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Session 7b

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Decision Models -- Prof. Juran2 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.

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Decision Models -- Prof. Juran3 The quality of the machine deteriorates over time, as shown here.

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Decision Models -- Prof. Juran4 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

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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

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Decision Models -- Prof. Juran10 “Not” gates Combining gates to compute 1 + 0 = 1 “Or” gates “And” gates

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Decision Models -- Prof. Juran11 Example of a Boolean operation:

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Decision 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.

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Decision Models -- Prof. Juran13 Selecting cell G3, click on the define assumption button. This opens the distribution gallery. Select Uniform, and click OK.

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Decision Models -- Prof. Juran14 We 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. Juran16 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.

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Decision Models -- Prof. Juran18 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:

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Decision Models -- Prof. Juran20 Make a spreadsheet for each replacement policy (contents of D6 shown).

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Decision Models -- Prof. Juran23 It looks like policies 2 and 3 are both reasonable, while policies 1 and 4 are clearly inferior.

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Decision Models -- Prof. Juran24 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

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