resource allocation
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Resource Allocation. BBUS541 Hiroshi Ochiumi. Introduction. Projects Compete With One Another for Resources resources that are not consumed resources that are consumed Goal of Resource Allocation is to Optimize Use of Limited Supply Requires making trade-offs time constrained - PowerPoint PPT PresentationTRANSCRIPT
01/22/2007
Resource Allocation
BBUS541Hiroshi Ochiumi
01/22/2007
Introduction
Projects Compete With One Another for Resources– resources that are not consumed– resources that are consumed
Goal of Resource Allocation is to Optimize Use of Limited SupplyRequires making trade-offs– time constrained– resource constrained
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Expediting a Project
BBUS541Hiroshi Ochiumi
01/22/2007
Expediting a Project
Time-Cost Trade-off Model– A model that develops the relationship between
direct project costs, indirect costs, and time to complete the project by minimizing the sum of direct and indirect costs.
Crash Costs– The additional costs of an activity when time to
complete it is shortened.
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Minimum Cost SchedulingStep 1:Prepare CPM-type network diagram.
a. Normal cost (NC) b. Normal time (NT)
c. Crash time (CT)d. Crash Cost (CC)
Step 2: Determine the cost per unit of time to expedite (or crash) each activity.
Step 3: Compute the critical path.Step 4: Shorten the critical path at the least cost.Step 5: Plot project direct, indirect, and total-cost curves and find the
minimum-cost schedule.
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Example 1
2
4
5
3
A
C
B
D
ES=0
EF=2
2
6
2
7
7
10
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Summary of Activity Times and Costs
Acrivity Normal Time Crash Time Normal Cost Crash CostA 2 1 6 10B 5 2 9 18C 4 3 6 8D 3 1 5 9
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Calculation of Cost Per Day to Expedite Each Activity
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Cost per day to Expedite
Activity Cost per day to expedite
#days activity may be shortened
A 4 1B 3 3C 2 1D 2 2
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Critical Path?
A-B-D2+5+3=10
A-C-D2+4+3=9
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“Crash” A-B-D path by 1
Where exactly do we want to crash?
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Network Diagram
2
4
5
2
A
C
B
D
ES=0
EF=2
2
6
2
7
7
9
Cost +2
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Cost per day to Expedite
Activity Cost per day to expedite
#days activity may be shortened
A 4 1B 3 3C 2 1D 2 1
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Critical Path?
A-B-D2+5+2=9
A-C-D2+4+2=8
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Crash A-B-D by 1
Where do we want to crash?
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Network Diagram
2
4
5
1
A
C
B
D
ES=0
EF=2
2
6
2
7
7
8
Cost +2+2
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Cost per day to Expedite
Activity Cost per day to expedite
#days activity may be shortened
A 4 1B 3 3C 2 1D 2 0
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Critical Path?
A-B-D2+5+1=8
A-C-D2+4+1=7
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Crash A-B-D by 1
Where do we want to crash?
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Network Diagram
2
4
4
1
A
C
B
D
ES=0
EF=2
2
6
2
6
6
7
Cost +2+2+3
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Cost per day to Expedite
Activity Cost per day to expedite
#days activity may be shortened
A 4 1B 3 2C 2 1D 2 0
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Critical Path?
A-B-D2+4+1=7
A-C-D2+4+1=7
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Crash both paths by 1
Where do we want to crash?– Do we want to crash C?
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Network Diagram
1
4
4
1
A
C
B
D
ES=0
EF=1
1
5
1
5
5
6
Cost +2+2+3+4
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Cost per day to Expedite
Activity Cost per day to expedite
#days activity may be shortened
A 4 0B 3 2C 2 1D 2 0
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Critical Path?
A-B-D1+4+1=6
A-C-D1+4+1=6
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Crash both paths by 1
Where do we want to crash?– Do we want to crash C only?
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Network Diagram
1
3
3
1
A
C
B
D
ES=0
EF=1
1
4
1
4
4
5
Cost +2+2+3+4+3+2
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Cost per day to Expedite
Can we continue?
Activity Cost per day to expedite
#days activity may be shortened
A 4 0B 3 1C 2 0D 2 0
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Example 2
ActivityImmediate
Predecessor Normal Time(hours)
A N/A 32
B A 40
C N/A 48
D C 24
E B,D 100
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Example 2
Can we use Excel Solver?
ActivityNormal
TimeNormal
Cost Crash Time Crash Cost
Maximum Crash Hours
Cost per Crash Hour ($)
A 32 640 20 760 12
B 40 480 30 720
C 48 1000 28 1200
D 24 288 15 360
E 100 4800 80 5600
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Using Excel Solver to Crash a Project
Objective– minimize crashing costs
Decision Variables– amount to crash activities– time events occur, or EST’s
Constraints– amount each activity can be crashed– precedence relationships– complete project by specified time– nonnegativity
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Resource Loading
BBUS541Hiroshi Ochiumi
01/22/2007
Resource Loading
Amount of specific resources that are scheduled for use on specific activities or projects at specific times.Usually a list or table.
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Resource Leveling
BBUS541Hiroshi Ochiumi
01/22/2007
Last week
We evaluated project durations only in terms of time.We have to consider when and for what purposes: – People– Equipment– Material– Facilities
are used.
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Resource Leveling
Overallocation must be resolved.Move activities so that resources do not exceed their capacities.– Without extending the project duration if possible