Monte Carlo Simulation Homework Solutions - Summer 2014

Monte Carlo Simulation Homework Solutions - Summer 2014 -...

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Modern Operations Management Page 1 Monte Carlo Simulation Homework Solutions Monte Carlo Simulation Problem #1: Post Office Monte Carlo Table Time between arrivals Frequency Probability Cum. Probability Assigned RNs 1 8 .08 .08 0-7 2 35 .35 .43 8-42 3 34 .34 .77 43-76 4 17 .17 .94 77-93 5 06 .06 1 94-99 Monte Carlo Table Service Frequency Probability Cum. Probability Assigned RNs 1 12 .12 .12 0-11 1.5 21 .21 .33 12-32 2 36 .36 .69 33-68 2.5 19 .19 .88 69-87 3 7 .07 .95 88-94 3.5 5 .05 1 95-99 Simulation Analysis Cus. RN Inter. Arr. RN Service Arrival Time Service Begins Service Ends Cust. Wait Clerk Idle 1 08 2 31 1.5 0 0 1.5 0 1.5 2 74 3 32 1.5 3 3 4.5 0 0.5 3 24 2 45 2 5 5 7 0 0 4 34 2 21 1.5 7 7 8.5 0 1.5 5 45 3 10 1 10 10 11 0 3 6 86 4 67 2 14 14 16 0 0
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Modern Operations Management Page 2 How to calculate the clerk idle time. The first customer’s service ended at time 1.5. The next customer did not arrive until time 3, so the clerk was idle from time 1.5 to 3. The second customer’s service ended at time 4.5. The next customer arrived at time 5, so the clerk idle time is 0.5. Average customer wait time = 0 Average clerk idle time = 6.5/6 = 1.08 min Monte Carlo Simulation Problem #2: Student Cafeteria Swipe Cards Monte Carlo Table Inter-arrival Time (secs) Probability Cum Probability Assigned RNs 1 .25 .25 00-24 2 .50 .75 25-74 3 .25 1 75-99 Monte Carlo Table Service Time (secs) Probability Cum Probability Assigned RNs 1 .30 .3 00-29 2 .30 .6 30-59 3 .20 .8 60-79 4 .20 1 80-99 Student RN Inter. Arrival Time RN Service/ Swipe Time Arrival Time Time Service Begins Time Service Ends Wait Time 1 56 2 32 2 0 0 2 0 2 19 1 81 4 1 2 6 1 3 78 3 34 2 4 6 8 2 4 03 1 86 4 5 8 12 3 5 90 3 23 1 8 12 13 4 a. At what time does the third student arrive?
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Modern Operations Management Page 3 The 3 rd student arrives at time 4. b. How long is the 4 th student’s swipe time? The 4 th student’s swipe time is 4 seconds.
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