session 7b

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Session 7b. Example: Preventive Maintenance. At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is \$100, \$90, \$50, or \$10, respectively. - PowerPoint PPT Presentation

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Session 7bDecision Models -- Prof. Juran1Decision Models -- Prof. Juran2Example: Preventive MaintenanceAt the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad.

The weekly revenue earned by a machine in state 1, 2, 3, or 4 is \$100, \$90, \$50, or \$10, respectively.

After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of \$200, of instantaneously replacing the machine with an excellent machine. Decision Models -- Prof. Juran2Decision Models -- Prof. Juran3The quality of the machine deteriorates over time, as shown here.

Decision Models -- Prof. Juran3Decision Models -- Prof. Juran4Four maintenance policies are under consideration:Policy 1: Never replace a machine.Policy 2: Immediately replace a bad machine.Policy 3: Immediately replace a bad or average machine.Policy 4: Immediately replace a bad, average, or good machine

Simulate each of these policies for 50 weeks (using 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent. Well make use of the IF and RAND() functions Decision Models -- Prof. Juran4Decision Models -- Prof. Juran5

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Boole argued that logic was principally a discipline of mathematics, rather than philosophyDeveloped a way to encode logical arguments into a language that could be manipulated and solved mathematicallyA binary system, with basic operations AND, OR and NOT, that is one of the principles of modern computing Decision Models -- Prof. Juran9Decision Models -- Prof. Juran10

Not gatesCombining gates to compute 1 + 0 = 1Or gatesAnd gatesDecision Models -- Prof. Juran10Decision Models -- Prof. Juran11

Example of a Boolean operation:Decision Models -- Prof. Juran11Decision Models -- Prof. Juran12=((G5\$K\$19)*(2))

In English, this translates as 1 if G5 is less than K19 and 2 if G5 is not less than K19.

We can have this cell return a 1 or a 2, based on the probability that G5 is less than K19. Our model uses statements like this, where G5 is a uniform random variable between 0 and 1.Decision Models -- Prof. Juran12Decision Models -- Prof. Juran13Selecting cell G3, click on the define assumption button.This opens the distribution gallery. Select Uniform, and click OK.

Decision Models -- Prof. Juran13Decision Models -- Prof. Juran14We want a uniform distribution from 0 to 1, so type in these values for the two parameters, and then click OK.

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Decision Models -- Prof. Juran15Decision Models -- Prof. Juran16We could use the same procedure to define all of the other assumption cells, but that would be tedious. Luckily, Crystal Ball has copy and paste buttons:Select the assumption cell you want to copy (G3), and click the Crystal Ball copy button (not the regular Excel copy button). Then select the cells you want to define as assumptions (G4:G52), and click the Crystal Ball paste button. They will all turn green.

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Decision Models -- Prof. Juran17Decision Models -- Prof. Juran18In our case, we are interested in the long-run average profit of the machine over 50 weeks, which is cell K2. Select cell K2 and click on the Crystal Ball define forecast button:

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Make a spreadsheet for each replacement policy (contents of D6 shown).Decision Models -- Prof. Juran20Decision Models -- Prof. Juran21

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It looks like policies 2 and 3 are both reasonable, while policies 1 and 4 are clearly inferior.Decision Models -- Prof. Juran23Decision Models -- Prof. Juran24SummaryMonte Carlo SimulationBasic concepts and historyExcel TricksRAND(), IF, BooleanCrystal BallProbability Distributions Normal, Gamma, Uniform, TriangularAssumption and Forecast cellsRun PreferencesOutput AnalysisExamplesCoin Toss, TSB Account, Preventive Maintenance, NPV

Decision Models -- Prof. Juran24

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

A

B

C

D

E

F

G

H

Simulation of policy 1 (never replace)

Week

Beginning state

Revenue

Replace?

Cost

Profit

Random #

Ending State

1

1

100

0

0

100

0.678

1

2

1

100

0

0

100

0.852

2

3

2

80

0

0

80

0.469

2

4

2

80

0

0

80

0.156

2

5

2

80

0

0

80

0.936

3

6

3

50

0

0

50

0.689

4

7

4

10

0

0

10

0.989

4

8

4

10

0

0

10

0.549

4

9

4

10

0

0

10

0.867

4

10

4

10

0

0

10

0.403

4

11

4

10

0

0

10

0.648

4

12

4

10

0

0

10

0.449

4

13

4

10

0

0

10

0.699

4

14

4

10

0

0

10

0.163

4

=K14

=H3

=VLOOKUP(B4,\$J\$9:\$K\$12,2,0)

=D4*\$K\$5

=C4-E4

This will contain a different decision rule for each proposed replacement policy. Depending on the

state of the machine at the end of the previous week we will have a zero or a one, where a one

represents the decision to replace the machine. Here, we never replace, so it's always a zero.

=IF(B4=1,(((G4\$K\$19)*(2))),IF((B4=2),(((G4\$L\$20)*(3))),IF((B4=3),(((G4\$M\$21)*(4))),4)))

1

2

3

4

5

6

7

8

A

B

C

D

E

F

G

H

Simulation of policy 3 (replace bad and average machines)

Week

Beginning state

Revenue

Replace?

Cost

Profit

Random #

Ending State

1

1

100

0

0

100

0.816

2

2

2

80

0

0

80

0.384

2

3

2

80

0

0

80

0.703

3

4

1

100

1

200

-100

0.115

1

5

1

100

0

0

100

0.333

1

6

1

100

0

0

100

0.415

1

=(H5>2)*(1)+(H5