Case Study: ABC Hospital has been receiving numerous customer complaints because of its
confusing, decentralised appointment and registration process. When customers
want to make appointments or register child patients, they must contact the clinic
or department they plan to visit. Several problems exist with this current strategy.
Parents do not always know the most appropriate clinic or department they must
visit to address their children's ailments. They therefore spend a significant
amount of time on the phone being transferred from clinic to clinic until they reach
the most appropriate clinic for their needs.The hospital also does not publish the phone numbers of all clinics and
departments, and parents must therefore invest a large amount of time in
detective work to track down the correct phone number. Finally, the various
clinics and departments do not communicate with each other. For example, when
a doctor schedules a referral with a colleague located in another department or
clinic, that department or clinic almost never receives word of the referral. The
parent must contact the correct department or clinic and provide the needed
referral information.In efforts to reengineer and improve its appointment and registration process, the
children's hospital has decided to centralise the process by establishing one call
center devoted exclusively to appointments and registration. The hospital is
currently in the middle of the planning stages for the call center. Jane Davison, the
hospital manager, plans to operate the call center from 7 AM to 9 PM during the
weekdays.Several months ago, the hospital hired an ambitious management-consulting firm,
XYZ Consultants, to forecast the number of calls the call center would receive each
hour of the day. Since all appointment and registration-related calls would be
received by the call center, the consultants decided that they could forecast the
calls at the call center by totaling the number of appointment and registrationrelated
calls received by all clinics and departments. The team members visited all
the clinics and departments, where they diligently recorded every call relating to
appointments and registration. They then totaled these calls and altered the totals
to account for calls missed during data collection. They also altered totals to
account for repeat calls that occurred when the same parent called the hospital
many times because. of the confusion surrounding the decentralised process. XYZ
Consultants determined the average number of calls the call center should expect
during each hour of a weekday. The following table provides the forecasts.
Work Shift Average Number of Calls.
After the consultants submitted these forecasts, Jane became interested in the
percentage of calls from Italian speakers since the hospital services many Italian
patients. Jane knows that he has to hire some operators who speak Italian to
handle these calls. The consultants performed further data collection and
determined that, on average, 20 percent of the calls were from Italian speakers.
Given these call forecasts, Jane must now decide how to staff the call center during
each two-hour shift of a weekday. During the forecasting project, XYZ Consultants
closely observed the operators working at the individual clinics and departments
and determined the number of calls operators process per hour. The consultants
informed Jane that an operator is able to process an average of six calls per hour.
Jane also knows that he has both full-time and part-time workers available to staff
the call center. A full-time employee works eight hours per day, but because of
paperwork that must also be completed, the employee spends only four hours per
day on the phone. To balance the schedule, the employee alternates the two-hour
shifts between answering phones and completing paperwork. Full-time
employees can start their day either by answering phones or by completing
paperwork on the first shift. The full-time employees speak either Italian or
English, but none of them are bilingual. Both Italian-speaking and Englishspeaking
employees are paid $10 per hour for work before 5 PM and $12 per hour
for work after 5 PM. The full-time employees can begin work at the beginning of
the 7 AM to 9 AM shift, 9 AM to 11 AM shift, 11 AM to 1 PM shift, or 1 PM to 3 PM
shift. The part-time employees work for four hours, only answer calls, and only
speak English. They can start work at the beginning of the 3 PM to 5 PM shift or
the 5 PM to 7 PM shift, and, like the full-time employees, they are paid $10 per
hour for work before 5 PM and $12 per hour for work after 5 PM.
For the following analysis, consider only the labor cost for the time employees
spend answering phones. The cost for paperwork time is charged to other cost
centers.
a. How many Italian-speaking operators and how many English-speaking
operators does the hospital need to staff the call center during each twohour
shift of the day in order to answer all calls? Please round up the results
to provide an integer number since half a human operator makes no sense.
b. Jane needs to determine how many full-time employees who speak Italian,
full-time employees who speak English, and part-time employees he
should hire to begin on each shift. XYZ Consultants advises him that linear
programming can be used to do this in such a way as to minimise operating
costs while answering all calls. Formulate a linear programming model of
this problem. Then obtain an optimal solution for the formulated linear
programming model to guide Jane's decision using Solver in Excel. You
must submit an Excel file along with the report to show how you solve the
problem.
c. Because many full-time workers do not want to work late into the evening,
Jane can find only one qualified English-speaking operator willing to begin
work at 1 PM. Given this new constraint, how many full-time Englishspeaking
operators, full-time Italian-speaking operators, and part-time
operators should Jane hire for each shift to minimise operating costs while
answering all calls? You must solve this scenario on a separate sheet in the
same Excel file.
d. Jane now has decided to investigate the option of hiring bilingual operators
instead of monolingual operators. If all the operators are bilingual, how
many operators should be working during each two-hour shift to answer
all phone calls? As in part a, please provide an integer answer.
e. If all employees are bilingual, how many full-time and part-time employees
should Jane hire to begin on each shift to minimise operating costs while
answering all calls? As in part b, formulate a linear programming model
and obtain an optimal solution to guide Jane's decision. You must submit an
Excel file along with the report to show how you solve the problem.
f. What is the maximum percentage increase in the hourly wage rate that Jane
can pay bilingual employees over monolingual employees without
increasing the total operating costs?
g. Based on part e, if the average number of phone calls on the 9AM–11AM
shift is increased and causes the number of operators needed for that shift
to increase by 1, how does this affect operating costs? You must conduct
sensitivity analysis based on part e.

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