Dupit Corporation

The Dupit Corporation is a long-term leader in the office photocopier marketplace. One reason for this leadership
position is the service the company provides its customers. Dupit has enjoyed a reputation of excellent service and
intends to maintain that reputation.

Dupit has a service division that is responsible for providing high-quality support to the company’s customers by promptly
repairing the Dupit machines when needed. This work is done on the customer’s site by the company’s service technical
representatives, more commonly known as tech reps.

Each tech rep is given responsibility for a specified territory. This enables providing personalized service, since a
customer sees the same tech rep on each service call. The tech rep generally feels like a one-person territory manager and
takes pride in this role.

John Fickitt is the Dupit senior vice president in charge of the service division. He has spent his entire career with the
company, and actually began as a tech rep. While in this initial position, John took classes in the evening for several years
to earn his business degree. Since then, he has moved steadily up the corporate ladder. He is well respected for his sound
judgment and his thorough understanding of the company’s business from the ground up.

John’s years as a tech rep impressed upon him the importance of the tech rep’s role as an ambassador of the company to
its customers. He continues to preach this message regularly. He has established high personnel standards for becoming
and remaining a tech rep and has built up the salaries accordingly. The morale in the division is quite high, largely
through his efforts.

John also emphasizes obtaining regular feedback from a random sample of the company’s customers on the quality of the
service being provided. He likes to refer to this as keeping his ear to the ground. The customer feedback is channeled to
both the tech reps and management for their information.

Another of John’s themes is the importance of not overloading the tech reps. When he was a tech rep himself, the
company policy had been to assign each tech rep enough machines in his or her territory that the tech rep would be active
repairing machines 90 percent of the time (during an eight-hour working day). The intent was to maintain a high
utilization of expensive personnel while providing some slack so that customers would not have to wait very long for
repairs. John’s own experience was that this did not work very well. He did have his idle periods about 10 percent of the
time, which was helpful for catching up on his paperwork and maintaining his equipment. However, he also had frequent
busy periods with many repair requests, including some long ones, and a large backlog of unhappy customers waiting for
repairs would build up.

Therefore, when he was appointed to his current position, one of his first moves was to make the case to Dupit top
management that tech reps needed to have more slack time to ensure providing prompt service to customers. A major part
of his argument was that customer feedback indicated that the company was failing to deliver on the second and third part
of the company slogan given below.

1. High-quality products.
2. High-quality service.
3. All delivered efficiently.

The company president had been promoting this slogan for years and so found this argument persuasive. Despite
continuing pressure to hold costs down, John won approval for changing company policy regarding tech reps as
summarized below.

Current Policy: Each tech rep’s territory should be assigned enough machines so that the tech
rep will be active repairing machines (or traveling to the repair site) approximately 75 percent
of the time. When working continuously, each tech rep should be able to repair an average of
four machines per day (an average of two hours per machine, including travel time). Therefore,
to minimize customer waiting times, the goal is to have an average of three repair calls per
 working day. Since the company’s machines now are averaging 50 workdays between needing
repairs, the target is to assign approximately 150 machines to each tech rep’s territory.

Under this policy, the company now has nearly 10,000 tech reps, with a total payroll (including benefits) of approximately
$600 million per year.

Dupit has had a long succession of very successful products that has maintained its position as a market leader for many
years. Furthermore, its latest product has been a particularly big winner. It is a color printer-copier that collates, staples,
and so on, as well as having faxing capabilities. Thus, it is a state-of-the-art, all-in-one copier for the modern office.
Sales have even exceeded the optimistic predications made by the vice president for marketing.

However, this success also has brought its problems. The fact that the machine performs so many key functions makes it
a vital part of the purchaser’s office. The owner has great difficulty in getting along without it for even a few hours when
it is down requiring repair. Consequently, even though the tech reps are giving the same level of service as they have in
the past, complaints about intolerable waits for repairs have skyrocketed.

This crisis has led to an emergency meeting of top management, with John Fickitt the man on the spot. He assures his
colleagues that service has not deteriorated in the least. There is agreement that the company is a victim of its own
success. The new machine is so valuable that a much higher level of service is required .

After considerable discussion about how to achieve the needed service, Dupit’s president suggests the following four-step
approach to dealing with the problem.

1. Agree on a tentative new standard for the level of service that needs to be provided.
2. Develop some proposals for alternative approaches that might achieve this standard.
3. Have an operations management team work with John Fickitt to analyze these alternative
approaches in detail to evaluate the effectiveness and cost of each one.
4. Reconvene this group of top management to make a final decision on what to do.

The group agrees.

Discussion then turns to what the new standard should be for the level of service. John proposes that this standard should
specify that a customer’s average waiting time before the tech rep can respond to the request for a repair should not
exceed some maximum quantity. The customer relation’s manager agrees and argues that this average waiting time
should not exceed two hours (versus about six hours now). The group agrees to adopt two hours as the tentative standard,
pending further analysis by the management science team.

Proposed New Service Standard: The average waiting time of customers before the tech rep begins the trip to the
customer site to repair the machine should not exceed two hours (T q < 2 hours).

After further discussion of various ideas about how to meet this service standard, the meeting concludes. The president
asks the participants who had proposed some approach to think further about their idea. If they conclude that their idea
should be a particularly sound approach to the problem, they are to send him a memorandum supporting that approach.
The president subsequently receives memoranda’s supporting the approaches summarized below.

Approach Suggested by John Fickitt: Modify the current policy by decreasing the percentage
of time that tech reps are expected to be active repairing machines. This involves simply
decreasing the number of machines assigned to each tech rep and adding more tech reps. This
approach would enable continuing the mode of operation for the service division that has served
the company so well in the past while increasing the level of service to meet the new demands of
the marketplace.

Approach Suggested by Vice President for Engineering: Provide a new-state-of-the-art

equipment to the tech reps that would substantially reduce the time required for the longer
repairs. Although expensive, this would significantly reduce the average repair time. Perhaps
 more importantly, it would greatly reduce the variability of repair times, which might decrease
average waiting times for repairs.

The new equipment would cost $50,000 per tech rep. It would reduce the mean service time
from the current 2 hours to 1.6 hours. In addition, the standard deviation of service time ()
would go down from 2 hours to 0.8 hours.

Approach Suggested by the Chief Financial Officer: Replace the current one-person tech rep
territories by larger territories that would be served by multiple tech reps. Having teams of tech
reps to back each other up during busy periods might decrease average waiting times for repairs
enough that the company would not need to hire additional tech reps.

The president is pleased to have three promising approaches to consider. As previously agreed, his next step is to set up
an operations management team (three from the company plus an outside consultant) to work with John Fickitt in
analyzing these approaches in detail. They are to report back to top management with their results and recommendations
in six weeks.

The operations management team quickly recognizes that queueing theory will be a key technique for analyzing this
problem. In particular, each tech rep’s territory can be viewed as including the basic queueing system described below.

The Queueing System for Each Tech Rep

1. The customers: The machines needing repair.
2. Customer arrivals: The calls to the tech rep on his or her cellular telephone requesting repairs.
3. The queue. The machines waiting for repair to begin at their sites.
4. The server: The tech rep.
5. Service time. The total time the tech rep is tied up with a machine, either traveling to the machine site or repairing the
machine. (Thus, a machine is viewed as leaving the queue and entering service when the tech rep begins the trip to the
machine site.)

With the approach suggested by the Chief Financial Officer (enlarge the territories with multiple tech reps for each
territory), this single-server queueing system would be changed to a multiple-server queueing system.

1. Find the minimum total cost for each of the three alternatives to provide the required service (T q < 2 hours). Show
your calculations. Identify the least-cost alternative.

2. Suggest another (fourth) alternative that may be effective in meeting customer expectations. [You are not required to
provide any analysis.]