1 Project Planning, Scheduling and Control Project – a set of partially ordered, interrelated activities that must be completed to achieve a goal.

2 Network Models PERT – Program Evaluation and Review Technique –probabilistic features CPM – Critical Path Method –cost/time trade-offs project scheduler

3 Objectives Planning, scheduling, and control of complex projects Find critical activities to manage resources (management by exception) Determine flexibility of non-critical activities (slack) Estimate earliest completion time of project Determine time – cost trade-offs

4 Service Industry Distribution Industry Producing Industry Business and Industry – a taxonomy Raw materials Continuous Processing Discrete Products Mining Drilling Farming Construction Manufacturing Chemicals Food Refinery BatchMass Processing Production

5 Production Systems Job shops Flow shops Batch production Mass production Cellular manufacturing Project Shop Continuous Processing Gosh. Can you tell us more about these?

6 Project Shop single product in fixed location material and labor brought to the site usually job shop/flow shop associated functionalized production system examples include construction and shipbuilding

7 The Elements of Project Scheduling Project Definition. Statement of project, goals, and resources required. Activity Definitions. Content and requirements of each activity. Project Scheduling. Specification of starting and ending times of all activities. Project Monitoring. Keeping track of the progress of the project.

8 Definitions Activity – an effort (task) that requires resources and takes a certain amount of time. Event – a specific accomplishment or milestone (the start or finish of an activity). Project – a collection of activities and events leading to a definable goal. Network – a graphical representation of a project depicting the precedence relationships among the activities and events. Critical Activity – an activity that if delayed will hold up the scheduled completion of a project. Critical Path – the sequence of critical activities that forms a continuous path from the start of a project to its completion.

9 Framework for Analysis Analyze project in terms of activities and events Determine sequence (precedence) of activities (develop network) Assign estimates of time, cost, and resources to all activities Identify the critical path monitor, evaluate, and control progress of project

10 Network Representation Projects may be represented as networks with: Arrows representing activities. Nodes representing completion of a set of activities (milestones). Pseudo activities may be required to satisfy precedence relationships.

11 Network Development 123 events (nodes) activities (arcs) Activities have duration and may have precedence. Define activities in terms of their beginning and ending events. e.g. Activity 1-2 must precede Activity 2-3

12 Network Development (continued) Event 1 is start of project Activities 1-2, 1-3, and 1-4 have no predecessors and may start simultaneously

13 Network Development (continued) n-2 n-3 n n-1 Event n is the end of the project. Activities (n-3 – n, (n-2) – n, and (n-1) - n must be completed for the project to be completed.

14 Network Development (continued) Activities 6-7, 6-8, and 6-9 cannot start until activity 5-6 has been completed. 5 burst event

15 Network Development (continued) Activities 5-8, 6-8, and 7-8 must be completed before activity 8-9 may begin. 9 merge event

16 Network Development (continued) Activities 5-8, 6-8, and 7-8 must be completed before activity 8-9, 8-10, or 8-11 may begin Gosh! A combined merge and burst event. Are these rare or what?

17 Dummy activity ACADBDACADBD W R O N G A B C D A B D C 8 dummy has no resources and no duration

18 Project Networks Collection of nodes and arcs Depicted graphically Events are uniquely numbered Arcs are labeled according to their beginning and ending events –Ending events always have higher numbers than beginning events Two activities cannot have the same beginning and ending events Activity lengths have no significance

19 Our Very Own Example product development activitydescriptionprecedence Adesign promotion campaign- Binitial pricing- Cproduct design- Dpromotion cost analysisA Emanufacture prototypeC Ftest and redesignE Gfinal pricingB,D,F Hmarket testG

20 product development A B C D E F G H

21 Notation i-j = an activity of a project d i-j = the duration of activity i-j E i = the earliest time event i can occur ES i-j = the earliest start time of activity i-j EF i-j = the earliest finish time of activity i-j LS i-j = the latest start time of activity i-j LF i-j = the latest finish time of activity i-j L i = the latest time event i can occur

22 Our Very Own Example product development activityprecedenceduration (days) A (1-2)-17 B (1-5)-7 C (1-3)-33 D (2-5)A6 E (3-4)C40 F (4-5)E7 G (5-6)B,D,F12 H (6-7)G48

23 product development – forward pass A(17) B(7) C(33) D(6) E(40) F(7) G(12) H(48) E 1 = 0 ES 1-2 = 0 ES 1-5 = 0 ES 1-3 = 0 EF 1-2 = 17 EF 1-5 = 7 EF 1-3 = 33 E 2 = 17 E 5 = 7 E 3 = 33 ES 5-6 = 80 EF 5-6 = 92 E 6 = 92 ES 2-5 = 17 ES 3-4 = 33 EF 2-5 = 23 EF 3-4 = 73 E 4 = 73 ES 4-5 = 73 EF 4-5 = 80 E 5 = 80 ES 6-7 = 92 EF 6-7 = 140 E 7 = 140

24 product development – backward pass A(17) B(7) C(33) D(6) E(40) F(7) G(12) H(48) L 1 = 0 LF 1-2 = 74 LF 1-5 = 80 LF 1-3 = 33 L 2 = 74 L 3 = 33 L 6 = 92 LF 5-6 = 92 LS 5-6 = 80 LF 2-5 = 80 LS 2-5 = 74 LF 3-4 = 73 LS 3-4 = 33 L 4 = 73 LF 4-5 = 80 LS 4-5 = 73 L 5 = 80 L 7 = 140 LF 6-7 = 140 LS 6-7 = 92 LS 1-2 = 57 LS 1-5 = 73 LS 1-3 = 0

25 Activity Slack S i-j = LS i-j – ES i-j S i-j = LF i-j – EF i-j or ActivityLSESSlack critical activities

26 Critical Path Method An analytical tool that provides a schedule that completes the project in minimum time subject to the precedence constraints. In addition, CPM provides: Starting and ending times for each activity Identification of the critical activities (i.e., the ones whose delay necessarily delay the project). Identification of the non-critical activities, and the amount of slack time available when scheduling these activities.

27 critical path A(17) B(7) C(33) D(6) E(40) F(7) G(12) H(48) ES 1-3 = 0 LS 1-3 = 0 ES 5-6 = 80 LS 5-6 = 80 ES 3-4 = 33 LS 3-4 = 33 ES 4-5 = 73 LS 4-5 = 73 ES 6-7 = 92 LS 6-7 = 92 ES 1-5 = 0 LS 1-5 = 73 ES 2-5 = 17 LS 2-5 = 74 ES 1-2 = 0 LS 1-2 = 57

28 Critical Path Activities focus management attention increase resources eliminate delays eliminate critical activities overlap critical activities break activity into smaller tasks outsource or subcontract

29 Critical Path by LP earliest start times latest start times

30 Activity Durations ab uniform triangular beta

31 More Activity Durations let a = optimistic time b = pessimistic time m = most likely time uniform: triangular: beta:

32 activity durations product development activityamb A (1-2) B (1-5) C (1-3) D (2-5) E (3-4) F (4-5) G (5-6) H (6-7) beta note: based upon a 6 day workweek

33 critical path analysis product development activityamb C (1-3) E (3-4) F (4-5) G (5-6) H (6-7) sum beta From the Central Limit Theorem, project completion time is normally distributed with a mean of 140 days and a standard deviation of = 10.5 days.

34 Probability Statements Probability project will be completed by day 150 is given by: Probability project will be completed after day 130 is given by:

35 Resource Constraints ActivityESDurationstaffing

36 Resource Profile – early start schedule This doesn’t work. We need too many people at the start of the project!

37 Late Start Staffing ActivityESDurationstaffing

38 Resource Profile – late start schedule Boss. Let’s go with the late start schedule. Then we can layoff some folks.

39 Time Costing Methods Suppose that projects can be expedited by reducing the time required for critical activities. Doing so results in an increase in some costs and a decrease in others. The goal is to determine the optimal number of days to schedule the project to minimize total cost. Assume that there is a linear time/cost relationship for each activity.

40 Time-Cost Trade-offs time crash time normal time crash cost normal cost

41 Heuristic Crashing = $ / day timecost activity normal crashnormal crashk C (1-3) E (3-4) F (4-5) G (5-6) H (6-7)

42 An LP approach let y i-j = number of time units activity i-j is crashed K = indirect cost per day

43 The End Backups Follow

44 Forward Pass set E i = 0 i=1; j=2 set ES i-j = E i EF i-j = E i + d i-j E j = max {E j, EF i-j } If i-j is an activity set j = j + 1 j <= n i = i + 1 j = 2 j > n i < n stop i = n If i-j not an activity

45 Backward Pass set L i = E n i=1; j=n set LF i-j = L i LS i-j = L i - d i-j L j = min {L j, LF i-j } If i-j is an activity set i = i + 1 i < n j = j - 1 i = 1 i = n j > 0 stop j = 0 If i-j not an activity