Transcript Quizx

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: 120 units / week
$135 / unit
50 units / week
D
5 min.
D
20 min.
Purchased Part
$5 / unit
C
10 min.
A
15 min.
RM1
$20 per
unit
Theory of Constraints 1- Basics
Q:
C
5 min.
B
10 min.
RM2
$20 per
unit
Ardavan Asef-Vaziri
Nov-2010
B
20 min.
A
10 min.
RM3
$20 per
unit
2
What Product to Produce?
Sales View: Suppose you are the sales manager and you will be
paid a 10% commission on the sales Price. What product do you
recommend to produce?
P: Sales Price = $90  commission /unit = $9
Q: Sales Price = $100  commission /unit = $10 P
Finance View: Suppose you are the financial manager and are in
favor of the product with more profit per unit.
P: Profit Margin = $90 - 45  Profit Margin= $45
Q: Profit Margin = $100-40  Profit Margin= $60 P
Production View: Profit per minute of production time
Product A
P
15
Q
10
B
15
30
C
15
5
Theory of Constraints 1- Basics
D
15
5
Minutes Profit Margin Profit/Minute
60
45
0.75
50
60
1.2
Ardavan Asef-Vaziri
Nov-2010
P
3
What Product to Produce?
Sales View: Suppose you are the sales manager and you will be
paid a 10% commission on the sales Price. What product do you
recommend to produce?
P: Sales Price = $90  commission /unit = $9
Q: Sales Price = $100  commission /unit = $10 P
Finance View: Suppose you are the financial manager and are in
favor of the product with more profit per unit.
P: Profit Margin = $90 - 45  Profit Margin= $45
Q: Profit Margin = $100-40  Profit Margin= $60 P
Production View: Profit per minute of production time
Product A
P
15
Q
10
B
15
30
C
15
5
Theory of Constraints 1- Basics
D
15
5
Minutes Profit Margin Profit/Minute
60
45
0.75
50
60
1.2
Ardavan Asef-Vaziri
Nov-2010
P
4
Cost World Solution
For 50 units of Q, need 50 ( 30 ) = 1500 min. on B,
leaving 900 min. on B, for product P.
Each unit of P requires 15 minutes on B. So, we can
produce 900/15 = 60 units of P.
If we sell 50 units of Q and 60 units of P, we get 50($60)
+60($45) = $5700 per week.
After factoring in operating expense ($6,000), we
LOSE $300!
Go and Exploit the Constraint– Find the best way to use
the constraint
Theory of Constraints 1- Basics
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Theory of Constraints (TOC)
 Think Globally not Locally. Link Performance of each





subsystem (Marketing, Finance, Operations, etc) to the
performance of the total system (the Business Enterprise)
The Goal of a Business Enterprise is to make more money, …
in the present and in the future  Max NPV.
There is one or at most few constraint(s) determine its output.
Just like the links of a chain, the processes within the enterprise
work together to generate profit for the stakeholders. The
chain is only as strong as its weakest link.
Time lost at a bottleneck resource results in a loss of
throughput for the whole enterprise. Time saved a nonbottleneck resources is a mirage.
Human Resources and Capital Resources are not variable cost.
Theory of Constraints 1- Basics
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1. Identify The Constraint(s. Can We Meet the
Demand of 100 Ps and 50Qs?
Can we satisfy the demand?
Resource requirements for 100 P’s and 50 Q’s:
 Resource A: 100 ×15 + 50 ×
10
=2000
minutes
30
 Resource B: 100 ×15 + 50 ×
=3000
minutes
 Resource C: 100 ×15 + 50 ×
5
1750
=
minutes
 Resource D: 100 ×15 + 50 ×
5
1750
=
minutes
Theory of Constraints 1- Basics
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2. Exploit the Constraint : Find the Throughput
World Best Solution
Resource B is Constraint - Bottleneck
Product
P
Profit $
45
Resource B needed (Min)
15
Profit per min of Bottleneck
45/15 =3
Q
60
30
60/30 =2
Per unit of bottleneck Product P creates more profit than
Product Q
Produce as much as P, then Q
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2. Exploit the Constraint : Find the
Throughput World Best Solution
For 100 units of P, need 100 ( 15 ) = 1500 min. on B,
leaving 900 min. on B, for product Q.
Each unit of Q requires 30 minutes on B. So, we can
produce 900/30 = 30 units of Q.
If we sell 100 units of P and 30 units of Q, we get 100($45 )
+30($60 ) = $6300 per week.
After factoring in operating expense ($6,000),
Profit $300!
Theory of Constraints 1- Basics
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2. Exploit the Constraint : Find the
Throughput World Best Solution
 How much additional profit can we make if market
for P increases from 100 to 102; by 2 units.
 We need 2(15) = 30 more minutes of resource B.
 Therefore we need to reduce 30 minutes of the time
allocated to Q and allocate it to P.
 For each unit of Q we need 30 minutes of resource B.
 Therefore we produce one unit less Q
 For each additional P we make $45, but $60 is lost for
each unit less of Q. Therefore if market for P is 102 our
profit will increase by 45(2)-60 = 30
Theory of Constraints 1- Basics
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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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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
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Needed
1800
2400
1650
1650
100
30
<=
<=
<=
<=
<=
<=
Available
2400
2400
2400
2400
100
50
300
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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
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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
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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
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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%.

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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
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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
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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
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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
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Nov-2010
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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
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