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 original were prepared by Professor M. M. Srinivasan.
Practice; Follow the 5 Steps Process
Two products, P and Q. Weekly demand for P is 100 units & for Q is 50
units.
$90 / unit
Q:
P: 100 units / week
$100 / unit
50 units / week
D
5 min.
D
15 min.
Purchased Part
$5 / unit
C
10 min.
C
5 min.
B
15 min.
Operating expenses per
week: $6,000. It includes
A
A
B
$2000 administrative costs
15 min.
15 min.
10 min.
for the manager who
works as operations,
RM1
RM2
RM3
$20 per
$20 per
$20 per
finances, and marketing
unit
unit
unit
manager, and $4000 non-administrative costs for the 4 operators working at the work-centers A, B, C,
and D. Time available at each work center is 2,400 minutes per week.
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
2
Facility Layout : Job Shop
RM 2
RM1
RM3
A
C
B
D
Product A
P
15
Q
10
B
15
30
C
15
5
D
15
5
Profit Margin
45
60
Product 1
Product 2
PP
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
3
Financial Throughput and Fixed Operating Costs
We define financial throughput as the rate at which the
enterprise generates money. By selling one unit of product
we generate P dollars, at the same time we incur V dollars
pure variable cost. Pure variable cost is the cost directly
related to the production of one additional unit - such as raw
material. It does not include fixed costs such as salary, rent,
and depreciation. Since we produce and sell X units per unit
of time. The financial throughput is X(P-V).
Fixed Operating Expenses (F) include all costs not directly
related to production of one additional unit. That includes
costs such as human and capital resources.
In our example, F = $6,000 per week, P1= 90, P2= $100, V1= 45,
V2= 40, and therefore, incoming $$ per unit of product is $45
for product P and $60 for product Q.
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
4
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 x
1
+60 x2 -6000
Nonnegativity
x1  0, x2  0
Ardavan Asef-Vaziri
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.
Do not allow starvation of B by purchased material RM2 or by
output of Process A. Do not allow blockage of B by D.
Minimize the number of switches (Setups) of Process B from RM2
to RM3-Through-A and vice versa.
Minimize variability at Process B. Minimize variability at Process
A and also in purchasing and arrival of RM2.
Do not miss even a single order of Product P.
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
7
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 ! But the
price discount, transportation cost, and other out of country
costs adds up to 20% of the domestic sales price. Production
costs remains as before.
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
8
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
 What is the pay-nack period (PBP)?
Theory of Constraints 1- Basics
Ardavan Asef-Vaziri
Nov-2010
10
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
13
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
14
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
15