Transcript Systems Thinking and the Theory of Constraints Any intelligent fool can make things bigger, more complex, and more violent.

Systems Thinking and the
Theory of Constraints
Any intelligent fool can make things
bigger, more complex, and more
violent. It takes a touch of genius -and a lot of courage -- to move in the
opposite direction.
Albert Einstein
These sides and note were prepared using
1. The book Streamlined: 14 Principles for Building and Managing the Lean Supply
Chain. 2004. Srinivasan. TOMPSON ISBN: 978-0-324-23277-6.
2. The slides originally prepared by Professor M. M. Srinivasan.
Practice; Follow the 5 Steps Process
$90 / unit
P: 100 units / week
B
15 min.
A
15 min.
RM1
$20 per
unit
C
15
5
Theory of Constraints 1- Basics
D
5 min.
C
5 min.
C
10 min.
B
15
30
$100 / unit
50 units / week
D
15 min.
Purchased Part
$5 / unit
Product A
P
15
Q
10
Q:
D
15
5
RM2
$20 per
unit
B
15 min.
A
10 min.
RM3
$20 per
unit
Profit Margin
45
60
Ardavan Asef-Vaziri
Nov-2010
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2. Exploit the Constraint : LP Formulation
Decision Variables
x1 : Volume of Product P
x2 : Volume of Product Q
Resource A
15 x1 + 10 x2  2400
Resource B
15 x1 + 30 x2  2400
Resource C
15 x1 + 5 x2  2400
Resource D
15 x1 + 5 x2  2400
Theory of Constraints 1- Basics
Product
A
B
C
D
P
Q
Capacity
15
10
15
30
15
5
15
5
Profit Margin Demand
45
60
100
50
2400 2400 2400 2400
Market for P
x1
 100
Market for Q
x2  50
Objective Function
Maximize Z = 45 x1 +60 x2 -6000
Nonnegativity
x1  0, x2  0
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Nov-2010
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2. Exploit the Constraint : LP Formulation and
Solution
Resource
Resource A
Resource B
Resource C
Resource D
Market P
Market Q
Product P Product Q
15
10
15
30
15
5
15
5
Needed
0
0
0
0
<=
<=
<=
<=
Available
2400
2400
2400
2400
1
0
0
<=
<=
100
50
60
-6000
1
45
Resource
Resource A
Resource B
Resource C
Resource D
Market P
Market Q
Theory of Constraints 1- Basics
Product P Product Q
15
10
15
30
15
5
15
5
1
1
45
60
100
30
Ardavan Asef-Vaziri
Needed
1800
2400
1650
1650
100
30
<=
<=
<=
<=
<=
<=
Available
2400
2400
2400
2400
100
50
300
Nov-2010
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Step 3: Subordinate Everything
Else to This Decision
Keep Resource B running at all times.
Resource B can first work on RM2 for
products P and Q, during which Resource
A would be processing RM3 to feed
Resource B to process RM3 for Q.
Never allow starvation of B by purchasing RM2 or by output of
Process A. Never allow blockage of B by Process D- Assembly.
Minimize the number of switches (Setups) of Process B from RM2
to RM3-Through-A and vice versa.
Minimize variability at Process A.
Minimize variability in arrival of RM2
Do not miss even a single order of Product P
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
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A Practice on Sensitivity Analysis
What is the value of the objective
function? Z= 45(100) + 60(?)-6000!
Adjustable Cells
Cell
Name
$B$10 Product P
$C$10 Product Q
Final Reduced Objective Allowable Allowable
Value
Cost
Coefficient Increase Decrease
100.00
0.00
45
1E+30
15
0
60
30
60
Constraints
Shadow prices?
Cell
$D$3
$D$4
$D$5
$D$6
$D$7
$D$8
Name
Resource A Needed
Resource B Needed
Resource C Needed
Resource D Needed
Market P Needed
Market Q Needed
Final
Shadow Constraint Allowable Allowable
Value
Price
R.H. Side
Increase Decrease
1800.0
2400
1E+30
600
2400.0
2.0
2400
600
900
1650.0
2400
1E+30
750
1650.0
2400
1E+30
750
100.0
15.0
100
60
40
30.0
50
1E+30
20
2400(Shadow Price A)+ 2400(Shadow Price C)+2400(Shadow
Price C) + 2400(Shadow Price D)+100(Shadow Price P) +
50(Shadow Price Q).
2400(0)+ 2400(2)+2400(0) +2400(0)+100(15)+ 50(0).
4800+1500 = 6300
Is the objective function Z = 6300?
6300-6000 = 300
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
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A Practice on Sensitivity Analysis
How many units of product Q?
What is the value of the objective function?
Z= 45(100) + 60(?)-6000 = 300.
4500+60X2-6000=300
60X2 = 1800
Adjustable Cells
X2 = 30
Final
Cell
Name
$B$10 Product P
$C$10 Product Q
Reduced Objective Allowable Allowable
Value
Cost
Coefficient Increase Decrease
100.00
0.00
45
1E+30
15
?????
0
60
30
60
Constraints
Cell
$D$3
$D$4
$D$5
$D$6
$D$7
$D$8
Theory of Constraints 1- Basics
Name
Resource A Needed
Resource B Needed
Resource C Needed
Resource D Needed
Market P Needed
Market Q Needed
Final
Shadow Constraint Allowable Allowable
Value
Price
R.H. Side
Increase Decrease
1800.0
2400
1E+30
600
2400.0
2.0
2400
600
900
1650.0
2400
1E+30
750
1650.0
2400
1E+30
750
100.0
15.0
100
60
40
30.0
50
1E+30
20
Ardavan Asef-Vaziri
Nov-2010
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Step 4 : Elevate the Constraint(s)
The bottleneck has now been exploited
 Besides Resource B, we have found a market
bottleneck.

Generate more demand for Product P
 Buy another Resource B
 The Marketing Director: A Great Market in Japan !
 Have to discount prices by 20%.

Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
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Step 4 : Elevate the Constraint(s). Do We Try To
Sell In Japan?
Processing Times
A
C
B
15
15
15
10
5
30
Product
P
Q
D
15
5
Product Costs and Profits
Product
Selling
Price
P (domestic)
90
Q (domestic) 100
P (Japan)
72
Q (Japan)
80
Theory of Constraints 1- Basics
Manufg.
Cost
45
40
45
40
Profit per $/Constraint
Minute
unit
45
3
2
60
1.8
27
40
1.33
Ardavan Asef-Vaziri
Nov-2010
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Step 4 : Elevate the Constraint(s). Do We Try To
Sell In Japan?
 Right now, we can get at least $
2 per constraint
minute in the domestic market.
 So, should we go to Japan at all? Perhaps not.
 Okay, suppose we do not go to Japan. Is there
something else we can do?
 Let’s buy another machine! Which one? B
 Cost of the machine = $100,000.
 Cost of operator: $400 per week.
 What is weekly operating expense now? $6,400
 How soon do we recover investment?
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
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Step 5: If a Constraint Was Broken in previous
Steps, Go to Step 1
Resource
Resource A
Resource B
Resource C
Resource D
Market P
Market Q
Product P Product Q Product PJ Product QJ Needed
15
15
15
15
1
Resource A
Resource B
Resource C
Resource D
Market P
Market Q
15
15
15
15
10
30
5
5
0
0
0
0
0
0
27
40
-6400
1
45
Resource
10
30
5
5
60
Available
<=
<=
<=
<=
<=
<=
Product P Product Q Product PJ Product QJ Needed
15
15
15
15
1
10
30
5
5
15
15
15
15
10
30
5
5
2400
4800
1800
1800
80
50
3000
1
45
60
27
40
80
50
0
70
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
2400
4800
2400
2400
100
50
Available
<=
<=
<=
<=
<=
<=
Nov-2010
2400
4800
2400
2400
100
50
11
Step 5: If a Constraint Was Broken in previous
Steps, Go to Step 1
80P, 50Q,0PJ, 70QJ
Total Profit = 3000
What is the payback period?
100000/3000 = 33.33 weeks
What is the payback period?
100000/(3000-300) = 37.03 weeks
The domestic P had the max profit per minute on B. Why we
have not satisfied all the domestic demand.
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
12
Practice: A Production System Manufacturing
Two Products, P and Q
$90 / unit
P: 110 units / week
Q:
$100 / unit
60 units / week
D
5 min.
D
10 min.
Purchased Part
$5 / unit
C
10 min.
C
5 min.
B
25 min.
A
15 min.
B
10 min.
A
10 min.
RM1
$20 per
unit
RM2
$20 per
unit
RM3
$25 per
unit
Time available at each work center: 2,400 minutes per week.
Operating expenses per week: $6,000. All the resources cost the same.
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
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