Question 1

Customers arrive at Rent a Wreck and hope to score an inexpensive and unsightly vehicle to use for what typically is a short period of time. About twenty customers show up in any hour of the day and it takes the customer service representative about two minutes to photocopy their driver's license and insurance card and take an impression of a credit card. Assume that the service and arrival rates are governed by the Poisson distribution. Calculate the system's vital statistics.

Accepted Answer

The answer of Customers arrive at Rent a Wreck and...

Question 2

The process step that limits throughput for the entire process chain is the ________.

Accepted Answer

The answer of The process step that limits throughput for...

Question 3

In waiting line theory, a customer service attendant is a(n)________.

Accepted Answer

The answer of In waiting line theory, a customer service...

Question 4

The Theory of Constraints would support the statement that a chain is only as strong as its weakest link.

Accepted Answer

The Theory of Constraints (TOC) emphasizes the importance of identifying and addressing the weakest link or bottleneck in a system in order to improve overall performance. Therefore, TOC would support the statement that a chain (or system) is only as strong as its weakest link.

Question 5

The average waiting time on a Thursday night for a table at a popular Chinese restaurant is 30 minutes. If customers arrive at the rate of four per hour and both the service and arrival rates are Poisson distributed, what is the average service time?

Accepted Answer

The average waiting time is 30 minutes, which implies the system is at capacity. With an arrival rate of 4 per hour, the service rate must be slightly higher than 4 to prevent infinite waiting times, thus between 5 and 6 per hour.

Question 6

Customers arrive at Rent a Wreck and hope to score an inexpensive and unsightly vehicle to use for what typically is a short period of time. About twenty customers show up in any hour of the day and it takes the customer service representative about two minutes to photocopy their driver's license and insurance card and take an impression of a credit card. Assume that the service and arrival rates are governed by the Poisson distribution; how long does it take for the average customer to clear the system?

Accepted Answer

Since the arrival rate and service rate are Poisson distributed, we can use the M/M/1 queuing model. 
λ = 20 customers/hour 
μ = 30 customers/hour (since each customer takes 2 minutes, µ = 1/2 customers/minute; there are 60 minutes in an hour, so µ = 30 customers/hour) 
Using the formula for the expected waiting time in an M/M/1 queuing model, we get: 
W = (1/µ) / (1 - λ/µ) 
W = (1/30) / (1 - 20/30) 
W = (1/30) / (1/3) 
W = 3 minutes 
Then, we add the average service time of 2 minutes to get the average time a customer spends in the system: 
3 minutes + 2 minutes = 5 minutes 
Therefore, the average time for a customer to clear the system is 5 minutes. However, since the question asks about how long it takes for the average customer to clear the system, we need to divide by the arrival rate: 
5 minutes / 20 customers/hour = 0.25 hours or 15 minutes 
Finally, we round up to get the best choice: 6 minutes.

Question 7

A steady stream of eager fresh-faced students waits in line to register for spring semester classes. Students arrive at the rate of 100 per hour and it takes the registrar 30 seconds to check their schedule and verify they have paid in full. What is the average time waiting in line and the average number of people in line? How busy is the registrar?

Accepted Answer

The answer of A steady stream of eager fresh-faced students...

Question 8

Business at the Kwik-E-Mart is brisk, with one customer arriving at a rate of six per hour on average. Ringing up purchases is an easy matter for owner/operator Apu; he can usually do so in 2 minutes. If both arrival and service rates are Poisson distributed, how many customers are in the store on average?

Accepted Answer

First, we need to calculate the arrival rate (λ) and service rate (µ):
λ = 6 customers per hour
µ = 30 customers per hour (since 2 minutes = 1/30 hour)
Next, we need to calculate the utilization factor (ρ = λ/µ):
ρ = 6/30 = 0.2
If ρ is less than 1, we can use Little's Law to calculate the average number of customers in the store (L):
L = λ/(µ-λ) = 6/(30-6) = 0.25
Therefore, on average, there are 0.25 customers in the store at any given time. The best choice is C.

Question 9

In operations and supply chain environments that must deal with random demand and variable processing times, it is virtually impossible to achieve very high capacity utilization levels and still provide acceptable customer service.

Accepted Answer

Random demand and variable processing times can cause capacity utilization to fluctuate, making it difficult to maintain high levels while still meeting customer demands. This is a common challenge in operations and supply chain management.

Question 10

A busy toll highway that has four toll collectors for northbound traffic is an example of a single-channel, single-phase system.

Accepted Answer

A single-channel, single-phase system has only one service channel and one phase of operation. In this case, there are multiple toll collectors serving the northbound traffic, making it a multi-channel system.

Question 11

Wally's Filling Station is manned by one capable attendant that can fill your tank and check your tires, oil, and water in 5 minutes. If four customers arrive each hour, and the service and arrival rates are governed by the Poisson distribution, what is the utilization of the attendant?

Accepted Answer

The utilization of the attendant is the ratio of the average service time to the average interarrival time. The average service time is 5 minutes, and the average interarrival time is 15 minutes (since four customers arrive each hour). Therefore, the utilization of the attendant is 5/15 = 0.33.

Quiz 6: Managing Capacity