Session 7b

1. Session 7b

2. 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. 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. Juran

3. The quality of the machine deteriorates over time, as shown here. Decision Models -- Prof. Juran

4. Four 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. • We’ll make use of the IF and RAND() functions Decision Models -- Prof. Juran

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

10. “Not” gates “And” gates Combining gates to compute 1 + 0 = 1 “Or” gates Decision Models -- Prof. Juran

11. Example of a Boolean operation: Decision Models -- Prof. Juran

12. =((G5<$K$19)*(1))+((G5>$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. Juran

13. Selecting cell G3, click on the define assumption button. This opens the distribution gallery. Select Uniform, and click OK. Decision Models -- Prof. Juran

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

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16. We 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. Decision Models -- Prof. Juran

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18. In 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: Decision Models -- Prof. Juran

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

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24. It looks like policies 2 and 3 are both reasonable, while policies 1 and 4 are clearly inferior. Decision Models -- Prof. Juran

25. Summary • Monte Carlo Simulation • Basic concepts and history • Excel Tricks • RAND(), IF, Boolean • Crystal Ball • Probability Distributions • Normal, Gamma, Uniform, Triangular • Assumption and Forecast cells • Run Preferences • Output Analysis • Examples • Coin Toss, TSB Account, Preventive Maintenance, NPV Decision Models -- Prof. Juran