Question 1. You want to estimate the average unit process time (a.k.a. activity time), p, at a server. You are told that there are three identical parallel resources (m = 3), the server works for 8 hours or 480 minutes each day, the average utilzation at this server is 0.7 (or 70%), and the customer arrival rate is 80 units / day.

Among the options below pick the one that most correctly estimates the average unit activity time, p, corresponding to the above data.

a. Less than 3 minutes
b. At least 3 minutes but less than 6 minutes
c. At least 6 minutes but less than 9 minutes
d. At least 9 minutes but less than 12 minutes
e. At least 12 minutes but less than 15 minutes
f. At least 15 minutes
g. Cannot say

Question 2. UP Fitness will install 3 new "trapezoidal gel-resistance toners" ("trappy" for short), the latest exercise gadget, specifically designed to contour upper back muscles. Clients who want to use these machines arrive at the rate of 72 per hour. The coefficient of variation of the inter-arrival times is 3. If all three machines are busy, UP Fitness clients use other pieces of equipment, waiting for one of the trappies to become available. The trappy experience is intense - 120 seconds of explosive exercise intensity. The standard deviation of the usage times (measured in seconds) is somewhat small - only 60 seconds.

On average, how many UP Fitness clients are waiting to use a trappy?

a. Less than 2
b. At least 2 but less than 5
c. At least 5 but less than 8
d. At least 8 but less than 11
e. At least 11 but lest than 14
f. At least 14

Question 3. A pediatric practice has 5 physicians. Historically, patients were assigned to one physician and the same physician always treated these patients. For example, Alice's patients always visited her (for "well visits" and "sick visits") and never interacted with the other physicians. However, they have decided to change how they see patients. Now patients will be seen by whoever is available (i.e., a working physician who is not busy treating other patients). Based on our discussion of queuing theory, which of the three outcomes below are likely to occur due to this change?

i) The coefficient of variation of patient inter-arrival times will increase

ii) The utilization of each physician will increase

iii) The average number of patients actually with a physician (that is, "inventory in process") will increase

a. i only
b. ii only
c. iii only
d. i and ii only
e. i and iii only
f. ii and iii only
g. all of them (i, ii and iii)
h. none of them (neither i, ii and iii)

Question 4. Dan's Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails at $30.00. The publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is Normal with a mean of 1200 and a standard deviation of 300.

Suppose Dan wants to maximize his expected profits from the sale of this book. How many copies should he order from the publisher? Choose the closest answer.

a. Less than 1000
b. At least 1000 but less than 1100
c. At least 1100 but less than 1200
d.At least 1200 but less than 1300
e. At least 1300 but less than 1400
f. At least 1400 but less than 1500
g. At least 1500
h. Cannot say

Question 5. Dan's Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails at $30.00. The publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is Normal with a mean of 1200 and a standard deviation of 300.

Suppose Dan orders 1300 copies. What is Dan's expected profit? Choose the closest answer.

a. Less than 9500$
b. At least 9500$ but less than 9750$
c. At least 9750$ but less than 10000$
d. At least 10000$ but less than 10250$
e. At least 10250$ but less than 10500$
f. At least 10500$ but less than 10750$
g. At least 10750$

Question 6. Suppose the news vendor model describes a firm's operations decision. Is it possible to have positive expected lost sales and positive expected left over inventory? Choose the best answer.

a. No - if there is left over inventory then there should not be lost sales.
b. No - if expected lost sales is positive, then expected left over inventory must be negative.
c. No - actual demand can differ from sales.
d. Yes - they are both expectations over numerous possible outcomes, among which there will be no outcome in which both are positive.
e. Yes - as long as the underage cost is greater than the overage cost.

Question 7. Inn at Penn has 250 rooms. For regular-fare customers, rooms are priced at $300 per night while the rooms are priced at $700 per night for the high-paying customers who generally arrive at the last minute. The demand for such high fare customers is distributed normally with mean 70 and std.dev. 22. Assume that there is ample demand for regular-fare customers, but rooms cannot be sold to these customers at the last minute (end of a day).

What should the protection level for the high fare customer be to maximize expected profit? Note: The protection level is the number of rooms not sold to regular customers and kept aside for sale to high fare customers. If you over-protect (i.e., the protection level is too high), and there are fewer high fare customers than the protection level, you lose the regular fare revenue opportunity; if you under-protect and there are more high fare customers than the protection levels, you lose the additional revenue from the high fare customers.

a. Less than 50
b. At least 50 but less than 60
c. At least 60 but less than 65
d. At least 65 but less than 70
e. At least 70 but less than 75
f. At least 75 but less than 80
g. At least 80

Question 8. Suppose that the Inn at Penn uses the newsvendor model to set the protection level optimally. Which of the following changes in the environment would be the best argument for lowering protection levels?

a. Low fare demand is Normally distributed with mean 1000 and standard deviation 50 (rather than unlimited).
b. The high fare price for the room has gone down to $600 from $700 (but the distribution of demand remains unchanged).
c. The hotel capacity has gone up from 200 to 300 rooms.
d. All low-fare demand customers stay for one day, while most high-fare customers stay for two nights.
e. None of the other answers apply.