Problem 1
Five executives share the services of a typing pool. The average number of jobs
submitted for typing is six per day per executive and a job takes 15 minutes on
average to type. Evaluate the situation, by fir
...
Problem 1
Five executives share the services of a typing pool. The average number of jobs
submitted for typing is six per day per executive and a job takes 15 minutes on
average to type. Evaluate the situation, by first describing the performance measures
of possible interest; and computing appropriate performance measures. A day consists
of 8 hours. Assume that the arrivals over any period of time are Poisson distributed
and that the service time per job is exponentially distributed.
Problem 2
Kristen offers lunch specials on weekends. (This has nothing to do with the cookie
business). She manages the weekend business by herself. On a typical weekend she
receives on the average about 6 orders per hour. It takes Kristen on the average 7.5
minutes to prepare and box an order (this time is the service time and does not include
the waiting time of the customer.) Kristen’s profit per order is $3. Assume that the
arrival process of orders follows a Poisson distribution and that the time to fill an
order is exponentially distributed.
(a) What is the arrival rate and what is the service rate in this example?
(b) What is the average time that a customer has to wait (from placing an order to
getting it filled)?
(c) Based on talking to customers, Kristen realizes that the waiting times her
customers experience could have a long term impact on her business. She
believes that if the average waiting time (from placing an order to getting it
filled) of a customer is x minutes, the impact on the net present value (NPV)
of her business is (- 1000 x)$. That is if she reduces the average waiting time
by one minute, somehow, the NPV increases by $1000. Kristen has an option
of investing in some resource that will help her reduce the “prepare and box”
time from 7.5 minutes per order on an average to 6 minutes per order on an
average. The time is still exponentially distributed. What is the maximum
amount Kristen should be willing to pay for this resource (assume there is no
maintenance costs etc.)?
Problem 3
There are two streams of customers arriving independently at a supermarket:
“Express” customers arrive at a rate 70 per hour, and stay on average 10 minutes
within the shop. Each of them spend on average $25. “Regular” customers arrive at a
rate 40 per hour. They stay within the shop for 30 minutes, spending $80 (on average).
(a) What is the average number of “express” customers in the supermarket, at a given
moment of time? What is the expected total number of customers at the
supermarket, at a given moment of time?
(b) What is the average revenue per hour?
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