Question

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, but the temp agency managing the part time staff will charge the steakhouse one extra dollar per hour for shifts starting after 3:00 PM. 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 11:00 a.m. - Noon 9 9 Noon - 1:00 p.m. 1:00 p.m. - 2:00 p.m. 2:00 p.m. - 3:00 p.m. 10 3 3:00 p.m. - 4:00 p.m. 3 4:00 p.m. - 5:00 p.m. 4 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 7 8:00 p.m. - 9:00 p.m. 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. 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?

Answer 1

a) Excel is used to determine the minimum cost schedule

16 SUMD2012) Sateer Pererater Oyun Employees Number of Full time Number of Part time Total employees 1 Tune needed employees employees on duty 2 11 AM TO 12 PM 9 12 PM to 1PM 9 1PM 2PM 10 2PM to 3 PM 3 10 3PM 4PM 3 7 4 PM SPM 3 7 8 SPM 6PM 6 9 6 1 2 12 7 14 10 PM 12 11 PM to 9 PM > . . 129 PM to 10 PM 7 8 13 Total 20 14 Our 16 Els carred Variable negatie Salary cost 17 Select the creators See the rolex 0 А Employees 1 Time needed 2 11 AM to 12 PM 9 3 12 PM to 1PM 9 4 1PM to 2 PM 9 5 2 PM to 3 PM 3 6 3PM to 4 PM 3 7 4 PM to 5 PM 3 8 5PM to 6 PM 6 9 6 PM to 7 PM 12 10 7 PM to 8 PM 12 11 8PM to 9 PM 7 12 9PM to 10 PM 7 13 14 15 She с D E Number of Full Number of Part- time employees time employees Total employees on duty 1 18 1=SUM(C2:02) =SUM(C3:03)+E2 1 0 =SUM(C4:04)+E3 0 =SUM(C5:05)+E4 2 =SUM(C6:06)+E5-D2-C2 3 =SUM(C7:07)+E6-D3+C2 o =SUM(C8:08)+E7-D4-C4 7 =SUM(09:09)+E8-05+C4 0 =SUM(C10:010)+E9-06 0 =SUM(C11:011)+E10-07-C2 =SUM(C12:012)+E11-08 Total =SUM(D2:012) 16 Salary cost = =D13*4*7.6 17

Optimal schedule for part-time employees

Number of part Starting Time time employees 11:00 A.M. 8 8 12:00 PM 0 1:00 PM 0 2:00 P.M. 0 3:00 P.M. 2 4:00 P.M. 0 5:00 PM 6:00 P.M.

Total daily salary cots= $608

How many part time shifts are needed? 20

b) Revised LP formulation is as follows:

16 Tue A Te: Oon So the Corso Employees needed 2 AM 12PM 212 PM to 1PM 9 4 PM to 2 PM 2 PM to 3 PM 5 PM & PM 9 7 4 PM to 5PM SPM to 6 PM 6 SPM to 7 PM 12 30 7PM 8PM 12 1 PM to 9 PM 7 12 9PM to 10 PM 7 Number of Nurmber of Part Number of Part Full time time employees time employees Total employees employees (4 how shit) 13 hours shift) 1 8 0 9 0 . 11 0 3 1 3 0 0 4 6 6 0 12 0 0 12 0 7 0 7 Total 14 34 Marconstad Valente taong the Salary cost re folie Formula are following 0 8 0 0 4 0 1 5 0 0 Number of Part- Employees Number of Full Number of Part-time time employees (3 Time needed time employees employees (4 hours shift) hours shift) Total employees on duty 2 11 AM to 12 PM 9 1 =SUM(C2:E2) 3 12 PM to 1PM 9 =SUM(C3:E3)+F2 1 PM to 2 PM 9 =SUM(C4:E4)•F3 2 PM to 3 PM 3 =SUM(CS:E5)•F4-E2 6 3 PM to 4 PM 3 1 =SUM(C6:E6)+F5-D2-C2-E3 7 4 PM to 5 PM 3 =SUM(C7:E7)+F6-D3.C2-E4 8 5PM to 6 PM 6 =SUM(C8:E8)+F7-04-C4-ES 6 PM to 7 PM 12 6 0 =SUM(09:19)• F8-05+C4-E6 10 7 PM to 8 PM 12 0 =SUM(C10:E10)+F9-06-E7 11 BPM to 9 PM 7 0 =SUM(C11:E11)F10-07-C2-E8 12 9PM to 10 PM 7 0 =SUM(C12:E12)+F11-08-E9 13 Total =SUM(D2:012) =SUM(E2:E12) 0 0 0 0 4 9 0 14 15 16 17 Salary cost = =D13*4*7.6+E13'3*7.6

Number of part Number of part- time employees time employees Starting Time (4-hour shifts) (3-hour shifts) 11:00 A.M. 0 12:00 PM 0 1:00 P.M. 0 1 2:00 PM 0 3:00 PM 0 1 4:00 PM 0 5:00 P.M. 0 4 6:00 PM 6 7:00 PM 0

How many part time shifts are needed? 20

Total cost reduced to $501.60