Simulation Supplement B

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Simulation Supplement B To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Average weekly production requirements = Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Average weekly production requirements = 200(0.05) Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Average weekly production requirements = 200(0.05) + 250(0.06) Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Average weekly production requirements = 200(0.05) + 250(0.06) + 300(0.17) + … + 600(0.02) = 400 hours Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Average weekly production requirements = 400 hours Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly production requirements = 400 hours Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 320(0.30) Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 320(0.30) + 360(0.40) + Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (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 B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (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 B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly production requirements = 400 hours Average weekly operating machine hours = 360 hours Example B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Weekly Production Relative Requirements (hr) Frequency 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Total 1.00 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Example B.1 Average weekly production requirements = 400 hours Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Event Weekly Regular Relative TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Demand (hr) Probability Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 Average weekly production requirements = 400 hours To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Event Weekly Regular Relative TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Demand (hr) Probability 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 Average weekly production requirements = 400 hours To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Event Weekly Random Weekly Random Regular Relative TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Random Weekly Random Demand (hr) Probability Numbers Capacity (hr) Probability Numbers 200 0.05 250 0.06 300 0.17 350 0.05 400 0.30 450 0.15 500 0.06 550 0.14 600 0.02 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 Average weekly production requirements = 400 hours To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Event Weekly Random Weekly Random Regular Relative TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Random Weekly Random Demand (hr) Probability Numbers Capacity (hr) Probability Numbers 200 0.05 00–04 250 0.06 05–10 300 0.17 11–27 350 0.05 28–32 400 0.30 33–62 450 0.15 63–77 500 0.06 78–83 550 0.14 84–97 600 0.02 98–99 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 Average weekly production requirements = 400 hours To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process Event Weekly Random Weekly Random Regular Relative TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Random Weekly Random Demand (hr) Probability Numbers Capacity (hr) Probability Numbers 200 0.05 00–04 320 0.30 00–29 250 0.06 05–10 360 0.40 30–69 300 0.17 11–27 400 0.30 70–99 350 0.05 28–32 400 0.30 33–62 450 0.15 63–77 500 0.06 78–83 550 0.14 84–97 600 0.02 98–99 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 Average weekly production requirements = 400 hours To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process 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 – 100. 9. Repeat steps 1–8 to simulate 20 weeks. TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Random Weekly Random Demand (hr) Probability Numbers Capacity (hr) Probability Numbers 200 0.05 00–04 320 0.30 00–29 250 0.06 05–10 360 0.40 30–69 300 0.17 11–27 400 0.30 70–99 350 0.05 28–32 400 0.30 33–62 450 0.15 63–77 500 0.06 78–83 550 0.14 84–97 600 0.02 98–99 Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 Average weekly production requirements = 400 hours To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process 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 – 100. 9. Repeat steps 1–8 to simulate 20 weeks. TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Random Weekly Random Demand (hr) Probability Numbers Capacity (hr) Probability Numbers 200 0.05 00–04 320 0.30 00–29 250 0.06 05–10 360 0.40 30–69 300 0.17 11–27 400 0.30 70–99 350 0.05 28–32 400 0.30 33–62 450 0.15 63–77 500 0.06 78–83 550 0.14 84–97 600 0.02 98–99 10 Machines Existing Demand Weekly Capacity Weekly Sub- Random Production Random Capacity Idle Overtime contract Week Number (hr) Number (hr) Hours Hours Hours TABLE B.2 20-WEEK SIMULATIONS OF ALTERNATIVES Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 1 71 450 50 360 90 2 68 450 54 360 90 3 48 400 11 320 80 4 99 600 36 360 100 140 5 64 450 82 400 50 6 13 300 87 400 100 7 36 400 41 360 40 8 58 400 71 400 9 13 300 00 320 20 10 93 550 60 360 100 90 Total 490 830 360 Weekly average 24.5 41.5 18.0 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Simulation Process 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 – 100. 9. Repeat steps 1–8 to simulate 20 weeks. TABLE B.1 RANDOM-NUMBER ASSIGNMENTS TO SIMULATION EVENTS Event Weekly Random Weekly Random Demand (hr) Probability Numbers Capacity (hr) Probability Numbers 200 0.05 00–04 320 0.30 00–29 250 0.06 05–10 360 0.40 30–69 300 0.17 11–27 400 0.30 70–99 350 0.05 28–32 400 0.30 33–62 450 0.15 63–77 500 0.06 78–83 550 0.14 84–97 600 0.02 98–99 10 Machines Existing Demand Weekly Capacity Weekly Sub- Random Production Random Capacity Idle Overtime contract Week Number (hr) Number (hr) Hours Hours Hours TABLE B.2 20-WEEK SIMULATIONS OF ALTERNATIVES Regular Relative Capacity (hr) Frequency 320 (8 machines) 0.30 360 (9 machines) 0.40 400 (10 machines) 0.30 Average weekly operating machine hours = 360 hours 360 (9 machines) 0.30 400 (10 machines) 0.40 440 (11 machines) 0.30 1 71 450 50 360 90 2 68 450 54 360 90 3 48 400 11 320 80 4 99 600 36 360 100 140 5 64 450 82 400 50 6 13 300 87 400 100 7 36 400 41 360 40 8 58 400 71 400 9 13 300 00 320 20 10 93 550 60 360 100 90 Total 490 830 360 Weekly average 24.5 41.5 18.0 Comparison of 1000-week Simulations 10 Machines 11 Machines Idle hours 26.0 42.2 Overtime hours 48.3 34.2 Subcontract hours 18.4 8.7 Cost $1,851.50 $1,159.50 TABLE B.2 COMPARISON OF 1,000 WEEK SIMULATIONS To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Random Numbers Figure B.1 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Best Car Simulation Model Example B.3 Figure B.2 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Inventory Simulation Model Figure B.3 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.