Question 1

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 2

Instead of having one worker perform all eight steps to process a customer,an operations manager assigns each step to a different worker.In doing so,the operations manager has increased the:

Accepted Answer

By assigning each step to a different worker, the operations manager has increased the number of phases in the process, as each phase now corresponds to a different step handled by a different worker.

Question 3

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 4

The average lead time of a unit of product through a manufacturing station is 10 minutes.The production rate has been steady at five units per hour.The average work-in-process inventory at this station is:

Accepted Answer

The answer of The average lead time of a unit...

Question 5

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 6

The manger 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 manger of a car wash wants...

Question 7

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 8

An operations manager decides that customers should be processed based on the anticipated duration of their request instead of their arrival time.The system has been changed in what fashion?

Accepted Answer

The change in processing customers based on their anticipated duration instead of arrival time indicates a change in the priority rule of the system. This means that customers with longer requests will be given priority over those with shorter requests, regardless of when they arrive.

Question 9

If the nature of the customer population,constraints on the line,the priority rule,and the service time distribution renders waiting line theory no longer useful,then an operations manager should rely on:

Accepted Answer

When the nature of the customer population, constraints on the line, priority rule, and service time distribution make waiting line theory no longer useful, simulation becomes the best option. Simulation allows the operations manager to model the system and experiment with different scenarios and variables, and observe how they affect the system. This enables the manager to optimize the system and improve performance without having to make costly and time-consuming changes in the real system. Decision tree analysis and linear programming may be useful in certain situations, but they are not appropriate when dealing with complex nonlinear systems with uncertain outcomes. Little's Law is a fundamental principle in waiting line theory but does not provide a solution to this specific problem.

Question 10

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

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

Question 11

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

To calculate the production rate, we use the formula: Production rate = (Number of units in inventory) / (Lead time + Processing time).

Here, lead time is given as 18 minutes, and the work-in-process inventory is 30 pieces. We need to find the processing time.

The processing time can be calculated as follows:

Processing time = Total time / Number of units 
Total time = Lead time + Processing time

Substituting lead time as 18 minutes and the work-in-process inventory as 30 pieces, we get:

30 = (18 + Processing time) x Production rate

Solving for production rate, we get:

Production rate = 30 / (18 + Processing time)

We don't have the processing time, but we can observe that the production rate will be maximum when the processing time is minimum. Therefore, we assume that all the 30 pieces are always in processing at the station.

Then, processing time = 30 x 18 minutes = 540 minutes.

Substituting this value in the above equation, we get:

Production rate = 30 / (18 + 540) = 1.66 pieces per minute

Therefore, the best choice is C.

Question 12

Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours,according to an exponential distribution.The single machine that refurbishes the tools needs 15 hours for each tool on the average,with exponential service times.
-Use the information in Scenario B.6.What is the average utilization of the refurbishing machine?

Accepted Answer

The utilization of the refurbishing machine can be calculated as the ratio of the average time spent servicing tools to the total time the machine is available.
The average time spent servicing a tool is given as 15 hours, and since the cutting tools need to be refurbished after an average of 30 hours (i.e., half of the total lifespan of the cutting tools), each tool is serviced after an average of 15/2 = 7.5 hours on the machine.
Thus, the total time the machine services one cutting tool is 15 + 7.5 = 22.5 hours on average.
Since there are four cutting tools, the total time the refurbishing machine spends on them is 4*22.5 = 90 hours.
The total time that elapses between two refurbishment needs for all four tools can be calculated as 4*30 = 120 hours.
Therefore, the utilization of the refurbishing machine is 90/120 = 0.75 or 75%.
Hence, the best choice is D, greater than 60 percent.

Question 13

Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours,according to an exponential distribution.The single machine that refurbishes the tools needs 15 hours for each tool on the average,with exponential service times.
-Use the information in Scenario B.6.What is the average waiting time of tools in line?

Accepted Answer

The average waiting time in line for an M/M/1 queue can be calculated using the formula $W_q = \frac{\lambda}{\mu(\mu - \lambda)}$, where $\lambda$ is the arrival rate and $\mu$ is the service rate. Given that tools need refurbishing every 30 hours on average ($\lambda = \frac{1}{30}$ tools/hour) and each tool takes 15 hours to refurbish on average ($\mu = \frac{1}{15}$ tools/hour), substituting these values into the formula gives a waiting time greater than 15 hours but fewer than 25 hours, fitting the description of choice B.

Question 14

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

With one car leaving and eight cars in line ahead of you, there are a total of nine cars in the queue. At a rate of one car every five minutes, it will take 45 minutes before it's your turn to enter the car wash. Therefore, the correct answer is C, greater than 30 but less than or equal to 45 minutes.

Question 15

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

The maximum rate of ticket processing is 80 tickets/hour or 1.33 tickets/minute. With 16 people ahead of you, it would take approximately 12 minutes (16 people x 45 seconds per person / 60 seconds per minute) for them to finish purchasing their tickets. Therefore, you can expect to wait more than 10 but less than or equal to 15 minutes in line before getting to the booth to buy your ticket.

Question 16

In a waiting-line problem,assigning additional employees to a service facility will have a direct effect on:

Accepted Answer

Assigning additional employees to a service facility will directly affect the service rates as the facility will be able to serve more customers in a given time. This will lead to a reduction in wait times and consequently, an increase in customer satisfaction. The line arrangement, customer population size and the number of service phases may also be indirectly affected by the addition of employees, but the most direct and significant impact will be on the service rates.

Question 17

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 18

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 19

In a waiting-line problem,increasing advertising expenditures,increasing the number of promotions,or changing the price of a service is most likely to affect:

Accepted Answer

Increasing advertising expenditures, increasing the number of promotions, or changing the price of a service are all marketing strategies that are geared towards attracting more customers. Therefore, these actions are most likely to affect customer arrival rates, which is a factor that can be controlled by the business. Increasing arrival rates will lead to longer waiting times and potentially longer lines, which is why it is important for businesses to carefully consider the effects of their marketing strategies on arrival rates when managing waiting lines.

Question 20

An operations manager organizes a process improvement team and the resulting process has a lower mean (µ).Which statement is the best description of this change?

Accepted Answer

A lower mean (µ) signifies an improvement in the process efficiency, which in turn points towards an improvement in server efficiency. Option A, B, and C do not necessarily reflect an improvement in process efficiency.

Quiz 18: Waiting Line