The Northside Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. On Fridays, the bank is open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here. Time No. of Tellers Time No. of Tellers 9:00 a.m.-10:00 a.m. 6 2:00 p.m.-3:00 p.m. 7 10:00 a.m.-11:00 a.m. 5 3:00 p.m.-4:00 p.m. 6 11:00 a.m.-Noon 7 4:00 p.m.-5:00 p.m. 8 Noon-1:00 p.m. 11 5:00 p.m.-6:00 p.m. 7 1:00 p.m.-2:00 p.m. 9 6:00 p.m.-7:00 p.m. 5 Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day). (a) Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let xi = number of full-time employees coming on duty at the beginning of hour i and yj = number of part-time employees coming on duty at the beginning of hour j.) If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. (b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. Total Cost: $ (c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. If your answer is zero enter “0”. Total Number of Full-Time Employees: Total Number of Part-Time Employees: (d) After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full-time and part-time employees required and the total cost under the revised optimal solution. If required, round your answers to the nearest whole number. If your answer is zero enter “0”. Total Number of Full-Time Employees: Total Number of Part-Time Employees: Total Cost: $

The Northside Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. On Fridays, the bank is open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here. Time No. of Tellers Time No. of Tellers 9:00 a.m.-10:00 a.m. 6 2:00 p.m.-3:00 p.m. 7 10:00 a.m.-11:00 a.m. 5 3:00 p.m.-4:00 p.m. 6 11:00 a.m.-Noon 7 4:00 p.m.-5:00 p.m. 8 Noon-1:00 p.m. 11 5:00 p.m.-6:00 p.m. 7 1:00 p.m.-2:00 p.m. 9 6:00 p.m.-7:00 p.m. 5 Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day). (a) Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let xi = number of full-time employees coming on duty at the beginning of hour i and yj = number of part-time employees coming on duty at the beginning of hour j.) If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. (b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution. Total Cost: $ (c) Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required. If your answer is zero enter “0”. Total Number of Full-Time Employees: Total Number of Part-Time Employees: (d) After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full-time and part-time employees required and the total cost under the revised optimal solution. If required, round your answers to the nearest whole number. If your answer is zero enter “0”. Total Number of Full-Time Employees: Total Number of Part-Time Employees: Total Cost: $

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

Time	No. of Tellers	Time	No. of Tellers
9:00 a.m.-10:00 a.m.	6	2:00 p.m.-3:00 p.m.	7
10:00 a.m.-11:00 a.m.	5	3:00 p.m.-4:00 p.m.	6
11:00 a.m.-Noon	7	4:00 p.m.-5:00 p.m.	8
Noon-1:00 p.m.	11	5:00 p.m.-6:00 p.m.	7
1:00 p.m.-2:00 p.m.	9	6:00 p.m.-7:00 p.m.	5

Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day).

(a)	Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let x_i = number of full-time employees coming on duty at the beginning of hour i and y_j = number of part-time employees coming on duty at the beginning of hour j.)
	If your answer is zero enter “0” and if the constant is "1" it must be entered in the box.

(b)	Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution.
	Total Cost: $

(c)	Solve for the optimal schedule of tellers. Enter the total number of full-time and part-time employees required.
	If your answer is zero enter “0”.
	Total Number of Full-Time Employees:
	Total Number of Part-Time Employees:

(d)	After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least four full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full-time and part-time employees required and the total cost under the revised optimal solution.
	If required, round your answers to the nearest whole number. If your answer is zero enter “0”.
	Total Number of Full-Time Employees:
	Total Number of Part-Time Employees:
	Total Cost: $

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Definition Definition Benefits in addition to compensation that companies give to their employees. Fringe benefits can boost morale and productivity and keep employees motivated. Companies often use fringe benefits as a competitive advantage to recruit and retain employees. Examples of fringe benefits include pensions, vacation time, tuition reimbursement, free or subsidized meals, and gym memberships.

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