Managing Projects

Project Management Questions zWhat activities are required to complete a project and in what sequence? zWhen should each activity be scheduled to begin and end? zWhich activities are critical to completing the project on time? zWhat is the probability of meeting the project completion due date? zHow should resources be allocated to activities?

Tennis Tournament Activities ID Activity Description Network Immediate Duration Node Predecessor (days) 1 Negotiate for Location A Contact Seeded Players B Plan Promotion C Locate Officials D Send RSVP Invitations E Sign Player Contracts F 2,3 4 7 Purchase Balls and Trophies G Negotiate Catering H 5,6 1 9 Prepare Location I 5, Tournament J 8,9 2

Notation for Critical Path Analysis Item Symbol Definition Activity duration t The expected duration of an activity Early start ES The earliest time an activity can begin if all previous activities are begun at their earliest times Early finish EF The earliest time an activity can be completed if it is started at its early start time Late start LS The latest time an activity can begin without delaying the completion of the project Late finish LF The latest time an activity can be completed if it is started at its latest start time Total slack TS The amount of time an activity can be delayed without delaying the completion of the project

Scheduling Formulas ES = EFpredecessor (max) (1) EF = ES + t (2) LF = LSsuccessor (min) (3) LS = LF - t (4) TS = LF - EF (5) TS = LS - ES (6) or

Tennis Tournament Activity on Node Diagram J2J2 B8B8 START A2A2 C3C3 D2D2 G4G4 E 10 I3I3 F4F4 H1H1 TS ESEF LSLF

Early Start Gantt Chart for Tennis Tournament ID Activity Days Day of Project Schedule A Negotiate for 2 Location B Contact Seeded 8 Players C Plan Promotion 3 D Locate Officials 2 E Send RSVP 10 Invitations F Sign Player 4 Contracts G Purchase Balls 4 and Trophies H Negotiate 1 Catering I Prepare Location 3 J Tournament 2 Personnel Required Critical Path Activities Activities with Slack

Resource Leveled Schedule for Tennis Tournament ID Activity Days Day of Project Schedule A Negotiate for 2 Location B Contact Seeded 8 Players C Plan Promotion 3 D Locate Officials 2 E Send RSVP 10 Invitations F Sign Player 4 Contracts G Purchase Balls 4 and Trophies H Negotiate 1 Catering I Prepare Location 3 J Tournament 2 Personnel Required Critical Path Activities Activities with Slack

Incorporating Uncertainty in Activity times A M D B F(D) P(D<A) =.01 P(D>B) =.01 optimistic most pessimistic likely TIME

Formulas for Beta Distribution of Activity Duration Expected Duration Variance Note: (B - A )= Range or

Activity Means and Variances for Tennis Tournament Activity A M B D V A B C D E F G H I J 2 2 2

Uncertainly Analysis Assumptions 1. Use of Beta Distribution and Formulas For D and V 2. Activities Statistically Independent 3. Central Limit Theorem Applies ( Use “student t” if less than 30 activities on CP) 4. Use of Critical Path Activities Leading Into Event Node Result Project Completion Time Distribution is Normal With: For Critical Path Activities

Completion Time Distribution for Tennis Tournament Critical Path Activities D V A 2 4/36 C 3 4/36 E /36 I 3 36/36 J 2 0 = /36 = 5.2 =

Question What is the probability of an overrun if a 24 day completion time is promised? 24 P (Time > 24) = =.04 or 4% Days

Costs for Hypothetical Project Cost (0,0) Schedule with Minimum Total Cost Duration of Project Total Cost Indirect Cost Opportunity Cost Direct Cost

Activity Cost-time Tradeoff C C*C* D*D* D Activity Duration (Days) Normal Crash Slope is cost to expedite per day Cost

Cost-Time Estimates for Tennis Tournament Time Estimate Direct Cost Expedite Cost Activity Normal Crash Normal Crash Slope A B C D E F G H I J Total 115

Progressive Crashing Project Activity Direct Indirect Opportunity Total Duration Crashed Cost Cost Cost Cost 20 Normal Normal Duration After Crashing Activity Project Paths Duration A-C-D-G-I-J 16 A-C-E-I-J 20 A-C-E-H-J 18 A-C-F-H-J 12 B-F-H-J 15

Applying Theory of Constraints to Project Management zWhy does activity safety time exist and is subsequently lost? 1. Dependencies between activities cause delays to accumulate. 2. The “student syndrome” procrastination phenomena. 3. Multi-tasking muddles priorities. zThe “Critical Chain” is the longest sequence of dependent activities and common resources. z Replacing safety time with buffers - Feeding buffer (FB) protects the critical chain from delays. - Project buffer (PB) is a safety time added to the end of the critical chain to protect the project completion date. - Resource buffer (RB) ensures that resources (e.g. rental equipment) are available to perform critical chain activities.

Accounting for Resource Contention Using Feeding Buffer J2J2 B8B8 START A2A2 C3C3 D2D2 G4G4 E 10 I3I3 F4F4 H1H1 FB=7 FB=5 NOTE: E and G cannot be performed simultaneously (same person) Set feeding buffer (FB) to allow one day total slack Project duration based on Critical Chain = 24 days

Incorporating Project Buffer J2J2 B4B4 START A2A2 C3C3 D2D2 G2G2 E5E5 I3I3 F2F2 H1H1 FB=2 FB=3 NOTE: Reduce by ½ all activity durations > 3 days to eliminate safety time Redefine Critical Chain = 17 days Reset feeding buffer (FB) values Project buffer (PB) = ½ (Original Critical Chain-Redefined Critical Chain) PB=4