Question 1

The production rate has been steady at 20 units per hour. The average work-in-process inventory at this station is 15 units. What is the average lead time through this manufacturing station?

Accepted Answer

The answer of The production rate has been steady at...

Question 2

The delivery wagon that the hominy man had used for the last three decades was beyond repair, so he decided to open a hominy stand at a busy intersection in downtown Luther. Customers arrive at the rate of 8 per hour and it takes 5 minutes on average to fill their buckets with hominy.
a. What is the likelihood that the line is longer than three people?
b. What is the average waiting time in line?
c. What is the average number of customers in line?

Accepted Answer

The answer of The delivery wagon that the hominy man...

Question 3

The manager of a car wash wants to know how fast his new crew is processing cars through the wash area. He notices that it takes cars an average of about 30 minutes in line to reach the car wash, and his spot checks during the day indicated an average of seven cars in line waiting to be washed. What was the processing rate for his new crew that day?

Accepted Answer

The answer of The manager of a car wash wants...

Question 4

Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don't meet the express line criterion go to the other checkout line where they spend an average of 10 minutes checking out. How many people are checking out in the express line on average?

Accepted Answer

The answer of Customers arrive at the local grocery store...

Question 5

A drive thru car wash can process cars at a rate of one every five minutes. When you arrive with your car, you see one car just leaving the washer and eight cars in line ahead of you. How long can you expect to wait before you will reach the car wash?

Accepted Answer

The number of cars ahead of you is eight, meaning that you are the ninth car in line. The car wash processes one car every five minutes, therefore, it will take the car wash 5 x 8 = 40 minutes to reach your car. Since the question is asking for an estimate, we can round up to the nearest multiple of 15, which would be 45 minutes. Therefore, the correct answer is C: greater than 30 but less than or equal to 45 minutes.

Question 6

A professor's teaching assistants sit in their communal office and answer questions from students the afternoon before the final exam. The class is a mass lecture of 350 students, and the teaching assistants have final exams of their own, so they concentrate on providing explanations as quickly as possible. On average, the three teaching assistants can answer 30 questions an hour and students arrive at their office every five minutes. Student arrivals are Poisson distributed, each student has only one question and answer times are exponentially distributed.
a. What fraction of their time do the teaching assistants spend answering questions?
b. What is the average number of students waiting outside their office?
c. What is the average time a student spends in line outside the teaching assistants' office and having their question answered?

Accepted Answer

The answer of A professor's teaching assistants sit in their...

Question 7

A drive thru car wash can process cars at a rate of one every five minutes. The manager notices that during one particular day it takes cars an average of about 30 minutes in line to reach the car wash. What was the average number of cars in line on that day?

Accepted Answer

Using Little's Law, which states that the average number of items in a queuing system (L) is equal to the average rate at which items arrive (λ) multiplied by the average time an item spends in the system (W), we can calculate the average number of cars in line. Given that it takes 30 minutes on average for a car to reach the car wash and a car is processed every 5 minutes, the arrival rate is 1 car per 5 minutes. Therefore, L = λW = (1 car/5 minutes) * 30 minutes = 6 cars. This means the average number of cars in line was between 4 to 6 cars.

Question 8

________ is a fundamental law that relates the number of customers in a waiting-line system to the waiting time of customers.

Accepted Answer

The answer of ________ is a fundamental law that relates...

Question 9

A harvesting firm has six combines, each requiring service at an average rate of once every 40 hours, according to an exponential distribution. The firm has a mechanic who needs four hours to complete the average repair with exponential service times.
a. What is the average utilization of the mechanic?
b. What is the average number of combines in the system?
c. What is the average number of combines in line?
d. What is the average time spent being repaired and waiting?
e. What is the average time spent in line waiting for repair?

Accepted Answer

The answer of A harvesting firm has six combines, each...

Question 10

Students arrive at a university business library during peak evening hours at a rate of 40 students every half hour. A periodic count shows that there are 200 students in the library at any one time. On average, how long is each student's stay in the library?

Accepted Answer

The answer of Students arrive at a university business library...

Question 11

Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don't meet the express line criterion go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out in line #2 on average?

Accepted Answer

70% of 40 customers go to line #2, which is 28 customers per hour. With an average checkout time of 10 minutes, the average number of people checking out in line #2 is (28 customers/hour) * (10 minutes/customer) / 60 minutes/hour = 4.67, which falls in the range greater than 3.0 but less than or equal to 5.0.

Question 12

Customer waiting times for a call center are extremely long. Two possible explanations for this phenomenon are low ________ or low ________.

Accepted Answer

The answer of Customer waiting times for a call center...

Question 13

What is Little's Law? How might it be applied to determine the average length of time it takes an MBA student to complete the program?

Accepted Answer

The answer of What is Little's Law? How might it...

Question 14

Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don't meet the express line criterion go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out in both lines on average?

Accepted Answer

The average number of people checking out in both lines can be calculated by first determining the number of people using each line per hour and then converting that into the number of people checking out per minute. For the express line, 30% of 40 customers, which is 12 customers, use it per hour. Since their checkout time is 5 minutes, this translates to 12 customers / 60 minutes * 5 minutes = 1 customer at any given time. For checkout line #2, 70% of 40 customers, which is 28 customers, use it per hour. With a checkout time of 10 minutes, this translates to 28 customers / 60 minutes * 10 minutes = 4.67 customers at any given time. Adding both gives 1 + 4.67 = 5.67 customers checking out on average at any given time, which is greater than 5.0.

Question 15

Customers in a small retail store arrive at the single cashier at the rate of 10 per hour. The average service time for the cashier is five minutes. Arrivals tend to follow a Poisson distribution, and service times follow an exponential distribution.
a. What is the average utilization of the cashier?
b. What is the average number of customers in the system?
c. What is the average number of customers in line?
d. What is the average time spent in the system?
e. What is the average time spent in line?

Accepted Answer

The answer of Customers in a small retail store arrive...

Question 16

Students arrive at a university business library during peak evening hours at a rate of 40 students every half hour. Each student stays an average of two hours. On average, how many students are in the library at any one time?

Accepted Answer

The answer of Students arrive at a university business library...

Question 17

Customer arrival rates vary throughout the day and the priority rules change depending on the customer mix and influence each has over the finances of the firm. Such a situation is best analyzed using simulation rather than one of the queuing formulas.

Accepted Answer

Simulation allows for a more realistic representation of complex systems with varying inputs and rules, making it a better approach for analyzing situations where queuing formulas may not be sufficient.

Question 18

The average lead time of a unit of product through a manufacturing station is 18 minutes. The average work-in-process inventory at this station has been 30 pieces. What is the production rate?

Accepted Answer

Production rate = 1 / (average lead time + average WIP inventory)
           = 1 / (18 minutes + 30 pieces/ rate)
           = 1 / (6/5 minutes) 
           = 5/6 pieces per minute
           = 1.66 pieces per minute (rounded to two decimal places)
Therefore, the correct answer is C.

Question 19

A professor sits in his office and answers questions from his students the afternoon before the final exam. His class is a mass lecture of 350 students, so he concentrates on providing explanations as quickly as possible. On average, he can answer 60 questions an hour and students arrive at his office every five minutes. Student arrivals are Poisson distributed, each student has only one question and answer times are exponentially distributed.
a. What fraction of his time does the professor spend answering questions?
b. What is the average number of students waiting outside his office?
c. What is the average time a student spends in line outside the professor's office?

Accepted Answer

The answer of A professor sits in his office and...

Question 20

A movie complex experiences its peak ticket sales in the early evening when several movies have about the same start times. The ticket booth can process customers buying tickets at a maximum rate of 45 seconds each (or 80 tickets sold per hour). You arrive to buy your ticket and count 16 people in line ahead of you. How long can you expect to wait in line before getting to the booth to buy your ticket?

Accepted Answer

Since there are 16 people ahead of you and the ticket booth can process customers at a rate of 80 tickets per hour, it would take approximately 12 minutes for all 16 people to buy their tickets (80 tickets per hour / 60 minutes = 1.33 tickets per minute; 16 people / 1.33 tickets per minute = 12.03 minutes). Therefore, you can expect to wait in line for greater than 10 but less than or equal to 15 minutes. So the correct choice is C.

Quiz 19: Supplement B Waiting Lines