Upload
jorge-joel
View
217
Download
2
Tags:
Embed Size (px)
Citation preview
Overview
What happens when activity times in a project are:
Not fixed Crashing the project
Not known with certainty PERT (Project Evaluation and Review Technique)
Project Crashing
Estimated time is fixed... no more.
Can reduce the length of time of a project through additional resources manpower, equipment
Direct cost of activity is always increased
Project Crashing: Motivation
Need to reduce time of project because: Requirement to complete in specified time frame Economic advantage
Three kinds of costs Crash costs (activity direct costs) Administration costs (or project indirect costs) Penalty costs
Incur crash costs to avoid administration and penalty costs
Calculating Crash Costs per Unit Time
CrashTime =3
Normal Time =7
Crash Cost = $9,000
Normal Cost = $3,000
Crash Cost / Unit Time = 9000 – 30007 – 3
= $1,500
Project Crashing: Procedure
Always crash one period at a time!
1. Identify critical activities
2. Select least expensive to crash
3. Savings? Implement if so. Update all paths
4. Repeat 1-3 until no cost savings are possible
2 1
5 3
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
ABCD AXYZ
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
NormalDuration:
MinimumDuration:
Path Duration
1615 Which
activity should we
crash?
(per period)
ABCD 16AXYZ 15
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
5 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
ABCD 16AXYZ 15
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
5
2 1
3NormalDuration:
MinimumDuration:
Path Duration
(per period)
ABCD 16AXYZ 15
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
5 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
5 5 3
3
ABCD 16AXYZ 15
Choose B because it is the cheapest of the three alternatives (A, B, or C)
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
5 3
12
NormalDuration:
MinimumDuration:
Path Duration
B
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
100 500 400 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
3
12
NormalDuration:
MinimumDuration:
Path Duration
Cost Save Net Cumul
Which activity(s) should we crash
next?
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
3
2 1
4NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
4 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
4 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
4 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
4 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
4 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
4 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
4
2
3
1
3
25
2
4 5 3
3
ABCD 16 15AXYZ 15 15
Cost 100Save 500Net 400Cumul 400
B
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
4 3
3
25
2
5
3
4 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
BY
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
3
25
2
3 5 3
3
ABCD 16 15 14AXYZ 15 15 14
Cost 100 225Save 500 500Net 400 275Cumul 400 675
B BY
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
3
25
2
5
3
3
2 1
NormalDuration:
MinimumDuration:
Path Duration
Which activity(s) should we crash
next?
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
3
25
2
3 5 3
3
ABCD 16 15 14AXYZ 15 15 14
Cost 100 225Save 500 500Net 400 275Cumul 400 675
B BY
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
3
25
2
5
3
3 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
3
25
2
3 5 3
3
ABCD 16 15 14AXYZ 15 15 14
Cost 100 225Save 500 500Net 400 275Cumul 400 675
B BY
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
3
25
2
5
3
3 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
3
25
2
3 5 3
3
ABCD 16 15 14AXYZ 15 15 14
Cost 100 225Save 500 500Net 400 275Cumul 400 675
B BY
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
3
25
2
5
3
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
3
25
2
3 5 3
3
ABCD 16 15 14AXYZ 15 15 14
Cost 100 225Save 500 500Net 400 275Cumul 400 675
B BY
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
3
25
2
5
3
3 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
3
25
2
3 5 3
3
ABCD 16 15 14AXYZ 15 15 14
Cost 100 225Save 500 500Net 400 275Cumul 400 675
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
3
25
2
5
3
3 3
2 1
NormalDuration:
MinimumDuration:
Path Duration
B BY A
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
2
25
2
3 5 3
3
ABCD 16 15 14 13AXYZ 15 15 14 13
Cost 100 225 250Save 500 500 500Net 400 275 250Cumul 400 675 925
B BY A
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
2
25
2
5
3
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
3
2
3
1
2
25
2
3 5 3
3
ABCD 16 15 14 13AXYZ 15 15 14 13
Cost 100 225 250Save 500 500 500Net 400 275 250Cumul 400 675 925
B BY A
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
3 3
2
25
2
5
3
NormalDuration:
MinimumDuration:
Path Duration
Which activity(s) should we
crash next?
(per period)
A
B C D
X Y Z
3 2
2
2
3
1
2
25
2
3 4 3
3
ABCD 16 15 14 13 12AXYZ 15 15 14 13 12
Cost 100 225 250 325Save 500 500 500 500Net 400 275 250 175Cumul 400 675 925 1100
B BY A CY
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
2 3
2
25
2
4
3
NormalDuration:
MinimumDuration:
Path Duration
(per period)
A
B C D
X Y Z
3 2
2
2
3
1
2
25
2
3 4 3
3
ABCD 16 15 14 13 12AXYZ 15 15 14 13 12
Cost 100 225 250 325Save 500 500 500 500Net 400 275 250 175Cumul 400 675 925 1100
B BY A CY
Crash Costs
A -$250
B-$100
C-$200
D-
X-$350
Y-$125
Z-$325
Admin Cost = $500
A
B C D
X Y Z
3 2
2 3
2
25
2
4
3
NormalDuration:
MinimumDuration:
Path Duration
Which activity(s)
should we crash
next?
(per period)
A
B C D
X Y Z
3 2
2
2
2
1
2
25
2
3 3 3
3
ABCD 16 15 14 13 12 11AXYZ 15 15 14 13 12 11
Cost 100 225 250 325 525Save 500 500 500 500 500Net 400 275 250 175 -25Cumul 400 675 925 1100 1075
B BY A CY CZ
We lose $$, so do not crashCZ
Admin Cost = $500
A
B C D
X Y Z
3 2
2 2
2
25
2
3
3
NormalDuration:
MinimumDuration:
Path Duration
A
B C D
X Y Z
3 2
2
2
3
1
2
25
2
3 4 3
3
ABCD 16 15 14 13 12AXYZ 15 15 14 13 12
Cost 100 225 250 325Save 500 500 500 500Net 400 275 250 175Cumul 400 675 925 1100
B BY A CY
A
B C D
X Y Z
3 2
2 3
2
25
2
4
3
NormalDuration:
MinimumDuration:
Path DurationMost economicalduration
Achievedby crashing
Spent $900 in increased direct costs
Avoided $2000 inadministration costs
Net savings
PERT (CPM With 3 Time Estimates)
In past, time estimate is firm Now… task duration is uncertain
New activity Natural variance
Use 3 time estimates to deal with uncertainty a = most optimistic estimate m = most likely b = most pessimistic
Formulas
et (expected time) = (a + 4m + b)/6
σ (standard dev) = (b - a)/6 σ 2 (variance) = (b - a)2/36 = [(b - a)/6]2
Z = (D - et)/σ
How many standard deviations awayD is from et
Activity List for Example Problem
Activity DescriptionImmediate
PredecessorsRequired Activity
Time (weeks)
ABCDEFGHIJ
Select office siteCreate organization and financial planDetermine personnel requirementsDesign facilityConstruct the interiorSelect personnel to moveHire new employeesMove records, key personnel, etc.Make financial arrangementsTrain new personnel
--B
A,CDCFFB
H,E,G
3534824253
Mean and Variance
Activity a m b ET ó ó2
ABCDEFGHIJ
132241
2.514
1.5
34.5347
1.53.5253
5946165
7.536
4.5
3534824253
2/31
1/32/32
2/35/61/31/31/2
4/91
1/94/94
4/925/361/91/91/4
et = (a + 4m + b)/6σ = (b - a)/6σ 2 = (b - a)2/36 = [(b - a)/6]2
(1+4·3+5)/6
(5-1)/6
[(5-1)/6]2
et =
=
=
For activity A,
et
Path Length
Path length is the sum of expected times of activities on the path not sum of most likely times
Longest expected path length is critical Path length is uncertain, and so is project
duration Path has variance equal to sum of variances of
individual activities on path
A
B
D
C
E
F
G
H
I
J
0 3
0 5 5 8
5 10
8 12
8 10
12 20
10 12
10 14 20 23
20 23
18 23
18 20
16 20
12 20
5 8 14 16
8 12 5 8
0 5
A
B
D
C
E
F
G
H
I
J
0 3
0 5 5 8
5 10
8 12
8 10
12 20
10 12
10 14 20 23
20 23
18 23
18 20
16 20
12 20
5 8 14 16
8 12 5 8
0 5
0
0.1
0.2
0.3
0.4
et = 2322
If we want to know the probability of completing the project in 22 weeks or less:
Calculating probability of different completion time
Calculations
et = 23 weeks
σ2CP =2
BCDEJ
Z = (D - et)/σ CP = (22-23)/2.4095 = -0.42 Take .42 to the Z table => 1-.66 = .34
Beware - never add standard deviations!
= 5.8056= σ 2B + σ 2
C + σ 2D + σ 2
E + σ 2J