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Category > Accounting Posted 15 Dec 2017 My Price 10.00

Linear Programming

You completed a case study on chase manhattan bank that involved linear programming. I was wondering if the constraints could be changed to 50%?


Linear Programming In order to solve, let Average cost per FT personnel = $10.11 Average cost per overtime personnel hour for FT = $8.08 Average cost per PT personnel = $7.82 Objective function: Minimize = ($10.11)(7)F $10.11 is the cost per hour for FT, 7 is 1 day of work minus lunch hour +[8.08]F1 1 hour overtime 2 hour overtime $7.82 is the cost/hr for PT, 4=hrs/shift Constraints Workforce Requirements 9-10am = (F) + P1+P2+P3+P4 10-11 am 11-12 pm 0.5 reflects lunch time 12-1pm 1-2 pm = (F) + P2+P3+P4+P5+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19 >=55 2-3pm 3-4pm 4-5pm 5-6pm = (F1+F2) +P12+P15+P16+P17+P20+P21+P22 >= 14 6-7pm = (F1+F2) +P16+P19+P21+P22 >= 9 For factor #1 – by corporate policy, part-time personnel hours are limited to a max of 40% of the day’s total requirement. <= 40% (321) 321=number of personnel required F1+3* F2 ≤ F The number of full-time employees doing overtime should be less than or equal to number of full time employees. F2 is multiplied by 3 because each employee can do only 5 hours OT in a week so each employee can do only 2 days of 2 hours OT and so we require 3 sets of people with 2 hours OT per week Excel Model F F1 F2 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22 30 1 8 0 0 0 0 0 0 0 0 9 2 0 0 14 0 0 0 0 0 0 4 1 0 Total Constraint 9-10am 1 1 1 1 1 30 ≥ 14 10-11 am 1 1 1 1 1 1 1 1 1 30 ≥ 25 11-12 pm 0.5 1 1 1 1 1 1 1 1 1 1 1 1 26 ≥ 26 12-1pm 0.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 40 ≥ 38 1-2 pm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 55 ≥ 55 2-3pm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 60 ≥ 60 3-4pm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 51 ≥ 51 4-5pm 1 1 1 1 1 1 1 1 1 1 1 1 1 35 ≥ 29 5-6pm 1 1 1 1 1 1 1 1 1 1 14 ≥ 14 6-7pm 1 1 1 1 1 9 ≥ 9 Additional constraints 25 ≤ 30 123 ≤ 128 Objective Function Minimize total Cost = $3,222.32 1. What is the minimum-cost schedule for the bank? 2. What are the limitations of the model used to answer question 1? F = # of full-time tellers without OT F 1 = # of full-time tellers with 1 hour OT from 5m -6pm F 2 = # of full-time tellers with 2 hours OT 5pm -7pm P 1 = PT tellers who work 4 hrs from 9am to 1pm P 2 = PT tellers who work 5 hrs from 9am to 2pm P 3 = PT tellers who work 6 hrs from 9am to 3pm P 4 = PT tellers who work 7 hrs from 9am to 4pm P 5 = PT tellers who work 4 hrs from 10am to 2pm P 6 = PT tellers who work 5 hrs from 10am to 3pm P 7 = PT tellers who work 6 hrs from 10am to 4pm P 8 = PT tellers who work 7 hrs from 10am to 5pm P 9 = PT tellers who work 4 hrs from 11am to 3pm P 10 = PT tellers who work 5 hrs from 11am to 4pm P 11 = PT tellers who work 6 hrs from 11am to 5pm P 12 = PT tellers who work 7 hrs from 11am to 6pm P 13 = PT tellers who work 4 hrs from 12pm to 4pm P 14 = PT tellers who work 5 hrs from 12pm to 5pm P 15 = PT tellers who work 6 hrs from 12pm to 6pm P 16 = PT tellers who work 7 hrs from 12pm to 7pm P 17 = PT tellers who work 4 hrs from 1pm to 5pm P 18 = PT tellers who work 5 hrs from 1pm to 6pm P 19 = PT tellers who work 6 hrs from 1pm to 7pm P 20 = PT tellers who work 4 hrs from 2pm to 6pm P 21 = PT tellers who work 5 hrs from 2pm to 7pm P 22 = PT teller who work 4 hrs from 3pm to 7pm +[(8.08)(2)] F 2 +[(7.82)(4)+[ P 1 + P 5 + P 9 + P 13 + P 17 + P 20 + P 22 ] +[(7.82)(5)+[ P 2 + P 6 + P 10 + P 14 + P 18 + P 21 ] +[(7.82)(6)+[ P 3 + P 7 + P 11 + P 15 + P 19 ] +[(7.82)(7)+[ P 4 + P 8 + P 12 + P 16 ] >= 14 = (F) + P 1 +P 2 +P 3 +P 4 +P 5 +P 6 +P 7 +P 8 >=25 = 0.5(F) + P 1 +P 2 +P 3 +P 4 +P 5 +P 6 +P 7 + = 0.5(F) + P 1 +P 2 +P 3 +P 4 +P 5 +P 6 +P 7 +P 8 +P 9 +P 10 +P 11 +P 12 +P 13 +P 14 +P 15 +P 16 >=38 = (F) + P 3 +P 4 +P 6 +P 7 +P 8 +P 9 +P 10 +P 11 +P 12 +P 13 +P 14 +P 15 +P 16 +P 17 +P 18 +P 19 +P 20 +P 21 >=60 = (F) + P 4 +P 7 +P 8 +P 10 +P 11 +P 12 +P 13 +P 14 +P 15 +P 16 +P 17 +P 18 +P 19 +P 20 +P 21 +P 22 >=51 = (F) + P 8 +P 11 +P 12 +P 13 +P 14 +P 15 +P 16 +P 17 +P 18 +P 19 +P 20 +P 21 +P 22 >= 29 4( P 1 + P 5 + P 9 + P 13 + P 17 + P 20 + P 22 ) + 5( P 2 + P 6 + P 10 + P 14 + P 18 + P 21 ) + 6( P 3 + P 7 + P 11 + P 15 + P 19 ) + 7( P 4 + P 8 + P 12 + P 16 ) Minimum cost is $ 3222.32. Total 16 full time employees do 2-hours of OT for 2 days and 8 employees do OT for 2-hours once a week . 1 employee does OT for 1 hour for 5 days a week. Limitations: 1) The model doesnot al ow different loading for different days in a week. 2) The model doesnot al ow flexi timings for ful time employees. If say ful -time employees are al owed to work from 11-7pm then the overtime cost could be reduced. 3. Costs might be reduced by relaxing the constraint that no more than 40% of the day’s requirement be met by parttimers. Would changing the 40% to a higher value significantly reduce costs? No the cost would not reduce as the optimal cost solution requires less no of full timers than 40 %. The constraint of 40 % has slack and therefore incresing this limit will not reduce cost.
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CourseLover
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Status NEW Posted 15 Dec 2017 04:12 PM My Price 10.00

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