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 employees that will minimize labor costs and still provide excellent customer service. The average 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.

Total Number

Time 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?