# Decisions Sciences

The Decisions Sciences Department is trying to determine wheter to rent a slow or a fast copier. The department believes that an employee's time is wort $15 per hour. The slow copier rents for $4 per hour and it takes an employee an average of 10 minutes to complete copying(exponentially distributed). The fast copier rents for $15 an hour and it takes an empoyee an average of 6 minutes to complete copying. An average of 4 employees per hour need to use the copying machine (interarrival times are exponential).

Which machine should the department rent?

Each airline passenger and his luggage must be checked to determine whether he is carrying weapons onto the airplane. Suppose that at Gotham City Airport, 2.6 passengers per minute arrive, on average. Also, assume that interarrival times are exponentially distributed. To check passengers for weapons, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of three passengers per minute, where the time to check a passenger is also exponentially distributed. Under the assumption that the airport has only one checkpoint, answer the following questions.

a. Why is an M/M/1 , not an M/M/2, model relevant here?

b. What is the probability that a passenger will have to wait before being checked for weapons?

c. On average, how many passengers are waiting in line to enter the checkpoint?

d. On average, how long will a passenger spend at the checkpoint (including waiting time in line)?

Question:

A small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 60 customers per day. On average, 50 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributes. If the delay cost per customer day is $100, how many tellers should the bank hire?

Which machine should the department rent?

Each airline passenger and his luggage must be checked to determine whether he is carrying weapons onto the airplane. Suppose that at Gotham City Airport, 2.6 passengers per minute arrive, on average. Also, assume that interarrival times are exponentially distributed. To check passengers for weapons, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of three passengers per minute, where the time to check a passenger is also exponentially distributed. Under the assumption that the airport has only one checkpoint, answer the following questions.

a. Why is an M/M/1 , not an M/M/2, model relevant here?

b. What is the probability that a passenger will have to wait before being checked for weapons?

c. On average, how many passengers are waiting in line to enter the checkpoint?

d. On average, how long will a passenger spend at the checkpoint (including waiting time in line)?

Question:

A small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 60 customers per day. On average, 50 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributes. If the delay cost per customer day is $100, how many tellers should the bank hire?

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