Managing Projects. Project Management Questions zWhat activities are required to complete a project...
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Transcript of Managing Projects. Project Management Questions zWhat activities are required to complete a project...
Managing Projects
Project Management Questions
What activities are required to complete a project and in what sequence?
When should each activity be scheduled to begin and end?
Which activities are critical to completing the project on time?
What is the probability of meeting the project completion due date?
How should resources be allocated to activities?
Tennis Tournament Activities
ID Activity Description Network Immediate Duration Node Predecessor (days)1 Negotiate for Location A - 22 Contact Seeded Players B - 83 Plan Promotion C 1 34 Locate Officials D 3 25 Send RSVP Invitations E 3 106 Sign Player Contracts F 2,3 47 Purchase Balls and Trophies G 4 48 Negotiate Catering H 5,6 19 Prepare Location I 5,7 310 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
J2
B8
START
A2 C3 D2 G4
E10 I3
F4 H1
TS ES EF
LS LF
Early Start Gantt Chart for Tennis Tournament
ID Activity Days Day of Project Schedule 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20A Negotiate for 2 LocationB Contact Seeded 8 PlayersC Plan Promotion 3
D Locate Officials 2
E Send RSVP 10 InvitationsF Sign Player 4 ContractsG Purchase Balls 4 and TrophiesH Negotiate 1 CateringI Prepare Location 3
J Tournament 2
Personnel Required 2 2 2 2 2 3 3 3 3 3 3 2 1 1 1 2 1 1 1 1
Critical Path ActivitiesActivities with Slack
Resource Leveled Schedule for Tennis Tournament
ID Activity Days Day of Project Schedule 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20A Negotiate for 2 LocationB Contact Seeded 8 PlayersC Plan Promotion 3
D Locate Officials 2
E Send RSVP 10 InvitationsF Sign Player 4 ContractsG Purchase Balls 4 and TrophiesH Negotiate 1 CateringI Prepare Location 3
J Tournament 2
Personnel Required 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 1 1
Critical Path ActivitiesActivities 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
DA M B_
4
6
Variance
VB A
6
2
Note: (B - A )= Range or 6
Activity Means and Variances for Tennis Tournament
Activity A M B D V A 1 2 3 B 5 8 11 C 2 3 4 D 1 2 3 E 6 9 18 F 2 4 6 G 1 3 11 H 1 1 1 I 2 2 8 J 2 2 2
Uncertainly Analysis
Assumptions1. Use of Beta Distribution and Formulas For D and V2. Activities Statistically Independent3. Central Limit Theorem Applies ( Use “student t” if less than 30 activities on CP) 4. Use of Critical Path Activities Leading Into Event Node
ResultProject Completion Time Distribution is Normal With:
For Critical Path Activities
For Critical Path Activities
D_
2 V
Completion Time Distribution for Tennis Tournament
Critical Path Activities D V A 2 4/36 C 3 4/36 E 10 144/36 I 3 36/36 J 2 0
= 20 188/36 = 5.2 = 2
Question
What is the probability of an overrun if a 24 day completion time is promised?
24
P (Time > 24) = .5 - .4599 = .04 or 4%
Days
2 52 .
ZX
Z
Z
24 20
52175
..
Costs for Hypothetical Project
Cos
t
(0,0)
Schedule with Minimum Total Cost
Duration of Project
Total Cost
Indirect Cost
Opportunity Cost
Direct Cost
Activity Cost-time Tradeoff
C
C*
D* D Activity Duration (Days)
Normal
CrashSlope is cost to expedite per day
Cost
Cost-Time Estimates for Tennis Tournament
Time Estimate Direct Cost Expedite CostActivity Normal Crash Normal Crash Slope A 2 1 5 15 B 8 6 22 30 C 3 2 10 13 D 2 1 11 17 E 10 6 20 40 F 4 3 8 15 G 4 3 9 10 H 1 1 10 10 I 3 2 8 10 J 2 1 12 20 Total 115
Progressive Crashing
Project Activity Direct Indirect Opportunity TotalDuration Crashed Cost Cost Cost Cost 20 Normal 115 45 8 168 19 41 6 18 37 4 17 33 2 16 29 0 15 25 -2 14 21 -4 13 17 -6 12 13 -8
Normal Duration After Crashing ActivityProject Paths DurationA-C-D-G-I-J 16A-C-E-I-J 20A-C-E-H-J 18A-C-F-H-J 12B-F-H-J 15
Applying Theory of Constraints to Project Management
Why 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.
The “Critical Chain” is the longest sequence of dependent activities and common resources.
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
J2
B8
START
A2 C3 D2 G4
E10 I3
F4 H1
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
J2
B4
START
A2 C3 D2 G2
E5 I3
F2 H1
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