1Ardavan 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 / unit100 units / week

$100 / unit50 units / week

P: Q:

D15 min.

D5 min.

C10 min.

C5 min.

B15 min.

A15 min.

B15 min.

A10 min.

Time available at each work center: 2,400 minutes per week.Operating expenses per week: $6,000. All the resources cost the same

2Ardavan 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 = $10

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= $45Q: Profit Margin = $100-40 Profit Margin= $60

3Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

What Product to Produce?

Production View:

So, is the star and is the dog. First we’ll offer the star to the market. If we have residual capacity, we’ll offer the dog! Okay?

Product A B C D

P 15 15 15 15

Q 10 30 5 5

Minutes

60

50

Profit Margin

45

60

Profit/Minute

0.75

1.2

Q P

4Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

Cost World Solution

For 50 units of Q, need 50 x = 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 x $60 + x $45 = $ per week.

After factoring in operating expense ($6,000), we

30 1500900

15900/15 = 60

6060 5700

LOSE $300!

50

Go and Exploit the Constraint– Find the best way to use the constraint

5Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

1. Identify The Constraint(s. Can We Meet the Demand of 100 Ps and 50Qs?

Resource requirements for 100 P’s and 50 Q’s:

Resource A: 100 × + 50 × = minutes

Resource B: 100 × + 50 × = minutes

Resource C: 100 × + 50 × = minutes

Resource D: 100 × + 50 × = minutes

15 10 2000

15 30 3000

15 5 1750

15 5 1750

6Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

2. Exploit the Constraint : Find the Throughput World Best Solution

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 Demand

P 15 15 15 15 45 100

Q 10 30 5 5 60 50

Capacity 2400 2400 2400 2400

7Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

2. Exploit the Constraint : Find the Throughput World Best Solution

Resource Product P Product Q Needed Available

Resource A 15 10 0.0 <= 2400Resource B 15 30 0.0 <= 2400Resource C 15 5 0.0 <= 2400Resource D 15 5 0.0 <= 2400

Market P 1 0.0 <= 100Market Q 1 0.0 <= 50

45 60 -6000

Resource Product P Product Q Needed Available

Resource A 15 10 1800.0 <= 2400Resource B 15 30 2400.0 <= 2400

Resource C 15 5 1650.0 <= 2400Resource D 15 5 1650.0 <= 2400Market P 1 100.0 <= 100

Market Q 1 30.0 <= 50

45 60 300100.00 30

8Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

2. Exploit the Constraint : Find the Throughput World Best Solution Choose the optimal product mix of 100P,30Q. 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 and vice versa.

Do not miss even a single order of Product P

9Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

Step 3: Subordinate Everything Else to This Decision Minimize variability at Process A. Minimize variability in arrival of RM2

10Ardavan 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 Analysis

What is the value of the objective function? Z= 45(100) + 60(?)-6000!

Shadow prices?

2400(2)+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

2400(Shadow Price A)+

11Ardavan 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 Analysis

How 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

12Ardavan 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 Speaks Up : Another constraint in our company. It is the market.

A Great Market in Japan! Have to discount prices by 20%.

13Ardavan 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

321.8

1.33

14Ardavan 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?

Step 4

Perhaps not.

2

B

$6,400

15Ardavan 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

What 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.

16Ardavan 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.

A Production System Manufacturing Two Products, P and Q

Problem 8

Time available at each work center: 2,400 minutes per week.Operating expenses per week: $6,000. All the resources cost the same

17Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

Product A B C D Profit Margin DemandP 15 10 15 10 45 110Q 10 35 5 5 55 60

Capacity 2400 2400 2400 2400

Decision Variablesx1 : Volume of Product Px2 : Volume of Product Q Resource A15 x1 + 10 x2 2400

Resource B10 x1 + 35 x2 2400

Resource C15 x1 + 5 x2 2400

Resource D10 x1 + 5 x2 2400

Market for Px1 110

Market for Q x2 60

Objective Function Maximize Z = 45 x1 +55 x2 -6000

Nonnegativityx1 0, x2 0

Problem 8

18Ardavan Asef-Vaziri Nov-2010Theory of Constraints 1- Basics

Resource Product P Product Q Needed Available

Resource A 15 10 1900.0 <= 2400Resource B 10 35 2400.0 <= 2400

Resource C 15 5 1700.0 <= 2400Resource D 10 5 1200.0 <= 2400Market P 1 100.0 <= 100

Market Q 1 40.0 <= 50

45 55 700100.00 40

Problem 8