6 4 8 The Northside Bank is working to develop an efficient work schedule for full-time and part-time tellers. The sched

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6 4 8 The Northside Bank Is Working To Develop An Efficient Work Schedule For Full Time And Part Time Tellers The Sched 1 (46.48 KiB) Viewed 76 times

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6 4 8 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 open from 9:00 AM 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. 2:00 p.m.-3:00p.m. 6 10:00 am-11:00a.m. 3:00p.m.-4:00p.m. 4 11:00a.m.-Noon 4:00 pm-5:00p.m. 7 Noon-1:00p.m. 10 5:00 pm-6:00p.m. 6 1:00p.m-2:00p.m. 9 6:00 pm - 7:00 pm 6 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 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 = nu number of part-time employees coming on duty at the beginning of hour If your answer is zero enter"0and if the constant is "1" it must be entered in the box 1 X9 + X10 19 Y10+ Y12 + 72 Min K11 + Y11 + y + X9 x10 11. + Y10+ V!! + 712 + 71 Y2+ x9 + X10 X11 YO+ Y10 + 711 + Y12 + v1 + 72 x9. X10 X11 y + Y10 - VII + 712 + V1 Y2 x9 + X10 + X11 + 710 + 711 + 712 + Y1+ 72 + x9. x10+ X11 Y9+ Y10+ 711 + 712 + y + Y2+ x9 + X10 X11 + Y10 + 711 + Y12 + Y1+ Y2 x9 X10 + x11 Y9+ Y10 711 + y12 + y + Y2 x9 + X10 - x11 y + Y10+ y11 + Y12 + Y1 + 72 +
(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 = nu number of part-time employees coming on duty at the beginning of hour 1.) If your answer is zero enter "O" and if the constant is "1" it must be entered in the box. Min 1 x9 + X10 + X11 + 1 yg + s.t. yio + Y11 + x9 + y12 + X10 + y + X11 + Y2 + 79 + y10 + 711 + X9 + y12 + X10 + y + X11 + 72 + yg + Y10+ x9 + 711 + y12 + X10 + y1 X11 Y2 + yg + Y10 + 711 + x9 + Y12 + X10 + yl X11 + Y2+ yg + Y10 - x9 + Y11 + y12 - X10 + y1 X11 Y2+ 79 + Y10 Y11 + x9 + Y12 + X10 + Y1 X11 Y2 yg + YO x9 + Y11 y12 X10 + y1 Y2 y9+ Y10 711 + x9 + Y12 X10 y + X11+ Y2 yg + Y10+ x9 Y11 y12 X10 + x11 + y + Y2+ YO+ 710 + 711 + x9+ y12 X10 y + X11 Y2 y9 Y10 120 and integer for/= 9, 10, 11 and) - 9, 10, 11, 12, 1, 2, 3 Y11 Y12 Y1 + Y2 (b) Solve the LP Relaxation of your model in part (n). 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 "o". Total Number of Full-Time Employees: Total Number of Part-Time Employees:
he box. y10 + y11 + y12 + y + y2 + y3 Y10 + y11 + y12 + y1 + y2 + y3 Select your answer y10 + 711 - Y12 + Y1 + y2 + y3 Select your answer y10+ Y11 Y12 + Y + Y2+ y3 Select your answer 10 + 711 - Y12 + y + y2 + 710 + 711 + Y12 + y + V2 + Time (9:00a.m.-10:00a.m.) Time (10:00 am-11:00 a.m.) Time (11:00a.m.-Noon.) Time (Noon. 1:00 p.m.) Time (1:00p.m.-2:00p.m.) Time (2:00 pm-3:00p.m.) Time (3:00 pm 4:00 p.m.) Time (4:00 p.m.-5:00p.m.) Time (5:00p.m.6:00p.m.) Time (6:00 pm - 7:00 p.m.) y10+ V11 + Y12 + y2 + y10+ 711 + Y12 + y + y3 Select your answer - y3 Select your answer y3 Select your answer Y3 Select your answer Y3 Select your answer 3 - Select your answer Y3 - Select your answer y2 + y10+ y11 - Y12 + Y1 + y2 + y10+ 11 - 712+ y + y2- y10+ 711 - Y12 + y + Y2+
(b) Solve the LP Relaxation of your model in part (a). Enter the total cost value under the optimal solution Total Cost: 5 (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-tin 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 employe If required, round your answers to the nearest whole number. If your answer is zero enter "o" Total Number of Full-Time Employees: Total Number of Part-Time Employees: Total Cost: $
er the optimal solution part-time employees required. ditional 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 | 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. zero enter "0"