8/27/04

Paul A. JensenOperations Research Models and Methods

Copyright 2004 - All rights reserved

The Theory of Constraints

Now that we know the Goal, how do we use it to improve our

system?

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The Theory of Constraints Step 1: Identify the system's constraint(s). Step 2: Decide how to exploit the system's

constraint(s). Step 3: Subordinate everything else to the

decisions of Step 2. Step 4: Elevate the system's constraint(s). Step 5: If a constraint is broken in Step 4, go

back to Step 1.

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Step 1: Identify the system’s constraint(s).

What is the Goal? What is Throughput? What is Inventory? What is Operating Expense?

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Step 2: Decide how to exploit the system’s constraint(s).

What is the constraint? How do we get as much throughput as

possible?

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Step 3: Subordinate everything else to the decisions of Step 2

Throughput? Inventory? Operating Expense?

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Step 4: Elevate the system’s constraint(s).

Throughput? Inventory? Operating Expense?

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Step 5: If a constraint is broken in Step 4, go back to Step 1.

What might happen if the constraint is elevated?

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Summary: The Theory of Constraints Step 1: Identify the system’s constraint(s). Step 2: Decide how to exploit the system’s

constraint(s). Step 3: Subordinate everything else to the

decisions of Step 2. Step 4: Elevate the system’s constraint(s). Step 5: If a constraint is broken in Step 4, go

back to Step 1.

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Application in Manufacturing

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$90/U 100 U/Wk

P

$100/U 50 U/Wk

Q

D 10 min./U

D 5 min./U

C 10 min./U

C 5 min./U

B 15 min./U

A 15 min./U

B 15 min./U

A 10 min./U

RM1 $20/U

RM2 $20/U

RM3 $20/U

Purchase Part $5/U

A,B,C,D: 1 each Available Time: 2400 Min/Wk OE not including RM: $6000 per wk

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Step 1: Identify the system’s constraint(s).

What is the Goal? What is Throughput? What is Inventory? What is Operating Expense?

$90/U 100 U/Wk

P

$100/U 50 U/Wk

Q

D 10 min./U

D 5 min./U

C 10 min./U

C 5 min./U

B 15 min./U

A 15 min./U

B 15 min./U

A 10 min./U

RM1 $20/U

RM2 $20/U

RM3 $20/U

Purchase Part $5/U

A,B,C,D: 1 each Available Time: 2400 Min/Wk OE not including RM: $6000 per wk

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To Identify the Resource Constraint Compute the load on each production

resource assuming market demands. Compare the resource loads with the

resource capacities. Those resources for which the loads exceed

the capacities are constraints (bottlenecks). If no production resource load exceeds its

capacity, the market demands are the constraints. the constraints are external to the manufacturing

system.

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Compute the loads and compare with capacities. Production P=100, Production Q=50 A: Load =2000, Capacity = 2400 Minutes B: Load =3000, Capacity = 2400 Minutes C: Load =1750, Capacity = 2400 Minutes D: Load =1250, Capacity = 2400 Minutes What is the constraint?

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Step 2: Decide how to exploit the system’s constraint(s).

$90/U 100 U/Wk

P

$100/U 50 U/Wk

Q

D 10 min./U

D 5 min./U

C 10 min./U

C 5 min./U

B 15 min./U

A 15 min./U

B 15 min./U

A 10 min./U

RM1 $20/U

RM2 $20/U

RM3 $20/U

Purchase Part $5/U

A,B,C,D: 1 each Available Time: 2400 Min/Wk OE not including RM: $6000 per wk

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Exploiting the constraint Assume a single constraint is identified. Rank the products in order of the ratio:

Throughput dollars per minute of constraint use. Select the product mix so that the products

with greater ratios are produced in preference to the products with smaller ratios.

What goal is this method trying to achieve? How does this method achieve the goal?

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What and how much to produce?

P: TP/Unit = 45, B Min/Unit=15

Q: TP/Unit = 60, B Min/Unit=30

TP/Min = 4515 $3 / min

TP/Min = 6030 $2 / min

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Calculate Solution Produce as much P as possible

Use the remainder of the constraint resource for Q

What is the profit for this product mix?

P 100

Q2400 15 100

30 90030 30

Profit = TP - OC

= 100 45 30 60 3000

4500 1800 6000 300

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Step 3: Subordinate everything else to the decisions of Step 2.

$90/U 100 U/Wk

P

$100/U 50 U/Wk

Q

D 10 min./U

D 5 min./U

C 10 min./U

C 5 min./U

B 15 min./U

A 15 min./U

B 15 min./U

A 10 min./U

RM1 $20/U

RM2 $20/U

RM3 $20/U

Purchase Part $5/U

A,B,C,D: 1 each Available Time: 2400 Min/Wk OE not including RM: $6000 per wk

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Subordinating Production Production P=100, Production Q=30 A: Load =1800, Capacity = 2400 Minutes B: Load =2400, Capacity = 2400 Minutes C: Load =1650, Capacity = 2400 Minutes D: Load =1150, Capacity = 2400 Minutes What determines the load on the non-

constraints?

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Step 4: Elevate the system’s constraint(s).

Where should process improvements be focused?

What is the benefit of elevating the constraint?

What is the benefit of elevating a non-constraint?

$90/U 100 U/Wk

P

$100/U 50 U/Wk

Q

D 10 min./U

D 5 min./U

C 10 min./U

C 5 min./U

B 15 min./U

A 15 min./U

B 15 min./U

A 10 min./U

RM1 $20/U

RM2 $20/U

RM3 $20/U

Purchase Part $5/U

A,B,C,D: 1 each Available Time: 2400 Min/Wk OE not including RM: $6000 per wk

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Step 5: If a constraint is broken in Step 4, go back to Step 1.

What might happen if the constraint is elevated?

What happens if there are no more internal constraints?

$90/U 100 U/Wk

P

$100/U 50 U/Wk

Q

D 10 min./U

D 5 min./U

C 10 min./U

C 5 min./U

B 15 min./U

A 15 min./U

B 15 min./U

A 10 min./U

RM1 $20/U

RM2 $20/U

RM3 $20/U

Purchase Part $5/U

A,B,C,D: 1 each Available Time: 2400 Min/Wk OE not including RM: $6000 per wk

22

Say we add another machine of type B. Production P=100, Production Q=50 A: Load =2000, Capacity = 2400 Minutes B: Load =3000, Capacity = 4800 Minutes C: Load =1750, Capacity = 2400 Minutes D: Load =1250, Capacity = 2400 Minutes How much should we produce? What is the new constraint? How do we elevate the new constraint?

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Summary: The Theory of Constraints Step 1: Identify the system’s constraint(s). Step 2: Decide how to exploit the system’s

constraint(s). Step 3: Subordinate everything else to the

decisions of Step 2. Step 4: Elevate the system’s constraint(s). Step 5: If a constraint is broken in Step 4, go

back to Step 1.