Chp. 2 simulation examples

Simulation Examples ,[object Object],[object Object],[object Object],[object Object],[object Object]

Simulation Table Repetitions Inputs Response y i x i1 x i2 .. x ij .. x ip 1 2 3 : n

Simulation of Queuing Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Simulation of Queuing Systems ,[object Object],[object Object],[object Object],[object Object],Departure event Another unit waiting? Begin Server idle time Remove waiting unit from queue Begin servicing the unit

Simulation of Queuing Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],Arrival event Server Busy? Unit enters service Unit enters queue for service

Simulation of Queuing Systems ,[object Object],[object Object],Queue status Not empty Empty Server status Busy Enter queue Enter queue Idle Impossible Enter service Queue status Not empty Empty Server outcomes Busy /////////////////// Impossible Idle Impossible ///////////////////

Simulation of Queuing Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Simulation of Queuing Systems ,[object Object],[object Object],[object Object],[object Object],[object Object]

Simulation of Queuing Systems ,[object Object],Customer Interarrival time Arrival time on clock 1 2 3 4 5 6 - 2 4 1 2 6 0 2 6 7 9 15

Simulation of Queuing Systems ,[object Object],Customer Service time 1 2 3 4 5 6 2 1 3 2 1 4

Simulation of Queuing Systems ,[object Object],A Customer Number B Arrival time (Clock) C Time Service Begins (Clock) D Service Time (Duration) E Time Service Ends (Clock) 1 2 3 4 5 6 0 2 6 7 9 15 0 2 6 9 11 15 2 1 3 2 1 4 2 3 9 11 12 19

Simulation of Queuing Systems ,[object Object],Event Type Customer number Clock Time Arrival Departure Arrival Departure Arrival Arrival Departure Arrival Departure Departure Arrival Departure 1 1 2 2 3 4 3 5 4 5 6 6 0 2 2 3 6 7 9 9 11 12 15 19

Simulation of Queuing Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1: Single-Channel Queue ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1: Single-Channel Queue ,[object Object],Time between Arrivals (minutes) Probability Cumulative Probability Random digit Assignment 1 2 3 4 5 6 7 8 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000 001 - 125 126 - 250 251 - 375 376 - 500 501 - 625 626 - 750 751 - 875 876 - 000

Example 1: Single-Channel Queue ,[object Object],Service Time (minutes) Probability Cumulative Probability Random digit Assignment 1 2 3 4 5 6 0.10 0.20 0.30 0.25 0.10 0.05 0.10 0.30 0.60 0.85 0.95 1.00 01 - 10 11 - 30 31 - 60 61 - 85 86 - 95 96 - 00

Example 1: Single-Channel Queue ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1: Single-Channel Queue ,[object Object],Customer Number Random Digits Time between Arrivals (Minutes) Customer Number Random Digits Time between Arrivals (Minutes) 1 2 3 4 5 6 7 8 9 10 - 064 112 678 289 871 583 139 423 039 - 1 1 6 3 7 5 2 4 1 11 12 13 14 15 16 17 18 : 100 413 462 843 738 359 888 902 212 : 538 4 4 7 6 3 8 8 2 : 5

Example 1: Single-Channel Queue ,[object Object],Customer Random Digits Service Time (Minutes) Customer Random Digits Service Time (Minutes) 1 2 3 4 5 6 7 8 9 10 84 18 87 81 06 91 79 09 64 38 4 2 5 4 1 5 4 1 4 3 11 12 13 14 15 16 17 18 : 100 94 32 79 92 46 21 73 55 : 26 5 3 4 5 3 2 4 3 : 2

Example 1: Single-Channel Queue ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1: Single-Channel Queue ,[object Object],Customer Interarrival time (minutes) Arrival Time Service Time (minutes) Time Service begins Waiting time in Queue Time Service ends Time Customer in system Idle Time of Server 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 : 100 Total - 1 1 6 3 7 5 2 4 1 4 4 7 6 3 8 8 2 7 4 : 5 415 0 1 2 8 11 18 23 25 29 30 34 38 45 51 54 62 70 72 79 83 : 415 4 2 5 4 1 5 4 1 4 3 5 3 4 5 3 2 4 3 1 2 : 2 317 0 4 6 11 15 18 23 27 29 33 36 41 45 51 56 62 70 74 79 83 : 416 0 3 4 3 4 0 0 2 0 3 2 3 0 0 2 0 0 2 0 0 : 1 174 4 6 11 15 16 23 27 28 33 36 41 44 49 56 59 64 74 77 80 85 : 418 4 5 9 7 5 5 4 3 4 6 7 6 4 5 5 2 4 5 1 2 : 3 491 - 0 0 0 0 2 0 0 1 0 0 0 1 2 0 3 6 0 2 3 : 0 101

Example 1: Single-Channel Queue ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1: Single-Channel Queue ,[object Object],[object Object],[object Object],[object Object]

Example 2: The Able-Baker Call Center Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 2: The Able-Baker Call Center Problem ,[object Object],Time between Arrivals (minutes) Probability Cumulative Probability Random digit Assignment 1 2 3 4 0.25 0.40 0.20 0.15 0.25 0.65 0.85 1.00 01 - 25 26 - 65 66 - 85 86 - 00

Example 2: The Able-Baker Call Center Problem ,[object Object],[object Object],Service Time (minutes) Probability Cumulative Probability Random digit Assignment 2 3 4 5 0.30 0.28 0.25 0.17 0.30 0.58 0.83 1.00 01 - 30 31 - 58 59 - 83 84 - 00 Service Time (minutes) Probability Cumulative Probability Random digit Assignment 3 4 5 6 0.35 0.25 0.20 0.20 0.35 0.60 0.80 1.00 01 - 35 36 - 60 61 - 80 81 - 00

Example 2: The Able-Baker Call Center Problem ,[object Object],[object Object],[object Object]

Example 2: The Able-Baker Call Center Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],Caller No. Interarrival time (minutes) Arrival Time (clock) When Able Avail (clock) When Baker Avail (clock) Server chosen Service Time (minutes) Time Service begins (clock) Able’s Svc Comp Time (clock) Baker’s Svc Comp time (clock) Caller delay (minutes) Time in Sys (minutes) 1 2 3 4 5 : 100 Total - 2 4 2 1 : 1 0 2 6 8 9 : 219 0 2 4 8 12 : 221 0 0 0 0 0 : 219 Able Able Able Able Baker : Baker 2 2 2 4 3 : 4 0 2 6 8 9 : 219 2 4 8 12 : 12 : 223 0 0 0 0 0 : 0 211 2 2 2 4 3 : 4 564

Simulation of Inventory Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Simulation of Inventory Systems ,[object Object],[object Object],[object Object],[object Object],[object Object]

Example 3: The News Dealer’s Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 3: The News Dealer’s Problem ,[object Object],Demand Demand Probability Distribution Good Fair Poor 40 50 60 70 80 90 100 0.03 0.05 0.15 0.20 0.35 0.15 0.07 0.10 0.18 0.40 0.20 0.08 0.04 0.00 0.44 0.22 0.16 0.12 0.06 0.00 0.00

Example 3: The News Dealer’s Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 3: The News Dealer’s Problem ,[object Object],Type of Newsday Probability Cumulative Probability Random digit Assignment Good Fair Poor 0.35 0.45 0.20 0.35 0.80 1.00 01 - 35 36 - 80 81 - 00

Example 3: The News Dealer’s Problem ,[object Object],Demand Cumulative Distribution Random Digit Assignments Good Fair Poor Good Fair Poor 40 50 60 70 80 90 100 0.03 0.08 0.23 0.43 0.78 0.93 1.00 0.10 0.28 0.68 0.88 0.96 1.00 1.00 0.44 0.66 0.82 0.94 1.00 1.00 1.00 01 - 03 04 - 08 09 - 23 24 - 43 44 - 78 79 - 93 94 - 00 01 - 10 11 - 28 29 - 68 69 - 88 89- 96 97 - 00 01 - 44 45 - 66 67 - 82 83 - 94 95 - 00

Example 3: The News Dealer’s Problem ,[object Object],Day Random Digits for Type of Newsday Type of Newsday Random digits for Demand Demand Revenue from Sales (Rupees) Lost Profit from Excess Demand Salvage from Sale of Scrap Daily profit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 58 17 21 45 43 36 27 73 86 19 93 45 47 30 12 41 65 57 18 98 Fair Good Good Fair Fair Fair Good Fair Poor Good Poor Fair Fair Good Good Fair Fair Fair Good Poor 93 63 31 19 91 75 84 37 23 02 53 96 33 86 16 07 64 94 55 13 80 80 70 50 80 70 90 60 40 40 50 80 60 90 60 40 60 80 80 40 35 35 35 25 35 35 35 30 20 20 25 35 30 35 30 20 30 35 35 20 600 1.70 1.70 - - 1.70 - 3.40 - - - - 1.70 - 3.40 - - - 1.70 1.70 - 17.00 - - - 1.00 - - - 0.50 1.50 1.50 1.00 - 0.50 - 0.50 1.50 0.50 - - 1.50 10.00 10.20 10.20 11.90 2.90 10.20 11.90 8.50 7.40 -1.60 -1.60 3.90 10.20 7.40 8.50 7.40 -1.60 7.40 10.20 10.20 -1.60 131.00

Example 3: The News Dealer’s Problem ,[object Object],[object Object],[object Object],[object Object]

Example 4: Order-Up-To-Level Inventory System ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 4: Order-Up-To-Level Inventory System ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 4: Order-Up-To-Level Inventory System ,[object Object],[object Object],[object Object],[object Object],[object Object]

Example 4: Order-Up-To-Level Inventory System ,[object Object],[object Object],Demand Probability Cumulative Probability Random digit Assignment 0 1 2 3 4 0.10 0.25 0.35 0.21 0.09 0.10 0.35 0.70 0.91 1.00 01 - 10 11 - 35 36 - 70 71 - 91 92 - 00

Example 4: Order-Up-To-Level Inventory System ,[object Object],Lead Time (Days) Probability Cumulative Probability Random digit Assignment 1 2 3 0.6 0.3 0.1 0.6 0.9 1.0 1 - 6 7 - 9 0

[object Object],Day Cycle Day within Cycle Beginning Inventory Random Digits for Demand Demand Ending Inventory Shortage Quantity Order Quantity Random Digits for Demand Lead Time (days) Days until Order Arrives 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Total 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 3 2 8 7 5 2 1 9 5 3 0 0 11 6 3 2 11 7 5 2 0 12 8 4 3 26 68 33 39 86 18 64 79 55 74 21 43 49 90 35 08 98 61 85 81 53 15 94 19 44 1 2 1 2 3 1 2 3 2 3 1 2 2 3 1 0 4 2 3 3 2 1 4 1 2 2 0 7 5 2 1 0 5 3 0 0 0 6 3 2 2 7 5 2 0 0 8 4 3 1 68 0 0 0 0 0 0 1 0 0 0 1 3 0 0 0 0 0 0 0 1 3 0 0 0 0 9 - - - - 9 - - - - 11 - - - - 9 - - - - 12 - - - - 10 - - - - 8 - - - - 7 - - - - 2 - - - - 3 - - - - 1 - - - - 2 - - - - 2 - - - - 1 - - - - 1 - - - - 1 1 - - - 2 1 - - - 2 1 - - - 1 - - - - 1 - - - - 1

Example 5: A Reliability Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 5: A Reliability Problem ,[object Object],Bearing Life (Hours) Probability Cumulative Probability Random digit Assignment 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 0.10 0.13 0.25 0.13 0.09 0.12 0.02 0.06 0.05 0.05 0.10 0.23 0.48 0.61 0.70 0.82 0.84 0.90 0.95 1.00 01 - 10 11 - 23 24 - 48 49 - 61 62 - 70 71 - 82 83 - 84 85 - 90 91 - 95 96 - 00

Example 5: A Reliability Problem ,[object Object],Delay Time (Minutes) Probability Cumulative Probability Random digit Assignment 5 10 15 0.6 0.3 0.1 0.6 0.9 1.0 1 - 6 7 - 9 0

Example 5: A Reliability Problem ,[object Object],Bearing 1 Bearing 2 Bearing 3 Random Digits Life (Hours) Random Digits Delay (Mins) Random Digits Life (Hours) Random Digits Delay (Mins) Random Digits Life (Hours) Random Digits Delay (Mins) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 67 55 98 76 53 69 80 93 35 02 99 65 53 87 90 1400 1300 1900 1500 1300 1400 1500 1800 1200 1000 1900 1400 1300 1700 1700 22300 7 3 1 6 4 8 5 7 0 5 9 4 7 1 2 10 5 5 5 5 10 5 10 15 5 10 5 10 5 5 110 71 21 79 88 93 77 08 21 13 03 14 5 29 07 20 1500 1100 1500 1700 1800 1500 1000 1100 1100 1100 1000 1000 1200 1000 1100 18700 8 3 3 1 0 6 9 8 3 2 1 0 2 4 3 10 5 5 5 15 5 10 10 5 5 5 15 5 5 5 110 18 17 65 03 54 17 19 09 61 84 11 25 86 65 44 1100 1100 1400 1000 1300 1100 1100 1000 1300 1600 1100 1200 1700 1400 1200 18600 6 2 2 9 8 3 6 7 1 0 5 2 8 3 4 5 5 5 10 10 5 5 10 5 15 5 5 10 5 5 105

Example 5: A Reliability Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 5: A Reliability Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 5: A Reliability Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 6: Random Normal Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 6: Random Normal Numbers ,[object Object],Bomb RNN X X Coordinate ( 400 RNN X ) RNN Y Y Coordinate ( 200 RNN Y ) Results 1 2 3 4 5 6 7 8 9 10 2.2296 -2.0035 -3.1432 -0.7968 1.0741 0.1265 0.0611 1.2182 -0.8026 0.7324 891.8 -801.4 -1257.3 -318.7 429.6 50.6 24.5 487.3 -321.0 293.0 -0.1932 1.3034 0.3286 -1.1417 0.7612 -0.3098 -1.1066 0.2487 -1.0098 0.2552 -38.6 260.7 65.7 -228.3 152.2 -62.0 -221.3 49.7 -202.0 -51.0 Miss Miss Miss Miss Hit Hit Hit Hit Miss Hit

Example 7: Lead-Time Demand ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 7: Lead-Time Demand ,[object Object],[object Object],[object Object],[object Object],[object Object],Daily Demand (Rolls) 3 4 5 6 Probability 0.20 0.35 0.30 0.15 Lead Time (Days) 1 2 3 Probability 0.36 0.42 0.22

Example 7: Lead-Time Demand ,[object Object],[object Object],Demand Probability Cumulative Probability Random digit Assignment 3 4 5 6 0.20 0.35 0.30 0.15 0.20 0.55 0.85 1.00 01 - 20 21 - 55 36 - 85 86 - 00

Example 7: Lead-Time Demand ,[object Object],Lead Time (Days) Probability Cumulative Probability Random digit Assignment 1 2 3 0.36 0.42 0.22 0.36 0.78 1.00 01 - 36 37 - 78 79 - 00

Example 7: Lead-Time Demand ,[object Object],[object Object],Cycle Random Digits for Lead Time Lead Time (Days) Random Digits for Demand Demand Lead-Time Demand 1 2 3 4 : : 57 33 46 91 2 1 2 3 : : 11 64 37 13 80 27 66 47 : : 3 5 4 3 5 4 5 4 : : 8 4 8 13 : :

Example 8: Project Simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 8: Project Simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],C Start A B Finish

Example 8: Project Simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 8: Project Simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 8: Project Simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Chp. 2 simulation examples

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Chp. 2 simulation examples