To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Supplement D - Simulation

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Average weekly production requirements = Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Average weekly production requirements = 200(0.05) Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Average weekly production requirements = 200(0.05) + 250(0.06) Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Average weekly production requirements = 200(0.05) + 250(0.06) + 300(0.17) + … + 600(0.02) = 400 hours Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 Average weekly production requirements = 400 hours Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly production requirements = 400 hours Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 320(0.30) Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 320(0.30) + 360(0.40) + Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 320(0.30) + 360(0.40) + 400(0.30) Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 320(0.30) + 360(0.40) + 400(0.30) = 360 hours Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 360 hours Example D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Weekly ProductionRelative Requirements (hr)Frequency Total1.00 RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Example D.1 Average weekly production requirements = 400 hours Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly Demand (hr)Probability

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly Demand (hr)Probability

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers – – – – – – – – –99

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers – – – – – – – – –99

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers – – – – – – – – – – – –99

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers – – – – – – – – – – – –99 Simulation Process

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.1 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers – – – – – – – – – – – –99 Simulation Process 1.Draw a random number. 2.Find the random number interval for production. 3.Record the production hours. 4.Draw another random number. 5.Find the random number interval for capacity. 6.Record the capacity hours. 7.If CAP ≥ PROD, then IDLE HR = CAP – PROD. 8.If CAP < PROD, then SHORT = PROD – CAP. If SHORT ≤ 100, then OVERTIME HR = SHORT and SUBCONTRACT HR = 0. If SHORT > 100, then OVERTIME HR = 100 and SUBCONTRACT HR = SHORT – Repeat steps 1–8 to simulate 20 weeks.

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.2 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers Simulation Process 1.Draw a random number. 2.Find the random number interval for production. 3.Record the production hours. 4.Draw another random number. 5.Find the random number interval for capacity. 6.Record the capacity hours. 7.If CAP ≥ PROD, then IDLE HR = CAP - PROD. 8.If CAP < PROD, then SHORT = PROD - CAP. If SHORT ≤ 100, then OVERTIME HR = SHORT and SUBCONTRACT HR = 0. If SHORT > 100, then OVERTIME HR = 100 and SUBCONTRACT HR = SHORT Repeat steps 1-8 to simulate 20 weeks. 10 Machines Existing DemandWeeklyCapacityWeeklySub- RandomProductionRandomCapacityIdleOvertimecontract WeekNumber(hr)Number(hr)HoursHoursHours

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.2 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers Simulation Process 1.Draw a random number. 2.Find the random number interval for production. 3.Record the production hours. 4.Draw another random number. 5.Find the random number interval for capacity. 6.Record the capacity hours. 7.If CAP ≥ PROD, then IDLE HR = CAP - PROD. 8.If CAP < PROD, then SHORT = PROD - CAP. If SHORT ≤ 100, then OVERTIME HR = SHORT and SUBCONTRACT HR = 0. If SHORT > 100, then OVERTIME HR = 100 and SUBCONTRACT HR = SHORT Repeat steps 1-8 to simulate 20 weeks. 10 Machines Existing DemandWeeklyCapacityWeeklySub- RandomProductionRandomCapacityIdleOvertimecontract WeekNumber(hr)Number(hr)HoursHoursHours Total Weekly average

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.2 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers Simulation Process 1.Draw a random number. 2.Find the random number interval for production. 3.Record the production hours. 4.Draw another random number. 5.Find the random number interval for capacity. 6.Record the capacity hours. 7.If CAP ≥ PROD, then IDLE HR = CAP - PROD. 8.If CAP < PROD, then SHORT = PROD - CAP. If SHORT ≤ 100, then OVERTIME HR = SHORT and SUBCONTRACT HR = 0. If SHORT > 100, then OVERTIME HR = 100 and SUBCONTRACT HR = SHORT Repeat steps 1-8 to simulate 20 weeks. 10 Machines Existing DemandWeeklyCapacityWeeklySub- RandomProductionRandomCapacityIdleOvertimecontract WeekNumber(hr)Number(hr)HoursHoursHours Total Weekly average Comparison of 1000-week Simulations 10 Machines11 Machines

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Average weekly production requirements = 400 hours RegularRelative Capacity (hr)Frequency 320 (8 machines) (9 machines) (10 machines)0.30 Average weekly operating machine hours = 360 hours RegularRelative Capacity (hr)Frequency 360 (9 machines) (10 machines) (11 machines)0.30 Table D.2 Simulation Process Event Weekly RandomWeeklyRandom Demand (hr)ProbabilityNumbersCapacity (hr)ProbabilityNumbers Simulation Process 1.Draw a random number. 2.Find the random number interval for production. 3.Record the production hours. 4.Draw another random number. 5.Find the random number interval for capacity. 6.Record the capacity hours. 7.If CAP ≥ PROD, then IDLE HR = CAP - PROD. 8.If CAP < PROD, then SHORT = PROD - CAP. If SHORT ≤ 100, then OVERTIME HR = SHORT and SUBCONTRACT HR = 0. If SHORT > 100, then OVERTIME HR = 100 and SUBCONTRACT HR = SHORT Repeat steps 1-8 to simulate 20 weeks. 10 Machines Existing DemandWeeklyCapacityWeeklySub- RandomProductionRandomCapacityIdleOvertimecontract WeekNumber(hr)Number(hr)HoursHoursHours Total Weekly average Comparison of 1000-week Simulations 10 Machines11 Machines Idle hours Overtime hours Subcontract hours Cost$1,851.50$1,159.50

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Example D.3

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process X X X X X X X Gate house Not to scale Checkpoint #1 Checkpoint #3 (rarely used) Checkpoint #2 Figure D.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process X X X X X X X Gate house Not to scale Checkpoint #1 Checkpoint #3 (rarely used) Checkpoint #2 Figure D.2 12 – 10 – 8 – 6 – 4 – 2 – 0 – |||||| 7:007:107:207:307:407:508:00 Time Arrivals (vehicles/min) STANDARD VEHICLEAVERAGEDEVIATION Cars10 3 Vanpools30 9 Buses5010 INSPECTION TIME (sec)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process Figure D.3(a)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process X X X X X X X Gate house Not to scale Checkpoint #1 Checkpoint #3 (rarely used) Checkpoint #2 12 – 10 – 8 – 6 – 4 – 2 – 0 – |||||| 7:007:107:207:307:407:508:00 Time Arrivals (vehicles/min) STANDARD VEHICLEAVERAGEDEVIATION Cars103 Vanpools309 Buses5010 INSPECTION TIME (sec) Figure D.3(b)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Simulation Process X X X X X X X Gate house Not to scale Checkpoint #1 Checkpoint #3 (rarely used) Checkpoint #2 12 – 10 – 8 – 6 – 4 – 2 – 0 – |||||| 7:007:107:207:307:407:508:00 Time Arrivals (vehicles/min) STANDARD VEHICLEAVERAGEDEVIATION Cars103 Vanpools309 Buses5010 INSPECTION TIME (sec) Figure D.3(c)