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Resource Allocation & Leveling
Resource Leveling: Reschedule the noncritical
tasks to smooth resource requirements
Resource Allocation: Minimize project
duration to meet resource availability constraints
Resource Allocation & Leveling
Three types of resources:1) Renewable resources: “renew” themselves
at the beginning of each time period (e.g.,
workers)
2) Non-Renewable resources: can be used at
any rate but constraint on total number
available
3) Doubly constrained resources: both
renewable and non-renewable
Resource Leveling
Task B2 wks
Task E3 wks
Task C9 wks
Task D5 wks
Task F2 wks
Task A3 wks
START Task G5 wks END
Task Workers Duration (t j) Early Start Late Start
A 7 3 0 0B 3 2 0 3C 2 9 3 4D 10 5 3 3E 4 3 2 5F 5 2 2 11G 6 5 8 8
Resource Leveling: Early Start Schedule
Early Start Schedule
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13
Week
Num
ber
of W
ork
ers
Needed
Task GTask FTask ETask DTask CTask BTask A
Resource Leveling: Late Start Schedule
Late Start Schedule
0
2
4
6
8
10
12
14
16
18
1 2 3 4 5 6 7 8 9 10 11 12 13
Week
Nu
mb
er
of
Wo
rke
rs N
ee
de
d
Task GTask FTask ETask DTask CTask BTask A
Resource Leveling: Microsoft Project
5
10
15
20
25
Workers Overallocated: Allocated:
T W T F S S M T W T F S S M T W T F S S M T W T F S
Dec 17, '00 Dec 24, '00 Dec 31, '00 Jan 7, '01
10 10 10 10 10 10 10 10 10 10 16 16 16 16 16 21 21 21
Renewable Resource Allocation Example (Single Resource Type)
Task B 3 wks
Task D 5 wks
Task A 4 wks
Task E 4
wksSTART
END
Task C 1 wk
3 workers
5 workers
6 workers
8 workers
7 workers
Maximum number of workers available = R = 9 workers
Resource Allocation Example: Early Start Schedule
Maximum number of workers available = R = 9 workers
Start End
Week 1 2 3 4 5 6 7 8 9 10 11 12No. of Workers/wk 8 8 8 11 14 8 8 8 7 7 7 7
Cumulative Workers 8 16 24 35 49 57 65 73 80 87 94 101"Wasted" worker-wks 1 1 1 - - - - - - - - -
Task B: 5 workers
Task A: 3 workers
Task C: 6 workers
Task E: 7 workers
Task D: 8 workers
Resource Allocation Example: Late Start Schedule
Maximum number of workers available = R = 9 workers
Start End
Week 1 2 3 4 5 6 7 8 9 10 11 12No. of Workers/wk 5 5 5 11 11 11 11 14 7 7 7 7
Cumulative Workers 5 10 15 26 37 48 59 73 80 87 94 101"Wasted" worker-wks - - - - - - - - 2 2 2 2
Task B: 5 workers
Task A: 3 workers
Task C: 6 workers
Task E: 7 workers
Task D: 8 workers
Resource Allocation Heuristicsn Some heuristics for assigning priorities to available tasks j, where denotes the
number of units of resource k used by task j
n 1) FCFS: Choose first available taskn 2) GRU: (Greatest) resource utilization = n 3) GRD: (Greatest) resource utilization x task duration = n 4) ROT: (Greatest) resource utilization/task duration =n 5) MTS: (Greatest) number of total successors
n 6) SPT: Shortest processing time = min {tj}
n 7) MINSLK: Minimum (total) slackn 8) LFS: Minimum (total) slack per successor
n 9) ACTIMj: (Greatest) time from start of task j to end of project = CP - LSj
n 10) ACTRESj: (max) (ACTIMj)
n 11) GENRESj: w ACTIMj + (1-w) ACTRESj where 0 ≤ w ≤ 1
Rjk
Rjk
k
Rjk / tj
k
Rjk
k
tj
Resource Allocation Problem #2
Task A1 6 days
Task A24 days
EndStart Task B1 3 days
Task C1 2 days
Task B2 5 days
Task C2 5 days
Purple Crew Gold Crew
How to schedule tasks to minimize project makespan?
Priority scheme: schedule tasks using total slack (i.e., tasks with smaller total slack have higher priority)
Task A1 Task B1 Task C1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Task A2 Task B2 Task C2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Gold Crew
Purple Crew
Resource Allocation Example (cont’d)
But, can we do better? Is there a better priority scheme?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Gold Crew
Purple Crew
Microsoft Project Solution (Resource Leveling Option)
Solution by: Microsoft Project 2000
Critical Chain Project Management
• Identify the critical chain: set of tasks that determine the overall duration of the project
• Use deterministic CPM model with buffers to deal with uncertainty
• Remove padding from activity estimates (otherwise, slack will be wasted). Estimate task durations at median.
• Place project buffer after last task to protect customer’s completion schedule
• Exploit constraining resource(s)
• Avoid wasting slack times by encouraging early task completions
• Have project team focus 100% effort on critical tasks
• Work to your plan and avoid tampering
• Carefully monitor and communicate buffer status
Critical Chain Buffers
Project Buffer: placed after last task in project to protect schedule
Feeding Buffers: placed between a noncritical task and a critical task
when the noncritical task is an immediate predecessor of the critical task
Resource Buffers: placed just before a critical task that uses a new
resource type
Critical Chain Illustrated
Task A1 6 days
Task A24 days
EndStart
Task B1 3 days
Task C1 2 days
Task B2 5 days
Task C2 5 days
Resource Buffers
Feeding Buffers
Non-Renewable Resources
Task B5 wks
Task D 2 wks
Task C 3 wks
Task A 6 wksSTART END
6 units
12 units
10 units
8 units
Task Duration
No. of Nonrenewable Resources Units
Needed Early Start Late Start
A 6 6 0 0B 5 12 6 6C 3 10 6 8D 2 8 11 11
Non-Renewable Resources: Graphical Solution
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
40
36
32
28
24
20
16
12
8
4
Cumulative Resources Supplied
Cum
ulat
ive
Res
ourc
es
Weeks
Cumulative Resources Required
Resource Allocation Problem #3Issue: When is it better to “team” two or more
workers versus letting them work separately?
• Have 2 workers, Bob and Barb, and 4 tasks: A, B, C, D
• Bob and Barb can work as a team, or they can work separately
• When should workers be assigned to tasks? Which configuration do you prefer?
How to Assign Project Teams?
Configuration #1
Bob and Barb work jointly on all four tasks; assume that they can complete each task in one-half the time needed if either did the tasks individually
A C
B D
Start End
Configuration #2
Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is assigned to tasks B and D
Bob and Barb: Configuration #1
TASK A TASK B TASK C TASK DDuration Prob Duration Prob Duration Prob Duration Prob
6 0.33 9 0.667 12 0.6 10 0.255 0.33 6 0.333 7 0.4 6 0.754 0.33
Expected duration 5.0 8.0 10.0 7.0
Configuration #1
Bob and Barb work jointly on all four tasks.
What is the expected project makespan?
Bob and Barb: Configuration #2Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is
assigned to tasks B and D
Realization # A B C DBob
A + CBarb B + D
max (A+C, B+D) Prob
1 6 9 12 10 18 19 19 0.032 6 9 12 6 18 15 18 0.103 6 9 7 10 13 19 19 0.024 6 9 7 6 13 15 15 0.075 6 6 12 10 18 16 18 0.026 6 6 12 6 18 12 18 0.057 6 6 7 10 13 16 16 0.018 6 6 7 6 13 12 13 0.039 5 9 12 10 17 19 19 0.03
10 5 9 12 6 17 15 17 0.1011 5 9 7 10 12 19 19 0.0212 5 9 7 6 12 15 15 0.0713 5 6 12 10 17 16 17 0.0214 5 6 12 6 17 12 17 0.0515 5 6 7 10 12 16 16 0.0116 5 6 7 6 12 12 12 0.0317 4 9 12 10 16 19 19 0.0318 4 9 12 6 16 15 16 0.1019 4 9 7 10 11 19 19 0.0220 4 9 7 6 11 15 15 0.0721 4 6 12 10 16 16 16 0.0222 4 6 12 6 16 12 16 0.0523 4 6 7 10 11 16 16 0.0124 4 6 7 6 11 12 12 0.03
Bob and Barb: Configuration #2
Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is assigned to tasks B and D
max (A+C, B+D) Prob
Cumulative Prob
12 0.07 0.0713 0.03 0.1015 0.20 0.3016 0.20 0.5017 0.17 0.6718 0.17 0.8319 0.17 1.00
Expected Project Makespan: 16.42
Parallel Tasks with Random Durations
STARTEND
Task B
Task A
• Assume that both Tasks A and B have possible durations:
8 days with probability = 0.5
10 days with probability = 0.5
• What is expected duration of project? (Is it 9 days?)
Project Monitoring and Control
n “It is of the highest importance in the art of detection to be able to recognize, out of a number of acts, which are incidental and which are vital. Otherwise your energy and attention must be dissipated instead of being concentrated.”
Sherlock Holmes
Status Reporting?
One day my Boss asked me to submit a status report to him concerning a project I was working on. I asked him if tomorrow would be soon enough. He said, "If I wanted it tomorrow, I would have waited until tomorrow to ask for it!"
New business manager, Hallmark Greeting Cards
Control System Issues
n What are appropriate performance metrics?
n What data should be used to estimate the value of each
performance metric?
n How should data be collected? From which sources? At
what frequency?
n How should data be analyzed to detect current and future
deviations?
n How should results of the analysis be reported? To
whom? How often?
Controlling Project Risks
Key issues to control risk during projecct:
(1) what is optimal review frequency, and
(2) what are appropriate review acceptance levels at each stage?
“Both over-managed and under-managed development processes result in lengthy design lead time and high development costs.”
Ahmadi & Wang. “Managing Development Risk in Product Design Processes”, 1999
Project Control & System Variation
Common cause variation: “in-control” or normal variation
Special cause variation: variation caused by forces that are outside of the system
According to Deming:
• Treating common cause variation as if it were special cause variation
is called “tampering”
• Tampering always degrades the performance of a system
Control System Example #1
n Project plan: We estimate that a task
will take 4 weeks and require
n 1600 worker-hours
At the end of Week 1, 420 worker-hours have been used
Is the task “out of control”?
Control System Example (cont’d)
Week 2: Task expenses = 460 worker-hours
Is the task “out of control”?
370
380
390
400
410
420
430
440
450
460
470
1 2 3 4
Week
Cos
t (i
n w
ork
er-h
ours
)Week
Planned Cost (BCWS) Actual Cost
Cumulative Actual Cost
(ACWP)
1 400 420 4202 400 460 880
Control System Example (cont’d)Week 3: Task expenses = 500 worker-hrs
Is the task “out of control”?
WeekPlanned cost
(worker-hours)Actual cost
(worker-hours)Cumulative cost (worker-hours)
1 400 420 4202 400 460 8803 400 500 1380
0
100
200
300
400
500
600
1 2 3 4
Week
Wor
ker
-hou
rs
Earned Value Analysis
• Integrates cost, schedule, and work performed
• Based on three metrics that are used as the basic building blocks:
BCWS: Budgeted cost of work scheduled
ACWP: Actual cost of work performed
BCWP: Budgeted cost of work performed
Schedule Variance (SV)
Schedule Variance (SV) = difference between value of work completed and value of scheduled work
Schedule Variance (SV) = Earned Value - Planned Value
= BCWP - BCWS
Cost Variance (CV)
Cost Variance (CV) = difference between value of work completed and actual expenditures
Cost Variance (CV) = Earned Value - Actual Cost
= BCWP - ACWP
Earned Values Metrics IllustratedW
orke
r-H
ours
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6
Present timeBAC
Actual Cost (ACWP)
Earned Value (BCWP)
Planned Value (BCWS)
Schedule Variance (SV)
Cost Variance (CV)
Relative Measure: Schedule Index
Schedule Index (SI ) = BCWPBCWS
If SI = 1, then task is on schedule
If SI > 1, then task is ahead of schedule
If SI < 1, then task is behind schedule
Relative Measure: Cost Index
Cost Index (CI) = BCWPACWP
If CI = 1, then work completed equals payments (actual expenditures)
If CI > 1, then work completed is ahead of payments
If CI < 1, then work completed is behind payments (cost overrun)
Example #2W E E K
1 2 3 4 5 6 7 8 9 10
6 6 6 8 10
12 12 12
10 10 12 12 12
Weekly Scheduled
Worker-Hrs 6 6 6 20 22 22 10 12 12 12Cumulative Scheduled
Worker-Hrs (BCWS) 6 12 18 38 60 82 92 104 116 128
Task A (36 worker-hrs)
Task B (36 worker-hrs)
Task C (56 worker-hrs)
Example #2 (cont’d)
Week 1 2 3 4 5Task A 15% 30% 40% 60% 80%
Task B 25% 65%
Task C Not started yet
Progress report at the end of week #5:
Cumulative Percent of Work Completed:
Worker-Hours Charged to Project:
Week 1 2 3 4 5Task A 5 6 8 10 10Task B 15 10Task C Not started yet
Example #2 (cont’d)Progress report at the end of week #5:
W E E K1 2 3 4 5 6 7 8 9 10
Cumulative Scheduled
Worker-Hrs (BCWS) 6 12 18 38 60 82 92 104 116 128
Actual Worker-Hrs Used (ACWP) 5 11 19 44 64
Earned Value (BCWP) 5.4 10.8 14.4 30.6 52.2
Schedule Variance (SV) -0.6 -1.2 -3.6 -7.4 -7.8Cost Variance
(CV) 0.4 -0.2 -4.6 -13.4 -11.8
Example #2 (cont’d)
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10
Week
Per
form
ance
Met
ric
ACWP
BCWP
BCWS
Schedule Variance
Cost Variance
BAC
Using a Fixed 20/80 RuleCumulative Percent of Work Completed:
W E E K1 2 3 4 5 6 7 8 9 10
Cumulative Scheduled
Worker-Hrs (BCWS) 6 12 18 38 60 82 92 104 116 128
Actual Worker-Hrs Used (ACWP) 5 11 19 44 64
Earned Value (BCWP) 7.2 7.2 7.2 14.4 14.4Schedule
Variance (SV) 1.2 -4.8 -10.8 -23.6 -45.6Cost Variance
(CV) 2.2 -3.8 -11.8 -29.6 -49.6
Week 1 2 3 4 5Task A 20% 20% 20% 20% 20%Task B 20% 20%Task C Not started yet
Using a Fixed 20/80 Rule
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10
Week
Cos
t (i
n W
orke
r-ho
urs)
BCWP
ACWPBCWS
Updating Forecasts: Pessimistic Viewpoint
= (64/52.2) 128 = 1.23 x 128 = 156.94 worker-hrs
Estimate at Completion (EAC) = ACWPBCWP
BAC = 1CI
BAC .
Assumes that rate of cost overrun will continue for life of project….
Updating Forecasts: Optimistic Viewpoint
Estimate at Completion (EAC) = BAC - CV = 128 + 11.8 = 139.8 worker -hrs .
Assumes that cost overrun experienced to date will cease and no further cost overruns will be
experienced for remainder of project life…
Multi-tasking with Multiple Projects
Project A Project B
A-1 B-1 A-2 B-2 A-3 A-4B-3 B-4
Consider two projects with and without multi-tasking
How to prioritize your work when you have multipleprojects and goals?
Due-Date Assignment with Dynamic Multiple Projects
• Projects arrive dynamically (common situation for both
manufacturing and service organizations)
• How to set completion (promise) date for new projects?
• Firms may have complete control over due-dates or only partial
control (i.e., some due dates are set by external sources)
• How to allocate resources among competing projects and tasks (so
that due dates can be realized)?
• What are appropriate metrics for evaluating various rules?
What Does the Research Tell Us?
• Study by Dumond and Mabert* investigated four due date assignment
rules and five scheduling heuristics
• Simulated 250 projects that randomly arrive over 2000 days
• average interarrival time = 8 days
• 6 - 49 tasks per project (average = 24); 1 - 3 resource types
• average critical path = 31.4 days (range from 8 to 78 days)
• Performance criteria: 1) mean completion time
2) mean project lateness
3) standard deviation of lateness
4) total tardiness of all projects
• Partial and complete control on setting due dates* Dumond, J. and V. Mabert. “Evaluating Project Scheduling and Due Date Assignment Procedures: An Experimental Analysis” Management Science, Vol 34, No 1 (1988), pp 101-118.
Experimental Results
• No one scheduling heuristic performs best across all due date
setting combinations
• Mean completion times for all scheduling and due date rules not
significantly different
• FCFS scheduling rules increase total tardiness
• SPT-related rules do not work well in PM (SASP)
• Best to use more detailed information to establish due dates
Project Management Maturity Models
• Methodologies to assess your organization’s current level of
PM capabilities
• Based on extensive empirical research that defines “best
practice” database as well as plan for improving PM process
• Process of improvement describes the PM process from
“ineffective” to “optimized”
• Also known as “Capability Maturity Models”
PM Maturity Model Example*1) Ad-Hoc The project management process is described as disorganized, and occasionally
even chaotic. Systems and processes are not defined. Project success depends on individual
effort. Chronic cost and schedule problems.
2) Abbreviated: Some project management processes are established to track cost, schedule,
and performance. Underlying disciplines, however, are not well understood or consistently
followed. Project success is largely unpredictable and cost and schedule problems are the norm.
3) Organized: Project management processes and systems are documented, standardized, and
integrated into an end-to-end process for the company. Project success is more predictable.
Cost and schedule performance is improved.
4) Managed: Detailed measures of the effectiveness of project management are collected and used
by management. The process is understood and controlled. Project success is more uniform.
Cost and schedule performance conforms to plan.
5) Adaptive: Continuous improvement of the project management process is enabled by feedback
from the process and from piloting innovative ideas and technologies. Project success is the
norm. Cost and schedule performance is continuously improving.
* source: The Project Management Institute PM Network (July, 1997), Micro Frame Technologies, Inc. and Project Management Technologies, Inc. (http://pm32.hypermart.net/)