OPSM 301 Operations Management

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OPSM 301 Operations Management
Koç University

• Class 9
• Project Management
• PERT and project crashing

Zeynep Aksin zaksin_at_ku.edu.tr
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Announcements

• Change in syllabus plan as follows
• Will swap last session on project management with
  decision trees
• Last session of project management will be after
  the bayram on 8/11
• Class will be held in the lab (TBA)
• Second group assignment will be due
• We will have quiz 2 on Project Management
• Decision Trees will be on 1/11
• Quiz 3 on 10/11 Thursday

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Example
Suppose you are an advertising manager
responsible for the launch of a new media
advertising campaign. The campaign (project) has
the following activities Activity Predecessors
Time A. Media bids none 2 wks B. Ad
concept none 6 C. Pilot layouts B 3 D.
Select media A 8 E. Client approval A,C 6 F.
Pre-production B 8 G. Final production E,F 5 H
. Launch campaign D,G 0
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CPM with Three Activity Time Estimates
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Some CPM/PERT Assumptions

• Project control should focus on the critical path
• The activity times in PERT follow the beta
  distribution, with the variance of the project
  assumed to equal the sum of the variances along
  the critical path

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Beta Distribution Assumption
Assume a Beta distribution
density
activity duration
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Beta Distribution Assumption
density
activity duration
m
a
b
8
Expected Time and Variance
a 4m b 6
Expected Time
(b - a)2 36
Variance
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Expected Times
10
21 32
7 21
C, 14
E, 11
0 7
32 36
21 32
7 21
H, 4
A, 7
0 7
7 12
32 36
12 19
36 54
0 0
D, 5
F, 7
Start 0
I, 18
25 32
20 25
0 0
36 54
0 5.33
5.33 16.33
B 5.33
G, 11
19.67 25
25 36
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Expected Completion Time 54 Days
C, 14
E, 11
H, 4
A, 7
D, 5
F, 7
Start 0
I, 18
B 5.33
G, 11
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What is the probability of finishing this project
in less than 53 days? We need the variance also!
D53
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Sum the variance along the critical path
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Pr(t lt D)
t
TE 54
D53
p(z lt -.156) .436, or 43.6
There is a 43.6 probability that this project
will be completed in less than 53 weeks.
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PERT Probability Example

• Youre a project planner for General Dynamics. A
  submarine project has an expected completion time
  of 40 weeks, with a standard deviation of 5
  weeks. What is the probability of finishing the
  sub in 50 weeks or less?

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Converting to Standardized Variable
-
-
X
T
50
40



Z
2
0
.
s
5
Normal Distribution
Standardized Normal Distribution
s
1
s
5
Z
40
50
X
m
T
Z
0
2.0
z
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Obtaining the Probability
Standardized Normal Probability Table (Portion)
Z
.00
.01
.02
s
1
0.0
.50000
.50399
.50798
Z




.97725
.97725
.97784
.97831
2.0
m
Z
0
2.0
.98214
.98257
.98300
2.1
z
Probabilities in body
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Variability of Completion Time for Noncritical
Paths

• Variability of times for activities on
  noncritical paths must be considered when finding
  the probability of finishing in a specified time.
• Variation in noncritical activity may cause
  change in critical path.

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Time-Cost Models

• Basic Assumption Relationship between activity
  completion time and project cost
• Time Cost Models Determine the optimum point in
  time-cost tradeoffs
• Activity direct costs
• Project indirect costs
• Activity completion times

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Project Costs vs. Project Duration
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Cost Analysis

• We assume a linear relation between activity
  duration and activity cost
• Regulate activity durations to minimize the total
  project cost

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Cost Analysis

• We require two time estimates and two associated
  cost estimates
• Normal Time Time required if a usual amount of
  resources are applied to the activity.
• Normal Cost Cost of completing an activity in
  normal time.
• Crash Time Least time that an activity can be
  performed in if all available resources are
  applied to it.
• Crash Cost Cost of completing an activity in
  crash time.
• Incremental Cost
• I (Crash Cost - Normal Cost)/(Normal Time -
  Crash Time)
• ICost of reducing duration of an acitivity by 1
  unit of time

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Crash and Normal Times and Costs for Activity B
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Steps for Solution

• 1. Perform PERT analysis using normal times and
  calculate I for all critical activities
• 2. Pick the activity (critical) with the smallest
  I and shorten its duration as much as possible.
  That is, until
• a. Duration reaches crash time
• b. Another path becomes critical
• 3. If duration of the project cannot be reduced
  any more, then stop otherwise return to the
  second step
• The above process results in the modified crash
  program.

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Example
NT,CT
NT
4,2
CC,NC
B
(normal time, crash time)
4
8
4
5
4,2
9
2,1
D
0
4
11
50,30
9
4
2
9
4
0
11
5, 2
C
4
9
70,10
100,10
4
5
9
(crash cost, normal cost)
65,50
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Solution Procedure

• Crash the activity with smallest I (least cost)
• Check if critical path changed at each step
• Continue crashing until satisfied or not possible
  
• Total Cost Indirect cost direct cost,
• Minimum Cost schedule is the one that has minimum
  total cost

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Advantages of PERT/CPM

• Especially useful when scheduling and controlling
  large projects.
• Straightforward concept and not mathematically
  complex.
• Graphical networks aid perception of
  relationships among project activities.
• Critical path slack time analyses help pinpoint
  activities that need to be closely watched.
• Project documentation and graphics point out who
  is responsible for various activities.
• Applicable to a wide variety of projects.
• Useful in monitoring schedules and costs.

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Limitations of PERT/CPM

• Assumes clearly defined, independent, stable
  activities
• Specified precedence relationships
• Activity times (PERT) follow beta distribution
• Subjective time estimates
• Over-emphasis on critical path