Staff Management at a Call Center
Problem Description
"Green River" hospital has a call center that helps to schedule doctors' appointments for patients (callers), schedule lab work, register new patients, etc. The call center operates from 7am to 9pm during the weekdays. As more patients are using the call center, a number of issues have arisen. Often, patients call to schedule an appointment about a health condition without knowing exactly to which department it should be directed. As a result, they spend a significant amount of time on the phone being transferred from one department to the other until they contact the most appropriate department, deferring other callers. The hospital has received complaints from patients about the long waiting times to schedule an appointment. The managers are concerned about the inefficiency of operations at the call center. They think that the call center is understaffed; however, they are not sure about how many employees to hire and how to schedule their working hours. A team of employees was assigned to observe the operations at the call center. The team observed the number of phone calls received during the operating hours. They considered seven time periods, each two hours long. Table 1 presents the expected number of calls per time period.
|
Hour
|
Expected No. Of Calls
|
|
7A.M. - 9 A.M.
|
55 calls
|
|
9 A.M. - 11 A.M.
|
90 calls
|
|
11 A.M. - 1 P.M.
|
80 calls
|
|
1 P.M. - 3 P.M.
|
93 calls
|
|
3 P.M. - 5 P.M.
|
85 calls
|
|
5 P.M. - 7 P.M.
|
45 calls
|
|
7 P.M. - 9 P.M.
|
20 calls
|
The team found out that an operator is able to process on average six calls per hour. The call center has part-time and full-time employees. The full-time employees work eight hours a day, and they can either begin working at 7A.M., 9A.M., 11A.M., or 1P.M. Full-time employees get paid $14 per hour for work before 5P.M. and $16 per hour after 5P.M. The part-time employees work only four hours a day, and they can begin work either at 1P.M., 3P.M., or 5P.M. Part-time employees get paid $10 per hour for work before 5P.M. and $12 per hour after 5P.M.
The aim of this project is to build a decision support system to manage the staff of the call center. We provide a mathematical model to solve this problem.
Integer Programming Model
The decision variables for this problem are as follows:
x1 The total number of full-time employees who work from 7A.M. to 3P.M. Their salary is $112 per day.
x2 The total number of full-time employees who work from 9A.M. to 5P.M. Their salary is $112 per day.
x3 The total number of full-time employees who work from 11A.M. to 7P.M. Their salary is $116 per day.
x4 The total number of full-time employees who work from 1P.M. to 9P.M.
Their salary is $120 per day.
x5 The total number of part-time employees who work from 1P.M. to 5P.M.
Their salary is $40 per day.
x6 The total number of part-time employees who work from 3P.M. to 7P.M.
Their salary is $44 per day.
x7 The total number of part-time employees who work from 5P.M. to 9P.M.
Their salary is $48 per day.
min :112x1 +112x2 +116x3 +120x4 + 40x5 + 42x6 + 44x7 + 46x8 + 48x9 Subject to:
x1≥ 55 6 x1 + x2 ≥ 90 6
x1 + x2 + x3 ≥ 80 6 x1 + x2 + x3 + x4 + x5 ≥ 93 6 x2 + x3 + x4 + x5 + x6 ≥ 85 6 x3 + x4 + x6 + x7 ≥ 45 6 x4 + x7 ≥ 20 6
x1,...,x7 ≥ 0 x1,...,x7 int
The objective is to minimize the total cost of operating the call center.
User Interface
1. Build a welcome form.
2. Build a data analysis form. The following are suggestions to help you design this form.
a. Insert a command button that, when clicked on, solves the problem using Excel.
b. Insert a frame titled "Reports" that includes a number of option buttons. The option buttons allow the user to select any of the reports described below. Insert a command button that, when clicked -on, opens the report selected by the user.
c. Insert a frame titled "Sensitivity Analysis." This frame allows the user to select a parameter to perform the sensitivity analysis. The user may be interested in observing the sensitivity of the optimal solution with respect to the following: changes in the hourly rate payment of full-time and part-time employees; distribution of phone calls received throughout the day; etc. Include in this frame text boxes, option buttons, check boxes, combo boxes, and command buttons as needed.
Design a logo for this project. Insert this logo in the forms created above. Pick a background color and a font color for the forms created. Include the following in the forms created: record navigation command buttons, record operations command buttons, and form operations command buttons as needed.
Reports
1. Report the optimal number of full-time and part-time employees to work in each shift. Report the optimal cost of operating the call center.
2. Present the results from the sensitivity analysis.