Brewer Services contracts with outsourcing partners to handle various customer service functions. The customer service department is open Monday through Friday from 8 a.m. to 5 p.m. Calls vary over the course of a typical day. Based on a study of call volumes provided by one of the firm’s partners, the minimum numbers of staff needed each hour of the day are:
HourMinimum Staff Required
8–9 ……………………………………5
9–10 …………………………………..12
10–11 …………………………………16
11–noon ………………………………12
Noon–1 ………………………………11
1–2 ……………………………………16
2–3 ……………………………………17
3–4 ……………………………………18
4–5 ……………………………………14
Mr. Brewer wants to hire some permanent employees and staff the remaining requirements using part-time employees who work four-hour shifts (four consecutive hours starting as early as 8 a.m. or as late as 1 p.m.). Develop and solve an integer optimization model to answer the following questions.
a. Suppose Mr. Brewer uses five permanent employees. What is the minimum number of part-time employees he will need for each four-hour shift to ensure meeting the staffing requirements?
b. What if he uses 11 permanent employees?
c. Investigate other possible numbers of permanent employees between 5 and 15, compare the differences, and make a recommendation.