Project Management: A
Managerial Approach
Chapter 9 – Resource Allocation
Overview
•
•
•
•
•
Critical Path Crashing
Resource Leveling
Resource Constrained Schedules
Multiproject Resource Management
Critical Chain
21-1
Resource Allocation
• Some definitions
• Resource allocation, loading, leveling
• Expediting and crashing projects
31-1
Some Definitions
• Resource allocation permits efficient use of
physical assets
– Within a project, or across multiple projects
– Drives both the identification of resources, and
timing of their application
• There are generally two conditions:
– “Normal”
– “Crashed”
41-1
Normal and Crashing
• Normal: Most likely task duration, like “m”
in Chapter 8
• Crash: Expedite an activity, by applying
additional resources
– Specialized or additional equipment
– More people (e.g., borrowed staff, temps)
– More hours (e.g., overtime, weekends)
51-1
No Free Lunch: Crashing
Creates a Ripple Effect
• Crashing buys time, but nothing comes free
• Potential cost areas
–
–
–
–
–
Additional equipment/material
Extra labor
Negative effects on other projects
Reduced morale, from excessive hours/shifts
Lower quality, from the pressure of time, inexperienced
and tired staff
• “If you want it bad, you’ll get it bad . . .”
– Recent Example: Miami’s New Art Center.
61-1
When Trying to Crash a Project …
• Two basic principles
– 1. Generally, focus on the critical path
• Usually not helpful to shorten non-critical activities
• Exception: When a scarce resource is needed
elsewhere, e.g., in another project
– 2. When shortening project duration, choose
least expensive way to do it
– (use slope formula to calculate ratio)
71-1
Compute Cost per Day of
Crashing a Project
• Compute cost/time slope for each
expeditable activity
• Slope = crash cost – normal cost
crash time – normal time
81-1
Another Approach to Expediting:
Fast-tracking/Concurrency
• Different terms for similar concept
• “Fast-tracking” (construction), “Concurrent
engineering” (manufacturing)
• Both refer to overlapping project phases
– E.g., design/build, or build/test
91-1
Fast-tracking/Concurrency
• Pros:
– Can shorten project duration
– Can reduce product development cycles
– Can help meet clients’ demands
• Cons:
– Can increase cost through redesigns,
excessive changes, rework, out-ofsequence installation, and more
101-1
The Resource Allocation Problem
• Most scheduling procedures do not address the
issues of resource utilization and availability
• Scheduling procedures tend to focus on time
rather than physical resources
• Time itself is always a critical resource in
project management
– It is unique because it can neither be inventoried nor
renewed
Chapter 9-5
111-1
The Resource Allocation Problem
• Schedules should be evaluated:
– in terms of meeting project milestones
– in terms of the timing and use of scarce resources
• Measure of the project manager’s success: skill
with which the trade-offs among:
– Performance
– Time
– Cost
Chapter 9-6
121-1
The Resource Allocation Problem
• The extreme points of the relationship between
time use and resource use are these:
– Time Limited: The project must be finished by a
certain time, using as few resources as possible.
But it is time, not resource usage, that is critical
– Resource Limited:The project must be finished as
soon as possible, but without exceeding some
specific level of resource usage or some general
resource constraint
Chapter 9-7
131-1
The Resource Allocation Problem
• If all three variables - time, cost, specifications are fixed, the system is “overdetermined”
• In this case, the project manager has lost all
flexibility to perform the trade-offs necessary to
successful completion of projects
• A system-constrained task requires a fixed
amount of time and known quantities of
resources
Chapter 9-8
141-1
Resource Loading
• Describes the amounts of individual
resources an existing schedule requires
during specific time periods
• The loads (requirements) of each resource
type are listed as a function of time period
• Gives a general understanding of the
demands a project or set of projects will
make on a firm’s resources
Chapter 9-9
151-1
Resource Usage Calendar, Figure 9-3
161-1
AOA Network, Figure 9-4
171-1
Modified PERT/CPM AOA, Figure 9-5
181-1
Resource Leveling
• Resource leveling aims to minimize the period-byperiod variations in resource loading by shifting tasks
within their slack allowances
• The purpose is to create a smoother distribution of
resource usage
• Several advantages include:
– Less day-to-day resource manipulation needed
– Better morale, fewer HR problems/costs
– Leveling resources also levels costs, simplifies budgeting
and funding
Chapter 9-12
191-1
Resource Leveling
• When resources are leveled, the associated costs
also tend to be leveled
• The project manager must be aware of the cash
flows associated with the project and of the means
of shifting them in ways that are useful to the
parent firm
• Resource leveling is a procedure that can be used
for almost all projects, whether or not resources are
constrained
Chapter 9-13
201-1
Resource Leveling – Fig 9-6
211-1
Network Before and After Resource Loading,
Figure 9-7
Duration
Qty Reqd.
221-1
Resource Loading Chart, Figure
9-9
231-1
Constrained Resource Scheduling
• There are two fundamental approaches to constrained
allocation problems:
– Heuristic Methods
– Optimization Models
• Heuristic approaches employ rules of thumb that have
been found to work reasonably well in similar situations
• Optimization approaches seek the best solutions but are
far more limited in their ability to handle complex
situations and large problems
Chapter 9-14
241-1
Examples of Simple Heuristics
1. ASAP
2. As late as possible (do not engage in anything unless you have
to)
3. SPT (shortest processing time – good to reduce congestion)
4. Most resources first (most requested resources first)
5. Minimum slack first (critical jobs go first to avoid lead time
delays)
6. Most critical followers (most critical jobs that go after you,
many jobs depend on that resource)
7. Most successors
8. Arbitrary
9. Combination of the above (compound rules).
Chapter 9-14
251-1
Examples of Complex Heuristics
•
•
•
•
Simulated annealing
Tabu search
Genetic algorithms
Greedy search with branch and bound
In the graduate course Advanced Production Planning
& Scheduling, focuses on scheduling heuristics.
It is good to know that they exist.
Chapter 9-14
261-1
Multiproject Scheduling and Resource Allocation
• The most common approach to scheduling and
allocating resources to multiple projects is to treat the
several projects as if they were each elements of a
single large project
• Another way of attacking the problem is to consider all
projects as completely independent
• To describe such a system properly, standards are
needed by which to measure scheduling effectiveness
Chapter 9-21
271-1
Multiproject Scheduling and Resource Allocation
• Much more difficult.
• May rely on an index called
TRPT: (Total Remaining Processing Time)
– Based on the critical ratio.
• Among all the projects under your control, look
at all the jobs of all the projects.
• Find out which are most critical.
Chapter 9-21
281-1
Multiproject Scheduling and Resource Allocation
• Most critical... How do you know?
– Based on the amount of time before due date and the total
amount of processing time remaining to be completed.
• This ratio is simple but helpful.
• Critical Ratio = TRPT (Total Remaining Processing Time)
TRT (Total Remaining Time)
• The smaller the ratio, the more critical it is, more
entitled to earlier allocation of resources.
Chapter 9-21
291-1
Multiproject Scheduling and Resource Allocation
• Based on this, you can do multiple project scheduling.
• Most critical tasks should be the first to be assigned resources.
•
This doesn’t mean that job will be assigned the resource first.
– Why? The resource in need may not be available.
– You can get first priority to claim it, but you may not get the first
assignment.
– You may get preference due to the type of resource that you need.
• In case you have multiple projects, you have some way to do it.
Chapter 9-21
301-1
Multiproject Scheduling and Resource Allocation
•
Three important parameters affected by project
scheduling are:
1.
Schedule slippage
2.
Resource utilization
3. In-process inventory
•
The organization (or the project manager) must select
the criterion most appropriate for its situation.
Chapter 9-22
311-1
Multiproject Scheduling and Resource Allocation
• Schedule slippage (how much delay it has caused or it
will cause) - often considered the most important of the
criteria, is the time past a project’s due date or delivery
date when the project is completed
• Resource utilization is of particular concern to
industrial firms because of the high cost of making
resources available (the more utilization the better, the
resource requirements become lower)
• WIP (to see how smooth your workflow is) concerns
the amount of work waiting to be processed because
there is a shortage of some resource
Chapter 9-23
321-1
Multiproject Scheduling and Resource Allocation
• All criteria cannot be optimized at the same
time
• As usual, the project manager will have to make
trade-offs among the criteria
• A firm must decide which criterion to evaluate
its various scheduling and resource allocation
options
Chapter 9-24
331-1
“Cost, Schedule, or Performance:
Pick Any Two . . .”
• Assuming fixed performance specifications,
tradeoff areas must be in time or cost
• Time-limited or resource-limited
• If all three dimensions are fixed, the system
is “overdetermined”
– Normally, no tradeoffs are possible
– But, something has to give . . .
341-1
Example: Project Crashing
• Compute cost/time slope for each
expeditable activity
• Slope = crash cost – normal cost
crash time – normal time
• Slope is the cost of crashing the project for
the potential (or estimated) crashing time.
351-1
An Example (Table 9-1)
Activity
Predecessor
Days
(normal, crash)
Cost
(normal, crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
* Partial crashing allowed
** Partial crashing not allowed
361-1
Example (cont’d):
Cost per Day to Crash (Table 9-2)
Activity
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
371-1
Example (cont’d): Crashing
What to crash depends on how much we need to
reduce the duration of the project.
Normal Time
Normal Cost
2
$60
b
3 $40
S
$20
a
c
$40
$20
d
- CP: a  b  e (ET=8)
- Ratios
- Total Cost: $120
- Total Lead Time: 8 days
3 $70
$30
Activity
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
2
4
$0
$10
F
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
$30
381-1
Example (cont’d): Crashing
Normal Cost
2
Ratios
$60
b
2
3 $40
S
a
$40
$80*
$20*
c
- Crash a: (lowest) for 1 day
- New Cost: $120 + $40 = $160
- New Lead Time: 7 days (still on CP)
v. a  c (4) vs a  d (6)
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
2
$0
4
$30
$10*
F
$20*
d
(max1)
3 $70
Activity
$30*
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 21
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
391-1
Example (cont’d): Crashing
1
2 $60
Normal Cost
Ratios
b
2
3 $40
S
$20 $80*
a
$40
$80*
c
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
2
$0
4
$30
$10*
F
$20*
d
- Crash b: (lowest) for 1 day (max)
3 $70
Activity
$30*
- New Cost*: $160 + $60 = $220
- New Lead Time: 6 days
-(2 paths with same LT: a  b  e (6) vs a  d (6)
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
401-1
Example (cont’d): Crashing
1
2 $60
Normal Cost
Ratios
b
2
3 $40
S
a
$40
$80*
$20 $80*
c
$30
Crash d for 1 day (partial crashing allowed)
New Cost*: $220 + $30 = $250
LT for path a  d = 5 (Not critical)
CP is again a  b  e (6 days)
2
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
$0
$10*
F
$20*
d
-
3 $70
Activity
4 $30
3 $60*
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
411-1
Example (cont’d): Crashing
1
2 $60
Normal Cost
Ratios
1
3 $70
b
2
3 $40
S
a
$40
$80*
$20 $80*
c
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
$0
$10 $80*
F
$20*
d
$30
- Crash e for 2 days (no partial crashing allowed)
- New Cost*: $250 + $70 = $320
- LT for path a  b  e = 4
2
Activity
4 $30
3 $60*
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
421-1
Example (cont’d): Crashing
2
1
2 $60
Normal Cost
Ratios
1
3 $70
b
2
3 $40
S
a
$40
$80*
$20 $80 $20*
c
$0
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
$10 $80*
F
$20*
d
-Say that lead time of 5 days is acceptable.
-Can backtrack and undo the earlier crashing at b.
-Add 1 day and subtract $60.
-Now (a  b  e ) and (a  d ) have LT =5.
-New Cost*: $320 - $60 = $260
2
Activity
$30
4 $30
3 $60*
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
431-1
Example (cont’d): Crashing
2
1
2 $60
Normal Cost
Ratios
1
3 $70
b
2
3 $40
S
a
$40
$80*
$20 $80 $20*
c
$0
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
$10 $80*
F
$20*
d
-LT (a  b  e ) = 4
-Say that lead time of 5 days is acceptable.
-Can backtrack and undo the earlier crashing at b.
-Add 1 day and $60 back.
-Now (a  b  e ) and (a  d ) have LT =5.
-New Cost*: $320 - $60 = $260
-If 5 days is acceptable, then stop.
2
Activity
$30
4 $30
3 $60*
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
441-1
Example (cont’d): Crashing
1
2
1
2 $60
Normal Cost
Ratios
1
3 $70
b
2
3
S
$40
a
$40
$80*
2
$20 $80 $20
$80*
c
$0
Activity
$ Saved/
Day (Slope)
a
40
b
60
c
-
d
30
e
70 (2 days)
e
$10 $80*
F
$20*
-LT (a  b  e ) = 5
d
-Assume that acceptable lead time is now 4 days.
$30
-Crash d for 1 more day.
-Cost*: $260 + $30 = $290
-Crash b again for 1 more day.
-New Cost*: $290 + $60 = $350
-Now (a  b  e, a  c and a  d ) have LT =4.
-Addtn. Cost of reducing project from 8 to 4 days: $230
-You could still crash d 1 more day, but it would be a waste
$30
4
3 $60
2 $90*
of $.
Activity
Pred.
Days
(normal,
crash)
Cost
(normal,
crash)
a
-
3, 2
$40, 80
b
a
2, 1
20, 80
c
a
2, 2
20, 20
d*
a
4, 1
30, 120
e**
b
3, 1
10, 80
451-1
Example (cont’d): Crashing
461-1
CPM Cost-Duration
471-1
Copyright 2006 John Wiley & Sons, Inc.
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481-1