Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 A.M. to 10:00 P.M. Management wants to develop a schedule for part-time employ- ees that will minimize labor costs and still provide excellent customer service. The aver- age wage rate for the part-time employees is $7.60 per hour. The total number of full-time and part-time employees needed varies with the time of day as shown.
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Time
|
Total Number of Employees Needed
|
|
11:00 a.m.-Noon
|
9
|
|
Noon-1:00 p.m.
|
9
|
|
1:00 p.m.-2:00 p.m.
|
9
|
|
2:00 p.m.-3:00 p.m.
|
3
|
|
3:00 p.m.- 4:00 p.m.
|
3
|
|
4:00 p.m.-5:00 p.m.
|
3
|
|
5:00 p.m.- 6:00 p.m.
|
6
|
|
6:00 p.m.-7:00 p.m.
|
12
|
|
7:00 p.m.-8:00 p.m.
|
12
|
|
8:00 p.m.-9:00 p.m.
|
7
|
|
9:00 p.m.-10:00 p.m.
|
7
|
One full-time employee comes on duty at 11:00 A.M., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 P.M. and works the same 4-hours-on, 1-hour-off, 4-hours-on pattern.
a. Develop a minimum-cost schedule for part-time employees.
b. What is the total payroll for the part-time employees? How many part-time shifts are needed? Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts.
c. Assume that part-time employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. How many part-time shifts are needed, and what is the cost savings compared to the previous schedule?