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

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1 2 3 4 5 6 7 8 9 10 11 12 13

Week

Nu

mb

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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

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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

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600

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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

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1 2 3 4 5 6 7 8 9 10

Week

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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/)