Quantiative Methods

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 hours shifts during peak meal times. On Saturdays the steakhouse is open from 11:00A to 10:00P. 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:

Time Total Number of
Employees Needed

11:00A-Noon 9
Noon-1:00P 9
1:00P-2:00P 9
2:00P-3:00P 3
3:00P-4:00P 3
4:00P-5:00P 3
5:00P-6:00P 6
6:00P-7:00P 12
7:00P-8:00P 12
8:00P-9:00P 7
9:00P-10:00P 7

One-full time employee comes on duty at 11:00A, works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00P 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 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?

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  1. This is a challenging assignment and will probably take at least an hour to complete. Good luck! :-)

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    Ms. Sue
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