Question
Use the following scenario and data for all questions An auto service center provides two types of services, Tire Replacement (T) and Oil Change (O).
Use the following scenario and data for all questions
An auto service center provides two types of services, Tire Replacement (T) and Oil Change (O). About 30% of the customers are for Tire Replacement and the other 7)% are for Oil Change. All customers are serviced on a first come first served basis.
During regular hours, customers arrive at the service center according to the probability distribution in the following table
Time-Between Arrivals (Minutes) | Probability |
5 | 0.15 |
10 | 0.25 |
15 | 0.40 |
20 | 0.20 |
Total | 1 |
Two technicians are working at the service center and both of them are skillful enough for both Tire Replacement and Oil Change. Once finishing the job for a customer, a technician will take care of the next customer waiting in line. When both technicians are idle, the one who finished the last job earlier will take care of the next incoming customer. The times taken by the two jobs by any of the technicians follow the probability distributions in the following tables. You are required to simulate the operations of the auto service center for 15 customers.
Tire Replacement Oil Change
Service Time (Minutes) | Probability | Service Time (Minutes) | Probability |
20 | 0.2 | 10 | 0.3 |
25 | 0.25 | 15 | 0.4 |
30 | 0.4 | 20 | 0.2 |
35 | 0.15 | 25 | 0.1 |
Total | 1 | Total | 1 |
Before answering the following questions, you may use the following tables to determine the cumulative probability distributions and assign random number intervals for customer arrivals, customer service types, and time needed for both types of services.
Customer Arrival Customer Service Types
Time between Arrivals (Minutes) | Probability | Cumulative Probability | Service Type | Probability | Cumulative Probability | Random Number Interval | |
5 | 0.15 | Tire (T) | 0.3 | ||||
10 | 0.25 | Oil (O) | 0.7 | ||||
15 | 0.4 | Total | 1 | ||||
20 | 0.2 | ||||||
Total | 1 |
Tire Replacement Oil Change
Service Time (Minutes) | Probability | Cumulative Probability | Service Time (Minutes) | Cumulative Probability | Random Number Interval | |
20 | 0.2 | 10 | .3 | |||
25 | 0.25 | 15 | 0.4 | |||
30 | 0.4 | 20 | 0.2 | |||
35 | 0.15 | 25 | 0.1 | |||
Total | 1 | Total | 1 |
You may also simulate the operations of this auto service center for the 15 customers using the random numbers given in the following table. The Start Time is the time point when the job for the customer starts and the Finish Time is the time point when the job for the customer finishes.
Customer | Random number | Time Between Arrival | Time of Arrival | Random Number | Time Needed (Minutes) | Technician | Start Time | Finish Time | Waiting Time (Minutes) |
1 | 0.1723 | 10 | 10 | 0.9237 | 20 | 1 | 10 | 30 | 0 |
2 | 0.0042 | 5 | 15 | 0.3328 | 20 | 2 | 15 | 35 | 0 |
3 | 0.2249 | 10 | 25 | 0.9420 | 15 | 1 | 30 | 45 | 5 |
4 | 0.2060 | 10 | 35 | 0.3458 | 15 | 2 | 35 | 50 | 0 |
5 | 0.2040 | 0.2180 | |||||||
6 | 0.5578 | 0.4262 | |||||||
7 | 0.4779 | 0.0285 | |||||||
8 | 0.6022 | 0.5997 | |||||||
9 | 0.3029 | 0.7520 | |||||||
10 | 0.9998 | 0.7155 | |||||||
11 | 0.11212 | 0.8780 | |||||||
12 | 0.0613 | 0.2989 | |||||||
13 | 0.2451 | 0.1682 | |||||||
14 | 0.3375 | 0.9130 | |||||||
15 | 0.3934 | 0.7647 |
1 For customer arrivals, the random number interval assigned to the Time between Arrivals of 5 minutes is
A. 0.0000-0.1499
B. 0.1500-0.3999
C. 0.4000-0.7999 (This choice is wrong)
D. 0.8000-0.9999
E. None of the above
2 For customer arrivals, the random number interval assigned to the Time between Arrivals of 15 minutes us
A. 0.0000-0.1499
B. 0.1500-0.3999
C. 0.4000-0.7999
D. 0.8000-0.9999 (This choice is wrong)
E. None of the above
3 For the Customer Service Type, the random number interval assigned to Tire Replacement is
A. 0.0000-0.6999
B. 0.0000-0.2999 (Correct choice)
C. 0.2999-0.9999
D. 0.3000-0.9999
E. None of the above
4 For the Customer Service Type, the random number interval assigned to Oil Change is
A. 0.0000-0.6999
B. 0.0000-0.2999 (This choice is incorrect)
C. 0.2999-0.9999
D. 0.3000-0.9999
E. None of the above
5 For the Tire Replacement, the random number interval assigned to the Service Time 25 minutes is
A. 0.0000-0.1999
B. 0.2000-0.4499
C. 0.4500-0.8499
D. 0.8500-0.9999 (This choice is incorrect)
E. None of the above
6 For the Tire Replacement, the random number interval assigned to Service Time 35 minutes is
A. 0.0000-0.1999 (This choice is incorrect)
B. 0.2000-0.4499
C. 0.4500-0.8499
D. 0.8500-0.9999
E. None of the above
7 For the Oil Change, the random number interval assigned to the Service Time 15 minutes is
A. 0.0000-0.2999
B. 0.3000-0.6999
C. 0.7000-0.8999 (This choice is incorrect)
D. 0.9000-0.9999
E. None of the above
8 For the Oil Change, the random number interval assigned to the Service Time 20 minutes is
A. 0.0000-0.2999
B. 0.3000-0.6999
C. 0.7000-0.8999 (This choice is correct)
D. 0.9000-0.9999
E. None of the above
9 For customer 5, the time between arrivals and the time of arrival are, respectively,
A. 10 and 45
B. 10 and 35 (This choice is incorrect)
C. 10 and 25
D. 10 and 15
E. None of the above
10 For customer 5, the service type and time needed are, respectively,
A. 0 and 20
B. 0 and 25 (This choice is incorrect)
C. T and 20
D. T and 25
E. None of the above
11 For customer 5, the service Start Time and Finish Time are, respectively,
A. 10 and 45 (This choice is incorrect)
B. 20 and 45
C. 20 and 40
D. 45 and 60
E. None of the above
12 For customer 10, the time between arrivals and the time of arrival are, respectively,
A. 20 and 90
B. 20 and 120
C. 15 and 90
D. 15 and 120 (This choice is incorrect)
E. None of the above
13 For customer 10, the service type and time needed are, respectively,
A. 0 and 20 (This choice is incorrect)
B. 0 and 25
C. T and 20
D. T and 25
E. None of the above
14 For customer 10, the service Start Time and Finish Time are, respectively,
A. 100 and 125
B. 100 and 145
C. 120 and 140 (This choice is incorrect)
D. 120 and 145
E. None of the above
15 For customer 15, the time between arrivals and the time of arrival are, respectively,
A. 10 and 160
B. 100 and 160 (This choice is incorrect)
C. 10 and 125
D. 10 and 150
E. None of the above
16 For customer 15, the service type and time needed are, respectively,
A. 0 and 20
B. 0 and 25
C. T and 20
D. T and 25 (This choice is incorrect)
E. None of the above
17 For customer 15, the service Start Time and Finish Time are, respectively,
A. 180 and 195 (This choice is incorrect)
B. 175 and 190
C. 175 and 185
D. 165 and 180
E. None of the above
18 On the average, a customer must wait for
A. 10 minutes
B. 5 minutes
C. 9/5 minutes (This choice is incorrect)
D. 10/3 minutes
E. None of the above
Step by Step Solution
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