Supplement
E Simulation
PROBLEMS
The Monte Carlo Simulation Process
1. Comet Dry Cleaners
a. NGNC = Number of garments needing cleaning
MNGD = Maximum number of garments that could be dry cleaned
Queue at Actual Queue at
New Start Garments End
Day RN Garments of Day NGNC RN MNGD Cleaned of Day
1 49 70 0 70 77 80 70 0
2 27 60 0 60 53 70 60 0
3 65 80 0 80 08 60 60 20
4 83 80 20 100 12 60 60 40
5 04 50 40 90 82 80 80 10
6 58 70 10 80 44 70 70 10
7 53 70 10 80 83 80 80 0
8 57 70 0 70 72 80 70 0
9 32 60 0 60 53 70 60 0
10 60 70 0 70 79 80 70 0
11 79 80 0 80 30 70 70 10
12 41 70 10 80 48 70 70 10
13 97 90 10 100 86 80 80 20
14 30 60 20 80 25 60 60 20
15 80 80 20 100 73 80 80 20
Total 160
The average daily number of garments held overnight is 160/15 = 10.67
garments.
b. The expansion reduces the number of garments held overnight from 20 to 10.67
(calculated as 160/15), saving $233.25 [$25(9.33)] per day. The saving exceeds
the $200 expansion cost, making expansion a good idea.
2. Precision Manufacturing Company. The following Table A simulates the arrival of
10 batches over a 60-minute horizon. With a different choice of random numbers,
the results will vary. Random numbers from the first row of the random number
table at the end of the supplement were used, 2-digits at a time, with the probability
distribution to simulate the number of units in each batch. Random numbers from
the second and third rows were similarly used to establish setup times and
processing times, respectively. Resulting assignments for setup and processing
times for each machine are also shown.
E-1
Copyright © 2016 Pearson Education, Inc.
, E-2 l SUPPLEMENT E l Simulation
Table B determines the work requirements of each machine, based on the job
arrivals and times selected in Table A. The totals are very similar, with NC
machine 1 being slightly more productive. The totals of 2,646 seconds and
2,680 seconds are considerably less than the capacity of 3,600 seconds for the
60-minute horizon. Capacity is more than sufficient for either machine.
Table A Job arrivals, setup times, and processing times
Setup Times Processing Times
(min) (sec)
Number Machine Machine Machine Machine
Batch RN of Units RN 1 2 RN 1 2
1 71 14 21 2 3 50 7 5
2 50 8 94 5 5 63 8 5
3 96 18 93 5 5 95 9 7
4 83 18 09 1 2 49 7 5
5 10 6 20 2 3 68 8 5
6 48 8 23 2 3 11 6 3
7 21 6 28 2 3 40 7 4
8 39 8 78 4 4 93 9 7
9 99 18 95 5 5 61 8 5
10 28 6 14 2 2 48 7 5
Table B Work Requirements
Machine 1 Requirements (sec) Machine 2 Requirements (sec)
Batch Setup Processing Total Setup Processing Total
1 120 98 218 180 70 250
2 300 64 364 300 40 340
3 300 162 462 300 126 426
4 60 126 186 120 90 210
5 120 48 168 180 30 210
6 120 48 168 180 24 204
7 120 42 162 180 24 204
8 240 72 312 240 56 296
9 300 144 444 300 90 390
10 120 42 162 120 30 150
Totals 2646 2680
The small sample size of just 10 batches may cause us some estimation errors.
Another approach is to work with the expected values of the five probability
distributions. They can be computed as:
Number of jobs = 10.3 units every 6 minutes
Machine 1 setup = 3.0 minutes/batch
Machine 2 setup = 3.4 minutes/batch
Machine 1 processing = 7.15 seconds/job
Machine 2 processing = 4.70 seconds/job
Using these expected values to estimate the work requirements for each
machine for a 60-minute horizon, we get
Machine 1: 10[3.0 min(60 sec/min) + 10.3 units(7.15 sec/job)] = 2,536 seconds
Machine 2: 10[3.4 min(60 sec/min) + 10.3 units(4.70 sec/job)] = 2,524 seconds
Copyright © 2016 Pearson Education, Inc.
E Simulation
PROBLEMS
The Monte Carlo Simulation Process
1. Comet Dry Cleaners
a. NGNC = Number of garments needing cleaning
MNGD = Maximum number of garments that could be dry cleaned
Queue at Actual Queue at
New Start Garments End
Day RN Garments of Day NGNC RN MNGD Cleaned of Day
1 49 70 0 70 77 80 70 0
2 27 60 0 60 53 70 60 0
3 65 80 0 80 08 60 60 20
4 83 80 20 100 12 60 60 40
5 04 50 40 90 82 80 80 10
6 58 70 10 80 44 70 70 10
7 53 70 10 80 83 80 80 0
8 57 70 0 70 72 80 70 0
9 32 60 0 60 53 70 60 0
10 60 70 0 70 79 80 70 0
11 79 80 0 80 30 70 70 10
12 41 70 10 80 48 70 70 10
13 97 90 10 100 86 80 80 20
14 30 60 20 80 25 60 60 20
15 80 80 20 100 73 80 80 20
Total 160
The average daily number of garments held overnight is 160/15 = 10.67
garments.
b. The expansion reduces the number of garments held overnight from 20 to 10.67
(calculated as 160/15), saving $233.25 [$25(9.33)] per day. The saving exceeds
the $200 expansion cost, making expansion a good idea.
2. Precision Manufacturing Company. The following Table A simulates the arrival of
10 batches over a 60-minute horizon. With a different choice of random numbers,
the results will vary. Random numbers from the first row of the random number
table at the end of the supplement were used, 2-digits at a time, with the probability
distribution to simulate the number of units in each batch. Random numbers from
the second and third rows were similarly used to establish setup times and
processing times, respectively. Resulting assignments for setup and processing
times for each machine are also shown.
E-1
Copyright © 2016 Pearson Education, Inc.
, E-2 l SUPPLEMENT E l Simulation
Table B determines the work requirements of each machine, based on the job
arrivals and times selected in Table A. The totals are very similar, with NC
machine 1 being slightly more productive. The totals of 2,646 seconds and
2,680 seconds are considerably less than the capacity of 3,600 seconds for the
60-minute horizon. Capacity is more than sufficient for either machine.
Table A Job arrivals, setup times, and processing times
Setup Times Processing Times
(min) (sec)
Number Machine Machine Machine Machine
Batch RN of Units RN 1 2 RN 1 2
1 71 14 21 2 3 50 7 5
2 50 8 94 5 5 63 8 5
3 96 18 93 5 5 95 9 7
4 83 18 09 1 2 49 7 5
5 10 6 20 2 3 68 8 5
6 48 8 23 2 3 11 6 3
7 21 6 28 2 3 40 7 4
8 39 8 78 4 4 93 9 7
9 99 18 95 5 5 61 8 5
10 28 6 14 2 2 48 7 5
Table B Work Requirements
Machine 1 Requirements (sec) Machine 2 Requirements (sec)
Batch Setup Processing Total Setup Processing Total
1 120 98 218 180 70 250
2 300 64 364 300 40 340
3 300 162 462 300 126 426
4 60 126 186 120 90 210
5 120 48 168 180 30 210
6 120 48 168 180 24 204
7 120 42 162 180 24 204
8 240 72 312 240 56 296
9 300 144 444 300 90 390
10 120 42 162 120 30 150
Totals 2646 2680
The small sample size of just 10 batches may cause us some estimation errors.
Another approach is to work with the expected values of the five probability
distributions. They can be computed as:
Number of jobs = 10.3 units every 6 minutes
Machine 1 setup = 3.0 minutes/batch
Machine 2 setup = 3.4 minutes/batch
Machine 1 processing = 7.15 seconds/job
Machine 2 processing = 4.70 seconds/job
Using these expected values to estimate the work requirements for each
machine for a 60-minute horizon, we get
Machine 1: 10[3.0 min(60 sec/min) + 10.3 units(7.15 sec/job)] = 2,536 seconds
Machine 2: 10[3.4 min(60 sec/min) + 10.3 units(4.70 sec/job)] = 2,524 seconds
Copyright © 2016 Pearson Education, Inc.
