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Chapter 13

Chapter 13. Simulation – Part 2. Brew-Thru Example. Service entrance. Service lane. Exit. Car 3. Car 2. Car 1. Waiting area. Note: Customers balk if more than 4 cars in line. Monte Carlo Simulation. Set up probability distributions for the exogenous variables

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Chapter 13

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  1. Chapter 13 Simulation – Part 2

  2. Brew-Thru Example Service entrance Service lane Exit Car 3 Car 2 Car 1 Waiting area Note: Customers balk if more than 4 cars in line

  3. Monte Carlo Simulation • Set up probability distributions for the exogenous variables • Build cumulative probability distributions • Establish an interval of random numbers for each exogenous variable • Generate a set of random numbers • Simulate the situation for many trials

  4. Brew-Thru Example Number of customers arriving every 3 min. Probability 0 1 2 3 4 0.19 0.39 0.19 0.15 0.08 1.00

  5. Brew-Thru Example Average time to fill order Average profit Probability Order size Small Medium Large 0.39 0.50 0.11 1.00 3 min. 6 min. 9 min. $ .75 1.50 3.00

  6. Monte Carlo Simulation • Set up probability distributions for the exogenous variables • Build cumulative probability distributions • Establish an interval of random numbers for each exogenous variable • Generate a set of random numbers • Simulate the situation for many trials

  7. Brew-Thru Example # of customers arriving every 3 min. Cumulative Prob. Prob. Interval 0.19 0.39 0.19 0.15 0.08 1.00 0.19 0.58 0.77 0.92 1.00 0<RN<=0.19 0.19<RN<=0.58 0.58<RN<=0.77 0.77<RN<=0.92 0.92<RN<=1.00 0 1 2 3 4

  8. Brew-Thru Example Order size Cumulative probability Interval Prob. Small Medium Large 0.39 0.50 0.11 1.00 0.39 0.89 1.00 0<RN<=0.39 0.39<RN<=0.89 0.89<RN<=1.00

  9. Monte Carlo Simulation • Set up probability distributions for the exogenous variables • Build cumulative probability distributions • Establish an interval of random numbers for each exogenous variable • Generate a set of random numbers • Simulate the situation for many trials

  10. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN 1 2 3 4 5 6 7

  11. Brew-Thru Example Service completed? Profit Period 1 2 3 4 5 6 7 8

  12. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 1 2 3 4 5 6 7

  13. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 1 2 3 4 5 6 7

  14. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes 1 2 3 4 5 6 7

  15. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 1 2 3 4 5 6 7

  16. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 1 2 3 4 5 6 7

  17. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 2 3 4 5 6 7

  18. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7

  19. Brew-Thru Example Service completed? Profit Period No 1 2 3 4 5 6 7

  20. Brew-Thru Example Service completed? Profit Period No --- 1 2 3 4 5 6 7

  21. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 .32

  22. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 1 .32

  23. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 no 1 .32

  24. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 -- -- -- no 1 .32

  25. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 -- 0 -- -- no 1 .32

  26. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32

  27. Brew-Thru Example Service completed? Profit Period No --- 1 2 3 4 5 6 7 1.50 Yes(1)

  28. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 .15

  29. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 0 .15

  30. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 yes 0 .15

  31. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 .73 yes 0 .15

  32. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 .73 1 yes Small 0 .15

  33. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 .73 1 0 yes Small 0 .15

  34. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15

  35. Brew-Thru Example Service completed? Profit Period No --- 1 2 3 4 5 6 7 1.50 Yes(1) Yes(2) .75

  36. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 .95

  37. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 .95 4

  38. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 yes .95 4

  39. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 .50 yes .95 4

  40. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 .50 Med yes .95 4

  41. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 0 2 .50 Med yes .95 4

  42. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 4 0 2 .50 Med yes .95 4

  43. Brew-Thru Example Service completed? Profit Period No --- 1 2 3 4 5 6 7 1.50 Yes(1) Yes(2) .75 No

  44. Brew-Thru Example Service completed? Profit Period No --- 1 2 3 4 5 6 7 1.50 Yes(1) Yes(2) .75 --- No

  45. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 4 0 2 .50 Med yes .95 4 .68

  46. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 4 0 2 .50 Med yes .95 4 2 .68

  47. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 4 0 2 .50 Med yes .95 4 no 2 .68

  48. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 4 0 2 .50 Med yes .95 4 -- -- -- no 2 .68

  49. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 4 0 2 .50 Med yes .95 4 2 -- -- -- no 2 .68

  50. Brew-Thru Example # of Lost Cust. # of New Cust. Service avail? Order Size Service Periods Number waiting Period RN RN .63 2 yes .41 Med 2 0 1 1 2 3 4 5 6 7 2 -- 0 -- -- no 1 .32 1 .73 1 0 yes Small 0 .15 4 0 2 .50 Med yes .95 4 4 2 -- -- -- no 2 .68

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