Project Management
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Transcript Project Management
Project Management
PERT
___________________________________________________________________________
Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Probabilistic time – 3 estimates
Optimistic
Pessimistic
Most likely
Expected
completion time
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Activity time β-distribution
Most
Likely
Expected
Optimistic
0
aij
Pessimistic
mij μij
bij
Time
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Expected completion time
ij
a ij 4 m ij b ij
6
Standard deviation
ij
b ij a ij
6
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
1) Using CPM ( tij = μij )
Critical
path
2) Expected duration of the project
M
ij
( i , j ) CP
Variance of the project duration
2
ij
2
( i , j ) CP
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Duration of the project - normal distribution
M – expected
duration
T – real
duration
σ – standard
deviation
M-σ
M
M+σ
T
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
3) Probability analysis
probabilty of
completion time
within TD
desired time TD
desired time TD
z
TD M
p
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
3) Probability analysis
completion
time
desired probability p
desired probability p
zp
T D M z p
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
Activity
Description
aij
mij
bij
μij
Predecessors
A
Songs Selection
11
15
19
15
None
B
Mastering
7
8
9
8
A
C
PM Elaborating
5
6
7
6
A
D
Customers Analysis
5
7
9
7
A
E
PM Production
2
3
10
4
C, D
F
PM to PH
3
4
11
5
E
G
Customers Selection
2
3
4
3
D
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
Activity
Description
aij
mij
bij
μij
Predecessors
H
Make CD Copies
8
11
20
12
B, D
I
Data to PH
2
3
4
3
G
J
Laser Print
6
8
16
9
F, I
K
Mailing
6
8
10
8
H, J
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
H
Critical path:
9
4
B
1
A
D
2
C
3
D2
G
7
I
D1
5
K
10
J
8
F
E
6
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
Critical activities
Activity
Description
aij
mij
bij
μij
σij
A
Songs Selection
11
15
19
15
8/6
D
Customers Analysis
5
7
9
7
4/6
E
PM Production
2
3
10
4
8/6
F
PM to PH
3
4
11
5
8/6
J
Laser Print
6
8
16
9
10/6
K
Mailing
6
8
10
8
4/6
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
Expected duration of the project
Variance of the project duration
Std. deviation of the project duration
M = 48
2 =9
=3
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
Duration of the project
45
48
51
Time (days)
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
Probability analysis
Desired time TD = 45
z
45 48
3
1
p 0 . 1587
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Quantitative Methods of Management
Jan Fábry
Project Management
PERT
Example - Music DM, Inc.
Probability analysis
Desired probability = 0.95
zp = 1.645
T D 48 1 . 645 ( 3 ) 52 . 935
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Quantitative Methods of Management
Jan Fábry
Inventory Models
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Inventory
Stored for use in future
Examples of inventories
- raw material
- finished goods
- semi-finished products
- spare parts
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Reasons for Maintaining Inventories
Fluctuating demand
Delayed supply
Savings on ordering cost
Benefits on large quantities
Inflation
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Management
How much to order?
When to order?
Objective – minimize total cost
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Partial Inventory Cost
Ordering & setup cost – fixed charge
frequency of ordering
cost
Unit purchasing cost – variable cost
quantity discounts
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Partial Inventory Cost
Holding & carrying cost – variable cost
- storage cost (space)
- store keeping operations (movement)
- insurance & taxes
- interest (invested capital )
- oportunity cost
- spoilage or obscolescence
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Partial Inventory Cost
Shortage (stockout) cost – variable cost
- idled production (idled machine)
- placing special expensive expediting order
- loss of customers due to late deliveries
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Inventory Terminology
Inventory level
Available size of the inventory
Demand & depletion
Rate of demand Depletion rate
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Inventory Terminology
Reordering
Reorder point = signal inventory level
Lead time
Time
Placing
order
Receiving shipment
&
Replenishment
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Inventory Terminology
Shortage !!
Shortage
Receiving
shipment
Lead time
Time
Optimal
reorder date
Inventory level = 0
Placing
order
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Inventory Terminology
Safety stock
Buffer being built to prevent shortage
In case of probabilistic demand
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Inventory Models
Deterministic models
Rate of demand is known with certainty
Probabilistic models
Probabilistic demand (random variable)
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Demand Classification
Demand
Deterministic
Static
Dynamic
Probabilistic
Stationary
Nonstationary
Increasing Level of Mathematical Difficulty
Probability
RateRate
of demand
density
ofdensity
demand
function
- function
known
- known
–with
unchanhged
with
certainty
certainty
over time
Probability
– varies
in time
- not- constant
constant
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Deterministic Models
Basic economic order quantity model
(EOQ model)
EOQ model with back orders allowed
(with planned shortages)
Economic production lot size model
EOQ model with quantity discounts
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Quantitative Methods of Management
Jan Fábry
Inventory Models
Probabilistic Models
Probabilistic model with continuous
demand
Single-period decision model
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Quantitative Methods of Management
Jan Fábry