Chapter 4: Linear Programming Applications in Marketing, Finance, and Operations Management 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 AM 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 of Employees Needed 9 Time 11:00 A.M.-Noon Noon1:00 P.M. 1:00 P.M.-2:00 P.M. 2:00 P.M.-3:00 P.M. 3:00 P.M.-4:00 PM 4:00 P.M.-5:00 P.M. 5:00 PM-6:00 PM 6:00 P.M.-7:00 P.M. 7:00 PM - 8:00 PM 8:00 P.M. 9:00 P.M. 9:00 P.M.-10:00 P.M. 3 3 3 6 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? (Refer to self-test 25, Page 201; An Introduction to Management Science: Quantitative Approaches to Decision Making, Revised Thirteenth Edition. David R. Anderson, Dennis J. Sweeney) 1 Page Problem B: 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 AM 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 of Employees Needed 9 3 Time 11:00 A.M.-Noon Noon1:00 P.M. 1:00 P.M.-2:00 P.M. 2:00 P.M.-3:00 P.M. 3:00 P.M.-4:00 PM 4:00 P.M.-5:00 P.M. 5:00 PM-6:00 PM 6:00 P.M.-7:00 PM 7:00 PM 8:00 PM 8:00 P.M.-9:00 P.M. 9:00 PM 10:00 PM 3 3 6 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? - (Refer to self-test Page 201; An Introduction to Management Science: Quantitative Approaches to Decision Making, Revised Thirteenth Edition. David R. Anderson, Dennis J. Sweeney) 2 Page Chapter 4: Linear Programming Applications in Marketing, Finance, and Operations Management 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 AM 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 of Employees Needed 9 Time 11:00 A.M.-Noon Noon1:00 P.M. 1:00 P.M.-2:00 P.M. 2:00 P.M.-3:00 P.M. 3:00 P.M.-4:00 PM 4:00 P.M.-5:00 P.M. 5:00 PM-6:00 PM 6:00 P.M.-7:00 P.M. 7:00 PM - 8:00 PM 8:00 P.M. 9:00 P.M. 9:00 P.M.-10:00 P.M. 3 3 3 6 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? (Refer to self-test 25, Page 201; An Introduction to Management Science: Quantitative Approaches to Decision Making, Revised Thirteenth Edition. David R. Anderson, Dennis J. Sweeney) 1 Page Problem B: 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 AM 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 of Employees Needed 9 3 Time 11:00 A.M.-Noon Noon1:00 P.M. 1:00 P.M.-2:00 P.M. 2:00 P.M.-3:00 P.M. 3:00 P.M.-4:00 PM 4:00 P.M.-5:00 P.M. 5:00 PM-6:00 PM 6:00 P.M.-7:00 PM 7:00 PM 8:00 PM 8:00 P.M.-9:00 P.M. 9:00 PM 10:00 PM 3 3 6 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? - (Refer to self-test Page 201; An Introduction to Management Science: Quantitative Approaches to Decision Making, Revised Thirteenth Edition. David R. Anderson, Dennis J. Sweeney) 2 Page