Problem 4-25 (Algorithmic)

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.

Time	Total # of Employees Needed
11 AM-Noon	9
Noon-1PM	9
1PM-2PM	9
2pm-3pm	3
3pm-4pm	3
4pm-5pm	3
5pm-6pm	6
6pm-7pm	12
7pm-8pm	12
8pm-9pm	7
9pm-10pm	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. Optimal schedule for part-time employees:

Starting Time	Number of part- time employees
11:00 A.M.
12:00 P.M.
1:00 P.M.
2:00 P.M.
3:00 P.M.
4:00 P.M.
5:00 P.M.
6:00 P.M.

b. What is the total payroll for the part-time employees? If required, round your answer to the nearest dollar. Total daily salary cost = $ 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.

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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. Optimal schedule for part-time employees:

Starting Time	Number of part- time employees (4-hour shifts)	Number of part- time employees (3-hour shifts)
11:00 A.M.
12:00 P.M.
1:00 P.M.
2:00 P.M.
3:00 P.M.
4:00 P.M.
5:00 P.M.
6:00 P.M.
7:00 P.M.

How many part-time shifts are needed? _____ What is the cost savings compared to the previous schedule? If required, round your answer to the nearest cent. ______ Total cost reduced to $ .