ ES of all immediate successors] - EFij • FSA= min [ESD, ESC] - EFA = min[2, 2] - 2 = 0 • FSB= ESE - EFB = 4 - 3 = 1 • FSC= ESF - EFC = 7 - 7 = 0 • FSD= ESE - EFD = 4 - 4 = 0 • FSE= ESF - EFE = 7 - 6 = 1 • FSF = 9 - 9 - 0

34. Project Scheduling • Total Slack - scheduling flexibility relative to the project completion time • TSij = LSij - ESij = LFij - Efij • TSA = 0 - 0 = 0 • TSB = 2 - 0 = 2 • TSC = 2 - 2 = 0 • TSD = 3 - 2 = 1 • TSE = 5 - 4 = 1 • TSF = 7 - 7 = 0 • Note that the activities on the critical path have 0 total slack

35. More Statistics Review • Distributions • All measurable things vary, even if we assume that they are constant. This is why we call them random variables. • A random variable can be described by its mean and its standard deviation and the shape of its distribution • Most natural phenomena are normally distributed. The normal distribution extends to plus and minus infinity, so it is not useful for variables that have definite minima and maxima • The beta distribution does have these cutoffs.