Use the following scenario and data for all questions An auto service center pro

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). About 30% of the customers are for Tire Replacement and the other 70% 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 Arivals Minutes)o 0.150 100 150 20a 0.400 Totalo 1.000 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. Oil Change Service Time (Minutes) Probability Service Time (Minutes) Probability 0.25 0.40 0.15 1.00 0.40 30 35 Total 0.10 1.00 Total 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. Custorner Service Types Service Probability Probability Interval Customer Arrival between Probability ProbabilityInterval CumulativeNumber CumulativeNumber 0.15 10 15 20 Tire (T oil (o) Total 0.70 1.00 .20 Total 1.00 CumulativNumber Probability Probability Interval Probability Probability Interval 25 30 35 Total 040 0.15 1.00 0.10 Total 1.00

Explanation / Answer

Simulation

Note here I have added an extra column for a better understanding

Arrival time is the cumulative time of arrival of customers i.e 1st customer arrives at the 10th minute of starting and then the second customer arrives after 5 minutes i.e 15th minute.Like this, it goes by.

Check the random number interval table and fill every column of simulation according to the range of the random numbers for different events.

1. The random number interval for tire replacement is 0.00000 - 0.29999 (I have taken it 0-0.3)

2.The random number interval for oil change is 0.3000 - 0.9999

Please comment if any doubt

Formula sheet of Excel

Time Between arrivals Probability Cumulative Probability Random Number Interval Customer service type Probability Cumulative probability Random number interval 5 0.15 0.15 0-0.15 Tire 0.3 0.3 0-0.3 10 0.25 0.4 0.16-0.4 Oil 0.7 1 0.31-1 15 0.4 0.8 0.41-0.8 20 0.2 1 0.81-1 Tire replacement Oil Change Servicetime Probability Cumuative Probability Random Number Interval Servicetime Probability Cumuative Probability Random Number Interval 20 0.2 0.2 0-0.2 10 0.3 0.3 0-0.3 25 0.25 0.45 0.21-0.45 15 0.4 0.7 0.31-0.7 30 0.4 0.85 0.46-0.85 20 0.2 0.9 0.71-0.9 35 0.15 1 0.86-1 25 0.1 1 0.91-1

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