The neighborhood coffee shop, K-Café, is opening a new store. Management expects that once the store is open, customers
Posted: Sun May 08, 2022 8:02 pm
The neighborhood coffee shop, K-Café, is opening a new store.
Management expects that once
the store is open, customers will arrive according to a Poisson
process with a mean of 32 customers
per hour. In designing the store, the management can choose between
two different operating
configurations using different kinds of espresso machines:
• Two “Classic” Machines
• One “2Xfaster” Machine
You have been tasked with analyzing these alternatives and
determining the customer waiting time
and queue size for each, both important metrics that impact
customer satisfaction and the
atmosphere in the store.
Consider first the Classic machine. One such machine can serve, on
average, 20 customers per
hour, and service times for this machine are exponentially
distributed. The management knows
that if they purchase this type of machine, they will require two
identical machines to meet
demand; any more machines would be impractical given the physical
layout of the store. The
customer orders will be placed in a single queue in front of both
machines, from which orders will
be routed to the first available machine.
1. What is the utilization of the Classic machines? Please enter
your answer as a value between
0 and 1. If your answer is not an integer, provide at least three
decimal places, e.g., 7.500.
2. With the two Classic machines, what is the expected total time
(in minutes) that a customer
spends in the store (i.e., the total time in queue and in service)?
If your answer is not an integer,
provide at least three decimal places, e.g., 7.500.
3. With the two Classic machines, what is the expected total number
of customers in the store
(i.e., in queue and in service)? If your answer is not an integer,
provide at least three decimal
places, e.g., 7.500.
Management expects that once
the store is open, customers will arrive according to a Poisson
process with a mean of 32 customers
per hour. In designing the store, the management can choose between
two different operating
configurations using different kinds of espresso machines:
• Two “Classic” Machines
• One “2Xfaster” Machine
You have been tasked with analyzing these alternatives and
determining the customer waiting time
and queue size for each, both important metrics that impact
customer satisfaction and the
atmosphere in the store.
Consider first the Classic machine. One such machine can serve, on
average, 20 customers per
hour, and service times for this machine are exponentially
distributed. The management knows
that if they purchase this type of machine, they will require two
identical machines to meet
demand; any more machines would be impractical given the physical
layout of the store. The
customer orders will be placed in a single queue in front of both
machines, from which orders will
be routed to the first available machine.
1. What is the utilization of the Classic machines? Please enter
your answer as a value between
0 and 1. If your answer is not an integer, provide at least three
decimal places, e.g., 7.500.
2. With the two Classic machines, what is the expected total time
(in minutes) that a customer
spends in the store (i.e., the total time in queue and in service)?
If your answer is not an integer,
provide at least three decimal places, e.g., 7.500.
3. With the two Classic machines, what is the expected total number
of customers in the store
(i.e., in queue and in service)? If your answer is not an integer,
provide at least three decimal
places, e.g., 7.500.