Supplement B Part 2 Designing and Managing Processes SIMULATION MODELS PROBLEMS 1. 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 in Appendix 2 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. 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 (min) Processing Times (sec) Batch Number of Units Machine 1 Machine 2 Machine 1 Machine 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 24 204 116
Simulation SUPPLEMENT B 117 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 These numbers suggest that a much longer simulation would show that machine 2 is the slightly better choice. Its shorter processing times more than compensate for the longer setup times, given the sizes of batches that arrive. Smaller batches favor machine 1. 2. Because either machine has plenty of capacity, and continuing to assume equal operation and maintenance costs, we should purchase the lower price machine. In other words, the decision should not favor the machine with higher capacity. Capacity in excess of that needed has no value. Greater capacity merely results in more idle time. 3. Comet Dry Cleaners a. NGNC = Number of garments needing cleaning MNGD = Maximum number of garments that could be dry cleaned Queue at Start of Day NGNC MNGD Actual Garments Cleaned Queue at End of Day Day New Garments 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
118 PART 2 Managing Processes 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. 4. Omega University a. Preliminary estimates or utilization and proportion of unanswered calls: arrival rate: 90 calls per hour 60% forwarded to office = 54 calls/hour answering service rate: 60 minutes/hour/1 minute/call = 60 calls per hour estimated utilization = 54/60 = 90% Of 90 calls, we would expect 36 (or 40% 90) to be answered by the professors. 54 would be forwarded, and because the clerk has some idle time, we might expect the lion s share of those calls to be answered as well. Surely only a few calls would go unanswered. b. Simulation. See table showing the simulation. The first three random numbers in the first row of the table are from the first two digits in the second column of Appendix 2, moving from top to bottom. The simulation shows that during the 60 minutes, 82 calls were placed. Of those, 68 were answered. Even though this simulation is for an hour when fewer than the expected average of 90 calls were received, 14 calls or 14/82 = 17% went unanswered by anyone. c. Professors answered 34 calls (41%) and 48 (59%) were forwarded to the department office. Of the 48 forwarded calls, only 34 calls (or 71%) were answered by the assistant. The assistant was idle 26 of 60 minutes. Utilization was only 34/60 = 57%, not the estimated 90%. The simulation shows that even though the assistant has lots of idle time, calls were being missed because they do not arrive at a steady pace. 5. Voice mailboxes. The office assistant is currently spending 57% of his time answering the telephone. See table showing the simulation. Assuming that time saved could be productively used elsewhere, Labor savings = $3,000/month 57% 60% = $1026/month. Voice mail cost = $25/month 32 telephones = $800/month. Yes, order voice-mail system. 6. Brakes-Only Service Shop a. # of Brake Jobs Relative Frequency Random Numbers 10 0.1 00 09 11 0.3 10 39
Simulation SUPPLEMENT B 119 12 0.3 40 69 13 0.2 70 89 14 0.1 90 99 b. 28 83 73 7 4 63 37 38 50 92 Demand 11 13 13 10 10 12 11 11 12 14 c. On 3 days, overtime will be necessary. On 5 days, mechanics will be underutilized. d. 3/10 = 30% of the days. 7. E-Z Mart a. Random Number Sales 00 09 60 10 23 61 24 57 62 58 79 63 80 91 64 92 99 65 b. Trial R.N. Demand Shortage Excess 1 97 65 3 2 02 60 2 3 80 64 2 4 66 63 1 5 99 65 3 6 56 62 0 0 7 54 62 0 0 8 28 62 0 0 9 64 63 1 10 47 62 0 0 Total 10 2 c. Average shortage = 10/10 = 1 jug Average excess = 2/10 = 0.2 jugs 8. BestCar with price variability. Now there are two uncontrollable variables: weekly demand and sales price. The spreadsheet shown below results in an average of 2.73 cars sold per week (compare with the 2.88 car average in Figure B.2 when only 50 weeks were simulated). The average revenue is $57,516 per week.
120 PART 2 Managing Processes 9. BestCar sales activity. The spreadsheet follows, showing the average sales at 4.75 cars per week and the average weekly revenue at $95,000. The frequency table in the lower left corner shows a close correspondence with the original frequency distribution with some small differences. For example, the simulation resulted in sales of 5 cars per week 29 percent of the time, rather than 30 percent.
Simulation SUPPLEMENT B 121 10. A machine center d. Two random numbers could be used for each client one for demand and one for processing time. Once this has been done for all four clients, it is possible to compute the value of R for the year just simulated. The result is one observation for constructing a frequency chart or probability distribution. b. For the first year simulated: Event 88 A s demand is 4200 units (in 70 99 range) 24 A s processing time is 10 hours/unit (in 0 34 range) 33 B s demand is 800 units (in 30 79 range) 29 B s processing time is 90 hours/unit (in 25 74 range) 52 C s demand is 3000 units (in 10 59 range) 84 C s processing time is 15 hours/unit (in 25 84 range) 37 D s demand is 600 units (in 0 39 range) 92 D s processing time is 80 hours/unit (in 95 99 range) Then for the first year: R = 4200(10) + 800(90) + 3000(15) + 600(80) = 207,000 hours.
122 PART 2 Managing Processes Table for Problem 4b: Simulation of Voice Mail System No. of Calls Made 1st Call Forward? (Yes/No) 2nd Call Forward? (Yes/No) 3rd Call Forward? (Yes/No) 4th Call Forward? (Yes/No) No. of Calls Not Answered Time 10:00 68 2 30 Yes 54 Yes 1 10:01 76 2 36 Yes 32 Yes 1 10:02 68 2 04 Yes 07 Yes 1 10:03 98 4 08 Yes 21 Yes 28 Yes 79 No 2 10:04 25 1 77 No 0 10:05 51 1 23 Yes 0 10:06 67 2 22 Yes 27 Yes 1 10:07 80 2 87 No 06 Yes 0 10:08 03 0 0 10:09 03 0 0 10:10 33 1 78 No 0 10:11 32 1 40 Yes 0 10:12 56 2 92 No 61 No 0 10:13 39 1 05 Yes 0 10:14 93 3 43 Yes 54 Yes 30 Yes 2 10:15 33 1 26 Yes 0 10:16 33 1 83 No 0 10:17 62 2 60 No 25 Yes 0 10:18 12 0 0 10:19 30 1 96 No 0 10:20 83 3 48 Yes 23 Yes 11 Yes 2 10:21 09 0 0 10:22 92 3 66 No 21 Yes 76 No 0 10:23 31 1 19 Yes 0 10:24 51 1 75 No 0 10:25 15 0 0 10:26 27 1 52 Yes 0 10:27 58 2 94 No 45 Yes 0 10:28 74 2 72 No 19 Yes 0 10:29 20 0 0 10:30 64 2 71 No 39 Yes 0 10:31 04 0 0 10:32 75 2 01 Yes 05 Yes 1 10:33 45 1 58 Yes 0 10:34 15 0 0 10:35 66 2 94 No 60 No 0 10:36 61 2 72 No 99 No 0 10:37 32 1 90 No 0 10:38 73 2 14 Yes 25 Yes 1 10:39 52 1 20 Yes 0 10:40 86 3 89 No 97 No 63 No 0 10:41 65 2 99 No 89 No 0 10:42 36 1 54 Yes 0 10:43 19 0 0 10:44 07 0 0 10:45 56 2 04 Yes 52 Yes 1 10:46 01 0 0 10:47 14 0 0 10:48 55 1 49 Yes 0 10:49 23 1 62 No 0 10:50 59 2 61 No 21 Yes 0 10:51 49 1 64 No 0 10:52 36 1 45 Yes 0 10:53 26 1 20 Yes 0 10:54 26 1 46 Yes 0 Asst Idle
Simulation SUPPLEMENT B 123 10:55 41 1 78 No 0 10:56 79 2 73 No 45 Yes 0 10:57 87 3 47 Yes 77 No 89 No 0 10:58 99 4 78 No 08 Yes 21 Yes 61 No 1 10:59 24 1 15 Yes 0