Chapter.9 Variability & Process Time Full Test Bank

Matching Supply with Demand: An Introduction to Operations Management, 4e (Cachon)

Chapter 09 Variability and Its Impact on Process Performance: Waiting Time Problems

[The following information applies to questions 1-2.]

UP Fitness will install 3 new trapezoidal gel-resistance toners, or "trappies," which are the latest exercise gadget specifically designed to contour upper back muscles. Clients who want to use these machines arrive at the rate of 85 per hour. The coefficient of variation of the interarrival 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 quite small—only 30.

1) On average, how many UP Fitness clients are using a trappy?

Difficulty: 3 Hard

Topic: Motivating Example: A Somewhat Unrealistic Call Center

AACSB: Knowledge Application

Blooms: Apply

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

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

3) Max Stamp approves study abroad documents for Penn. Students must wait in line with their forms outside Max's office. One student at a time is allowed in his office, and Max takes precisely 25 minutes to evaluate each student's set of documents. On average, 2.2 students per hour go to his office, and they spend on average 160 minutes trying to get their forms approved (time waiting in queue plus time in Max's office for him to evaluate their documents). On average, how many students are waiting outside of Max's office? (Note: Ignore start-of-the-day and end-of-the-day effects.)

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

4) Larry Ellison starts a company that manufactures high-end custom leather bags. He hires two employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.8 days with a standard deviation of 2.7 days. Larry expects to receive one customer order, per day on average. The interarrival times of orders have a coefficient of variation of 1. What is the expected duration, in days, between when an order is received and when production begins on the bag? (Note: Include the time waiting to start production, but do not include the time in production.)

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

[The following information applies to questions 5-6.]

Find a Doctor, or FaD, is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc.). During a "slow" time for them, they have 7 staff members taking calls from customers. On average, one call arrives every 6 minutes (with a standard deviation of 6). Each staff member spends 20 minutes with each customer (on average, with a standard deviation of 30).

5) What is the probability that one of their staff members is busy (as a %)?

Difficulty: 3 Hard

Topic: Processing Time Variability

AACSB: Knowledge Application

Blooms: Apply

6) How long (in minutes) does a customer spend on average waiting on hold before they can start speaking to a representative from FaD?

Difficulty: 3 Hard

Topic: Processing Time Variability

AACSB: Knowledge Application

Blooms: Apply

7) The organizers of a conference in the Philadelphia Convention Center are evaluating the possibility of setting up a computer area where attendees can check their e-mail on computers provided by the organization. There will be one common queue for all computers, and only one person uses a computer at a time. On average, there are 15 attendee arrivals per hour, the standard deviation of the time between arrivals is 4, and the average time a person spends on the computer is 10 minutes (with standard deviation 3). To ensure that waiting times are not too long, the organizers want to ensure that the utilization of the computers doesn't exceed 90%. At least how many computers do they need to have?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

8) A small call center normally has 5 employees answering calls while open. On average, 5 calls arrive every 4 minutes with a CVa = 1. Under normal operating conditions each employee on average handles each call in 3.5 minutes with a standard deviation of 3. Today, however, one employee has the flu, and they need to operate with 4 employees during this time. The manager is nervous that they may be supply constrained and so she directs her employees to hurry their processing of calls today. What is the maximum average processing time for each call that they need to achieve today so that they have a stable queue? (Note: there will be supply constrained if their processing time is higher than this target and there will be demand constrained if it is lower than this target. Choose the closest answer. Assume CVa and CVp don't change even after the potential change in processing times).

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

[The following information applies to questions 9-10]

CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 5 supercomputers that can be accessed through the Internet. Their customers send jobs that arrive on average every 4 minutes. The standard deviation of the interarrival times is 4 minutes. Executing each job takes on average 16 minutes on one of the supercomputers (during this time, the computer cannot perform any other work). The standard deviation of this processing time is 24 minutes.

9) What is the utilization (as a %) of each supercomputer?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

10) On average, how many jobs are waiting to start processing?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

[The following information applies to questions 11-12.]

FestEvents is a concert organizer that is evaluating the installation of portable toilets at an outdoor venue where a concert is going to take place. In particular, it is considering an area of the venue that is far away from the existing restrooms. Assume there will be one single queue to access all the portable toilets in this area and that only one person uses a toilet at a time. FestEvents is concerned that if the line is too long, people will find other ways and places to answer nature's call.

FestEvents estimates that there will be 4 arrivals per minute on average to the toilets, with a standard deviation of the time between arrivals of 15 seconds. The average time a person spends using the toilet is 3.12 minutes with a standard deviation of 2 minutes.

11) Suppose FestEvents installs 20 portable toilets. On average, what fraction of the toilets will be occupied during the event?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of Multiple Resources

AACSB: Knowledge Application

Blooms: Apply

12) What is the minimum number of portable toilets that FestEvents must install to ensure that the queue length will not continue to grow without limit (i.e., so that the queue will be stable)? (Note: Your answer should be an integer—they can install 2 toilets or 3 toilets, but they cannot install 2.6 toilets.)

Difficulty: 3 Hard

Topic: Impact of Pooling: Economies of Scale

AACSB: Knowledge Application

Blooms: Apply

13) The Journal of Cryptic Psychology follows the following process to decide what to print. First, authors submit their papers to one of the 40 Associate Editors who either "reject" the papers or allow the authors to "revise" their papers. If the decision is "revise," then an author revises his/her paper based on the Associate Editor's comments, and when finished, submits the revision to the Editor.

The Editor decides to "reject" or "accept" the paper, and only accepted papers are printed in the journal. Associate Editors choose "revise" with only 20% of papers they see, and the Editor accepts only 75% of the papers she sees. The average and standard deviation of processing times are given in the table below:

The journal prints, on average, 30 papers per year. On average, how many manuscripts are currently being revised by authors?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

14) You currently have 7 items on your "to-do" list. Below are the items, and the estimated times to complete them.

Restring your snowshoes so you can get to class - 120 minutes

Take a nap - 100 minutes

Work on a homework assignment - 80 minutes

Update your Facebook account - 60 minutes

Call your mother - 30 minutes

Eat some food - 20 minutes

Call a friend to discuss weekend plans - 10 minutes

Suppose you immediately start with your tasks, no other tasks get added to your to-do list today, and you sequence them to minimize the average time the tasks wait before you start them. What will you be doing in 190 minutes from the time you start? (Note: Record the underlined task name above for your answer.)

Difficulty: 3 Hard

Topic: Reducing Variability

AACSB: Knowledge Application

Blooms: Apply

15) A computer server currently has a queue of 5 jobs, sequenced from A to E. A is the one that has been waiting the longest and E is the one that was most recently received. The following table provides their processing times in milliseconds.

Suppose the server is designed to minimize the average waiting time across jobs (i.e., time in the queue waiting to start processing). Ignore the amount of time these jobs have already been waiting. Suppose the server is immediately available to start working on one of the jobs and the server is aware of each job's processing time. What is the minimum total time these five jobs will wait before beginning processing? (Note: Additional jobs may or may not arrive before the processing of these jobs is completed. For example, if A is processed first and B next, then A's wait will be 0 and B's wait will be 5 (the time to complete A) so the total time for these two jobs alone is 0+5=5.)

Difficulty: 3 Hard

Topic: Economic Implications: Generating a Staffing Plan

AACSB: Knowledge Application

Blooms: Apply

16) Which of the following best reflects pooling capacity to reduce restroom queue lengths?

A) Add more toilets to increase capacity.

B) Install a flexible partition that can alter the size of the women's and the men's restrooms.

C) Convert the separate men's and women's rooms into a single unisex restroom (that both men and women can use).

D) Remove mirrors in the restroom to decrease the time users spend in the restroom.

E) Add automatic flush capability to each toilet to decrease processing times.

Difficulty: 2 Medium

Topic: Impact of Pooling: Economies of Scale

AACSB: Reflective Thinking

Blooms: Evaluate

17) The following four graphs (labeled A, B, C, and D in the upper right corner) display the number of customers in a queuing system (y-axis) over a long period of time (x-axis). Which of the following is most likely a stable system?

A) Only A

B) Only B

C) Only C

D) Only D

E) Only B and C

F) None of them

G) All of them

Difficulty: 2 Medium

Topic: Variability: Where It Comes from and How It Can Be Measured

AACSB: Analytical Thinking

Blooms: Analyze

18) 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., not treating 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 interarrival 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, nor iii)

Difficulty: 2 Medium

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Reflective Thinking

Blooms: Analyze

19) YourNurse (YN) Inc. uses certified nurses to answer medical queries from customers over the phone. When patients call into YN, they are first asked to provide their zip code which then allows YN to route their call to the call center nearest to the patient (they operate 10 across the country). Which single suggestion in the following list (and explanation) is most likely to reduce the average time callers wait before speaking with a nurse?

A) Run an advertising campaign to increase demand and to utilize their nurses better.

B) Train their nurses so that they spend more time answering the patients' questions.

C) Instead of using callers' zip codes, route calls to the call center with the fewest callers to help prevent situations in which there are idle nurses at the same time that there are callers on hold.

D) Play a recording of useful medical information while callers are on hold to decrease their perception of how long they are waiting.

E) None of the above

Difficulty: 2 Medium

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

[The following information applies to questions 20-22.]

The Right to Vote (and not to wait)

In the previous two presidential elections in the United States, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In Philadelphia as well, some voters complained about the long lines in some precincts, with most of the complaints coming from precinct A. In 2004, the average number of voters arriving at Precinct A was 35 per hour and the arrivals of voters was random with interarrival times that had a coefficient of variation of 1 (CVa=1). Philadelphia deployed 1 voting machine in Precinct A. Suppose that each voter spent, on average, 100 seconds in the voting booth (this is the time needed to cast his/her vote using a voting machine), with a standard deviation of 120 seconds.

20) How long, on average, did a voter have to wait in line at precinct A in 2004 before entering a booth to cast his/her vote? Circle the closest answer.

A) 56 minutes

B) 58 minutes

C) 60 minutes

D) 62 minutes

E) 71 minutes

F) 75 minutes

G) There is not sufficient information to answer the question.

Difficulty: 2 Medium

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

21) Given the long wait times for Precinct A, the city of Philadelphia is thinking of alternative solutions to improve voting conditions. One of the proposed solutions is as follows.

Proposal 1: Deploy an additional voting machine in precinct A. Assume that the voter turnout is expected to have similar characteristics in 2008 as in the previous election.

Under Proposal 1, how long, on average, would a voter have to wait in line in precinct A in 2008 before casting his/her vote? Circle the closest answer.

A) 1 minute

B) 5 minutes

C) 6 minutes

D) 10 minutes

E) 11 minutes

F) There is not sufficient information to answer the question.

Difficulty: 2 Medium

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

22) Under Proposal 1, on average, at precinct A, what would be the ratio of the average number of people voting at a booth over the average number of people waiting in line. Circle the closest answer.

A) 0.4

B) 1.4

C) 2.4

D) 3.4

E) 4.4

F) 5.4

G) There is not sufficient information to answer the question.

Difficulty: 2 Medium

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

[The following information applies to questions 23-27]

Philly Barber Shops

Newt Philly needs to decide where to get a haircut. He has narrowed the choice down to two local hair salons—Large Hair Salon (LHS) and Small Hair Cutters (SHC).

During busy periods, a new customer walks into LHS every 15 minutes (with a standard deviation of 15 minutes). At SHC, a customer walks in every hour (with a standard deviation of 1 hour). LHS has a staff of 4 barbers, while SHC has 1 barber. Typical service time at either salon lasts 30 minutes (with a standard deviation of 30 minutes).

23) If Newt walks into LHS during a busy period, how long must he wait in line before he can see a barber? (Note: Only include the waiting time, not any service time.)

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

24) If Newt goes to SHC, how long must he wait in line before his haircut starts?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

25) Assume that it takes Newt 10 minutes to leave work and walk to LHS and 10 minutes to walk back (i.e., each way of the walk takes 10 minutes). How long will he need to leave work for to get a haircut at LHS?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

26) LHS will buy out SHC. LHS will then close SHC's operations and serve all customers, including existing SHC customers, at the LHS location only. Assuming that the previous traffic of SHC customers now flows to the LHS location, what is the new interarrival time at LHS?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

27) To accommodate the new flow rate, LHS now staffs one additional barber (to increase the headcount to 5). Is the new waiting time at LHS less than or greater than the waiting time of LHS before the merger? (Note: Assume that the coefficient of variation of customer interarrival times is 1).

A) The new waiting time at LHS is less than the waiting time before the merger.

B) The new waiting time at LHS is greater than the waiting time before the merger.

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

[The following information applies to questions 28-33.]

Pharma Dev

Pharma Dev develops and markets new technological products to be used in health care. The development of a new product operates as follows.

When a new technology meets the requisite market potential, a new patent is filed. Patents are granted for 12 years starting from the date of issue. Once the patent is filed, the new technology is developed at one of its three independent development centers and is then launched to the market. Each product is developed at only one center, and each center can only develop a single patented technology at a time.

On average, Pharma Dev files a new patent every 5 months (with a standard deviation of 5 months). The average development process lasts 12 months (with a standard deviation of 24 months).

28) What is the utilization of Pharma Dev's development facilities?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

29) How long does it take for an average technology from winning a patent to start the development process?

Difficulty: 3 Hard

Topic: Processing Time Variability

AACSB: Analytical Thinking

Blooms: Analyze

30) How many years of patent life are left for an average product launched to the market?

98.75/12 = 8.229 years.

Difficulty: 3 Hard

Topic: Processing Time Variability

AACSB: Knowledge Application

Blooms: Apply

31) On average how many patented products are undergoing development or waiting to be developed?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Knowledge Application

Blooms: Apply

32) Pharma Dev is considering leasing an additional development center to shorten the time to market of patented products. If this center is used in addition to the three centers, how will the total time-to-market (waiting time plus development time) of a patented product change?

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

33) After a product is launched to the market, it generates gross margins of $40 million per year of patent life. After the patent expires, the product generates no gross margins. Leasing the new facility would increase Pharma Dev's average total annual gross margins by $ ________.

Difficulty: 3 Hard

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Analytical Thinking

Blooms: Analyze

34) Which of the following will increase the waiting time in a call center in which the incoming call gets assigned to the first available server?

A) Add more servers

B) Implement the Shortest Processing Rule

C) Implement a First-In-First-Out (FIFO) system

D) Increase the service time coefficient of variation

E) Increase the average service time

F) Decrease the interarrival time

G) B, C, D, and E

H) Both D and E

J) D, E, and F

Difficulty: 2 Medium

Topic: Predicting the Average Waiting Time for the Case of One Resource

AACSB: Reflective Thinking

Blooms: Analyze

35) Consider the following three process designs to organize a call center with 12 employees. The center handles calls for two customer types. Type 1 customers call with credit card related questions and type 2 customers call with questions related to the online account opening. On a busy day, the call center receives 60 calls per hour from type 1 customers and 30 calls per hour from type 2 customers. It takes, on average, 2 minutes to service both kinds of calls.

Process design 1: 6 employees handle type 1 calls; the other 6 employees handle type 2 calls

Process design 2: 8 employees handle type 1 calls; 4 employees handle type 2 calls

Process design 3: 12 cross-trained employees handle all calls

Which of the three process designs leads to the shortest and longest average waiting time for a random incoming request?

A) 1 is the shortest, 2 is the longest

B) 2 is the shortest, 1 is the longest

C) 3 is the shortest, 2 is the longest

D) 2 is the shortest, 3 is the longest

E) 3 is the shortest, 1 is the longest

F) 1 is the shortest, 3 is the longest

G) 3 is the shortest, 1 and 2 are the same

H) Cannot be determined

J) None of the above

Difficulty: 2 Medium

Topic: Predicting the Average Waiting Time for the Case of Multiple Resources

AACSB: Reflective Thinking

Blooms: Analyze