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Types of Constraints
Time
Resource
Mixed
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Resources• Definition: anything that is scarce and required for any activity
in the project. Resources are constraints for the project.• Resources can be:
– Non-storable: has to be renewed for each periode.g. work
– Storable: depleted only by usage (remains available if not used)e.g. money
• The most common resource typology, the 4Ms:– Men
– Machines
– Money (cost)
– Material
– Other
Loading (resource allocation)• The assignment of work to an worker, machine or
unit (generally: to a workstation) in time.• A workstation can be:
– underloaded (load < capacity)– fully loaded (load = capacity)– overloaded (load > capacity)
• Fully loading is nearly impossible to reach except in flow production.
• Underloading is the most common, because it respects time. Overloading leads to be late.
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Resource LoadingThe amounts of individual resources that a schedule requires during
specific time periods.
Resource loading table
Resource Name Work Details 5/5 5/12 5/19 5/26
Tom 40 hrs Work 8h 32h
Assign Bids 40 hrs Work 8h 32h
Jeff 40 hrs Work 8h 32h
Calculate Cost 40 hrs Work 8h 32h
Sue 40 hrs Work 8h 32h
Select Bid 40 hrs Work 8h 32h
Carol 8 hrs Work 8h
PR Campaign 8 hrs Work 8h
What to do with non-linear duration-resource functions?
• Use a computer• Focus on quasi-linear parts of the functions
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Resource Leveling (Smoothing)
A multivariate, combinatorial problem
Objectives• To determine the resource requirements so that
they will be available at the right time• To allow each activity to be scheduled with the
smoothest possible transition across resource usage levels
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Prioritization Rules for Leveling
Smallest amount of slack
Smallest duration
Lowest ID number
Greatest number of successor tasks
Requiring the most resources
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General Procedure for Leveling
1. Create a project activity precedence table and network diagram,
2. Develop resource loading tables and a resource profile
3. Determine activity late finish times
4. Identify resource over allocation
5. Level the resource loading table
6. Recalculate net activity slacks and project delay
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Creating Resource Loading Charts (1/4)
Display the amount of resources required as a function of time.
0 A 4 Res = 6
4 B 5 Res = 2
5 D 9 Res = 7
9 E 11 Res = 3
4 C 7 Res = 2
11 F 12 Res = 6
1. Start with a network diagram
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Creating Resource Loading Charts 2/4
Activity Resource Duration ES Slack LF
A 6 4 0 0 4
B 2 1 4 0 5
C 2 3 4 4 11
D 7 4 5 0 9
E 3 2 9 0 11
F 6 1 11 0 12
2. Produce a table that shows the duration, early start, late finish, slack, and resource(s) required for each activity.
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Creating Resource Loading Charts 3/4
A
2
4
6
8
2 1210864 14
C
BD
E
F
Project Days
Res
ourc
es
3. Draw an initial loading chart with each activity scheduled at its ES.
Resource imbalance
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Creating Resource Loading Charts 4/44. Rearrange activities within their slack
to create a more level profile. Splitting C creates a more level project.
A
2
4
6
8
2 1210864 14
C
BD
E
F
Project Days
Res
ourc
es
C
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Key Parameters in Multi-Project Environments
Schedule slippage
Resource utilization
In-process inventory
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Prioritizing Resource Allocations in Multi-Project Environments
• First come first served
• Greatest resource demand
• Greatest resource utilization
• Minimum late finish time
• Mathematical programming
Network with single resource data
START (0)
0 00
0 00
0
e (1)
10 130
10 133
0
d (2)
2 73
5 105
3
c (3)
2 100
2 108
0
b (4)
0 55
5 105
5
a (1)
0 20
0 22
0
FINISH (0)
13 130
13 130
0
Aggregation with a bar chart(single resource, earliest start)
activity 1 2 3 4 5 6 7 8 9 10 11 12 13
a 1 1
b 4 4 4 4 4
c 3 3 3 3 3 3 3 3
d 2 2 2 2 2
e 1 1 1
Res. aggr. 5 5 9 9 9 5 5 3 3 3 1 1 1
Cum. res. 5 10 19 28 37 42 47 50 53 56 57 58 59Resource units
11 10
987654321
1 2 3 4 5 6 7 8 9 10 11 12 13
Time
Aggregation with a bar chart(single resource, latest start)
activity 1 2 3 4 5 6 7 8 9 10 11 12 13
a 1 1
b 4 4 4 4 4
c 3 3 3 3 3 3 3 3
d 2 2 2 2 2
e 1 1 1
Res. aggr. 1 1 3 3 3 9 9 9 9 9 1 1 1
Cum. res. 1 2 5 8 11 20 29 38 47 56 57 58 59Resource units
11 10
987654321
1 2 3 4 5 6 7 8 9 10 11 12 13
Time
The S Curve analysis
• The minimum slope level is the less ‘critical’ from the viewpoint of availability
Other possibilities
• Alternative resources• Alternative methods• Alternative sequences
(if there is no technical dependency)
Levelling the load• We must have a starting allocation of activities over time
and a resource constraint (previous example).
Resource units
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 11 12 13
Time
• Trying to keep the original TPT unchanged means that critical activities should not be moved. Thus try to move activities with free float.
Resource units
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 11 12 13
Time
Solution
• There are only 2 activities with free float: b & d• Which one to move and to where?
• Moving activity d 3 days in advance is eliminating the peak.
Resource units
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 11 12 13
Time
activity 1 2 3 4 5 6 7 8 9 10 11 12 13
a 1 1
b 4 4 4 4 4
c 3 3 3 3 3 3 3 3
d - - - 2 2 2 2 2
e 1 1 1
Res. aggr. 5 5 7 7 7 5 5 5 5 5 1 1 1
Cum. res. 5 10 17 24 31 36 41 46 51 56 57 58 59
Solution
Effect of levelling• New „activity”: waiting for the resource
(it is a lag, not a true activity)
START (0)
0 00
0 00
0
e (1)
10 130
10 133
0
d (2)
5 100
5 105
0
c (3)
2 100
2 108
0
b (4)
0 50
0 55
0
a (1)
0 20
0 22
0
FINISH (0)
13 130
13 130
0
• Changes: new precedence relationship, floats, late start and finish times