The Northshore Bank is working to develop an efficient work schedule

| August 30, 2017

Question
The Northshore 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 customerservice during each hour of operation is summarized here:

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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:Letxi= number of full-time employees coming on duty at the beginning of houriandyi= number of part-time employees coming on duty at the beginning of houri.) ?

B.Solve the LP Relaxation of your model in part a. ?

C.Solve your model in part a for the optimal schedule of tellers. Comment on the solution. ?

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 five full-time employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. ?

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