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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.
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2Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Practice; Follow the 5 Steps Process
Purchased Part$5 / unit
RM1$20 per
unit
RM2$20 per
unit
RM3$20 per
unit
$90 / unit120 units / week $135 / unit
50 units / weekP: Q:
D20 min.
D5 min.
C10 min.
C5 min.
B20 min.
A15 min. B10 min.A
10 min.
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3Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
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 = $9Q: Sales Price = $100 commission /unit = $10Finance 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= $45Q: Profit Margin = $100-40 Profit Margin= $60 Production View: Profit per minute of production timeProduct A B C D
P 15 15 15 15Q 10 30 5 5
Minutes6050
Profit Margin4560
Profit/Minute0.751.2
P
P
P
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4Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
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 = $9Q: Sales Price = $100 commission /unit = $10Finance 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= $45Q: Profit Margin = $100-40 Profit Margin= $60 Production View: Profit per minute of production timeProduct A B C D
P 15 15 15 15Q 10 30 5 5
Minutes6050
Profit Margin4560
Profit/Minute0.751.2
P
P
P
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5Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Cost World SolutionFor 50 units of Q, need 50 ( ) = min.
on B, leaving min. on B, for product P. Each unit of P requires minutes on B. So, we
can produce units of P.If we sell units of Q and units of P, we get
50($60) +60($45) = per week.
After factoring in operating expense ($6,000), we
30 150090
0 15900/15 = 60
60$5700
LOSE $300!
50
Go and Exploit the Constraint– Find the best way to use the constraint
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6Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
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 non-bottleneck resources is a mirage.
Human Resources and Capital Resources are not variable cost.
Theory of Constraints (TOC)
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7Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
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 × + 50 × =
minutes
Resource B: 100 × + 50 × =
minutesResource C: 100 × + 50 × =
minutes
Resource D: 100 × + 50 × =
minutes
15 10 2000
15 30 3000
15 5 1750
15 5 1750
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8Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Resource B is Constraint - BottleneckProduct P
QProfit $ 45
60Resource B needed (Min) 15
30Profit per min of Bottleneck 45/15 =3
60/30 =2
Per unit of bottleneck Product P creates more profit than Product Q
Produce as much as P, then Q
2. Exploit the Constraint : Find the Throughput World Best Solution
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9Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
For 100 units of P, need 100 ( ) = min. on B, leaving min. on B, for product Q.
Each unit of Q requires minutes on B. So, we can produce units of Q.
If we sell units of P and units of Q, we get 100( ) +30( ) = per week.
After factoring in operating expense ($6,000),
15 150090
0 30900/30 = 30
30$60
$6300
Profit $300!
100 $45
2. Exploit the Constraint : Find the Throughput World Best Solution
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10Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
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 QFor 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
2. Exploit the Constraint : Find the Throughput World Best Solution
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11Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
2. Exploit the Constraint : LP Formulation
Decision Variablesx1 : Volume of Product Px2 : Volume of Product Q Resource A15 x1 + 10 x2 2400
Resource B15 x1 + 30 x2 2400
Resource C15 x1 + 5 x2 2400
Resource D15 x1 + 5 x2 2400
Market for Px1 100
Market for Q x2 50
Objective Function Maximize Z = 45 x1 +60 x2 -6000
Nonnegativityx1 0, x2 0
Product A B C D Profit Margin DemandP 15 15 15 15 45 100Q 10 30 5 5 60 50
Capacity 2400 2400 2400 2400
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12Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
2. Exploit the Constraint : LP Formulation and SolutionResource Product P Product Q Needed AvailableResource A 15 10 0 <= 2400Resource B 15 30 0 <= 2400Resource C 15 5 0 <= 2400Resource D 15 5 0 <= 2400Market P 1 0 <= 100Market Q 1 0 <= 50
45 60 -6000
Resource Product P Product Q Needed AvailableResource A 15 10 1800 <= 2400Resource B 15 30 2400 <= 2400Resource C 15 5 1650 <= 2400Resource D 15 5 1650 <= 2400Market P 1 100 <= 100Market Q 1 30 <= 50
45 60 300100 30
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13Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
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.
Step 3: Subordinate Everything Else to This Decision
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
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14Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Adjustable CellsFinal Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease$B$10 Product P 100.00 0.00 45 1E+30 15$C$10 Product Q 0 60 30 60
ConstraintsFinal Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease$D$3 Resource A Needed 1800.0 2400 1E+30 600$D$4 Resource B Needed 2400.0 2.0 2400 600 900$D$5 Resource C Needed 1650.0 2400 1E+30 750$D$6 Resource D Needed 1650.0 2400 1E+30 750$D$7 Market P Needed 100.0 15.0 100 60 40$D$8 Market Q Needed 30.0 50 1E+30 20
A Practice on Sensitivity AnalysisWhat is the value of the objective function? Z= 45(100) + 60(?)-6000!
Shadow prices?
2400(Shadow Price A)+ 2400(Shadow Price C)+2400(Shadow Price C) + 2400(Shadow Price D)+100(Shadow Price P) + 50(Shadow Price Q). 2400(0)+ 2400(2)+2400(0) +2400(0)+100(15)+ 50(0).4800+1500 = 6300Is the objective function Z = 6300?6300-6000 = 300
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15Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Adjustable CellsFinal Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease$B$10 Product P 100.00 0.00 45 1E+30 15$C$10 Product Q ????? 0 60 30 60
ConstraintsFinal Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease$D$3 Resource A Needed 1800.0 2400 1E+30 600$D$4 Resource B Needed 2400.0 2.0 2400 600 900$D$5 Resource C Needed 1650.0 2400 1E+30 750$D$6 Resource D Needed 1650.0 2400 1E+30 750$D$7 Market P Needed 100.0 15.0 100 60 40$D$8 Market Q Needed 30.0 50 1E+30 20
A Practice on Sensitivity AnalysisHow many units of product Q?What is the value of the objective function? Z= 45(100) + 60(?)-6000 = 300.4500+60X2-6000=30060X2 = 1800X2 = 30
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16Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
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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17Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Step 4 : Elevate the Constraint(s). Do We Try To Sell In Japan?
Processing Times
Product A B C D P 15 15 15 15 Q 10 30 5 5
Product Costs and Profits
Product Selling Price
Manufg. Cost
Profit per unit
P (domestic) 90 45 45 Q (domestic) 100 40 60 P (Japan) 72 45 27 Q (Japan) 80 40 40
$/Constraint Minute
32
1.81.33
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18Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Right now, we can get at least $ per constraint minute in the domestic market.
So, should we go to Japan at all?Okay, suppose we do not go to Japan. Is there
something else we can do? Let’s buy another machine! Which one? Cost of the machine = $100,000. Cost of operator: $400 per week. What is weekly operating expense now? How soon do we recover investment?
Perhaps not.
2
B
$6,400
Step 4 : Elevate the Constraint(s). Do We Try To Sell In Japan?
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19Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Step 5: If a Constraint Was Broken in previous Steps, Go to Step 1
Resource Product P Product Q Product PJ Product QJ Needed AvailableResource A 15 10 15 10 2400 <= 2400Resource B 15 30 15 30 4800 <= 4800Resource C 15 5 15 5 1800 <= 2400Resource D 15 5 15 5 1800 <= 2400Market P 1 80 <= 100Market Q 1 50 <= 50
45 60 27 40 300080 50 0 70
Resource Product P Product Q Product PJ Product QJ Needed AvailableResource A 15 10 15 10 0 <= 2400Resource B 15 30 15 30 0 <= 4800Resource C 15 5 15 5 0 <= 2400Resource D 15 5 15 5 0 <= 2400Market P 1 0 <= 100Market Q 1 0 <= 50
45 60 27 40 -6400
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20Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Step 5: If a Constraint Was Broken in previous Steps, Go to Step 180P, 50Q,0PJ, 70QJTotal Profit = 3000What is the payback period?100000/3000 = 33.33 weeksWhat is the payback period?100000/(3000-300) = 37.03 weeksThe domestic P had the max profit per minute on B. Why we have not satisfied all the domestic demand.
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21Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics
Purchased Part$5 / unit
RM1$20 per
unit
RM2$20 per
unit
RM3$25 per
unit
$90 / unit110 units / week
$100 / unit60 units / weekP: Q:
D10 min.
D5 min.
C10 min.
C5 min.
B25 min.
A15 min. B10 min.
A10 min.
Practice: A Production System Manufacturing Two Products, P and Q
Time available at each work center: 2,400 minutes per week.Operating expenses per week: $6,000. All the resources cost the same.