Checker Credit Service provides credit information to its customers throughout the country twenty-four hours a day. Rosalind Hanks is the manager of phone services. She supervises credit reps who answer customer calls. From historical data she has estimated that the following number of credit reps are needed during various times of the day.
|
Time Period |
No. of Reps Needed |
|
Midnight to 4 AM |
3 |
|
4 AM to 8 AM |
6 |
|
8 AM to Noon |
13 |
|
Noon to 4 PM |
15 |
|
4 PM to 8 PM |
12 |
|
8 PM to Midnight |
9 |
Employees work shifts of eight consecutive hours, and shifts can start at the beginning of any of the six periods shown in the table. Ms. Hanks has complete freedom in deciding the number of days each employee works each week, so she is interested only in knowing how many employees should start work at the beginning of each time period to minimize the total number of employees needed each day. (15 points)
(a) Formulate the problem as a linear program to determine the minimum number of employees that should start at the beginning of each time period. Include the objective, decision variables, and constraints (Hint: there will be six decision variables).
(b) Solve the problem presented in part (a) using Microsoft Excel solver.
(c) Suppose full-time employees were paid $8 per hour, and suppose part-time employees could be hired to work four-hour shifts for $5 per hour. But part-time employees are only half as efficient as full-time employees (i.e. Checker needs two part-time employees to do the work of one full-time employee). Formulate and solve the new problem to minimize cost by determining the number of part-time and fulltime employees that should start at the beginning of each time period using solver.
