Please see the attached document for your reference. This is a Case Study of Chase Manhattan Bank.

Chase Manhattan Bank Case Study Review, analyze, and complete the Chase Manhattan Bank Case Study below. The workload in many areas of bank operations has the characteristics of a no uniform distribution with respect to time of day. For example, at Chase Manhattan Bank in New York, the number of domestic money transfer requests received from customers, if plotted against time of day, would appear to have the shape of an inverted U curve with the peak around 1 P.M. For efficient use of resources, the personnel available should, therefore, vary correspondingly. A variable capacity can be achieved effectively by employing part-time personnel. Because part-timers are not entitled to all the fringe benefits, they are often more economical than full-time employees. Other considerations, however, may limit the extent to which part-time people can be hired in a given department. The problem is to find an optimum workforce schedule that would meet personnel requirements at any given time and also be economical. Some of the factors affecting personnel assignment are listed here: 1 By corporate policy, part-time personnel hours are limited to a maximum of 40% of the day's total requirement. 2 Full-time employees work for 8 hours (1 hour for lunch included) per day. Thus, a full-timer's productive time is 35 hours per week. 3 Part-timers work for at least 4 hours per day but less than 8 hours and are not allowed a lunch break. 4 Fifty percent of the full-timers go to lunch between 11 A.M. and noon, and the remaining 50% go between noon and 1 P.M. 5 The shift starts at 9 A.M. and ends at 7 P.M. (i.e., overtime is limited to 2 hours). Any work left over at 7 P.M. is considered holdover for the next day. 6 A full-time employee is not allowed to work more than 5 hours overtime per week. He or she is paid at the normal rate for overtime hoursnot at one-and-a-half times the normal rate applicable to hours in excess of 40 per week. Fringe benefits are not applied to overtime hours. In addition, the following costs are pertinent: 1. The average cost per full-time personnel hour (fringe benefits included) is $10.11. 2. The average cost per overtime personnel hour for full-timers (straight rate excluding fringe benefits) is $8.08. 3. The average cost per part-time personnel hour is $7.82. The personnel hours required, by hour of day, are given in the following Table. TABLE: Workforce Requirements Workforce Requirements Time Period 9-10am 10-11 11-12 12-1pm 1-2 2-3 3-4 4-5 5-6 6-7 Number of Personnel Required 14 25 26 38 55 60 51 29 14 9 The bank's goal is to achieve the minimum possible personnel cost subject to meeting or exceeding the hourly workforce requirements as well as the constraints on the workers listed earlier. Discussion Questions: 1. What is the minimum-cost schedule for the bank? 2. What are the limitations of the model used to answer question 1? 3. Costs might be reduced by relaxing the constraint that no more than 40% of the day's requirement be met by part-timers. Would changing the 40% to a higher value significantly reduce costs? Hint: For Question 3, please choose a hypothetical higher number, say 45% or 50%, to illustrate your analysis and conclusion. You also need to explain why. In some cases, you may use the "QM for Windows" software (rather than Excel QM) to obtain the Linear Programming diagram to support your finding. After solving your LP program, you may click on "Windows" and the select "Graphs" to get to the graph output. You may then copy and paste any graph into your word document. Linear Programming In order to solve, let F = # of full-time tellers without OT F1 = # of full-time tellers with 1 hour OT from 5m -6pm F2 = # of full-time tellers with 2 hours OT 5pm -7pm P1 = PT tellers who work 4 hrs from 9am to 1pm P2 = PT tellers who work 5 hrs from 9am to 2pm P3 = PT tellers who work 6 hrs from 9am to 3pm P4 = PT tellers who work 7 hrs from 9am to 4pm P5 = PT tellers who work 4 hrs from 10am to 2pm P6 = PT tellers who work 5 hrs from 10am to 3pm P7 = PT tellers who work 6 hrs from 10am to 4pm P8 = PT tellers who work 7 hrs from 10am to 5pm P9 = PT tellers who work 4 hrs from 11am to 3pm P10 = PT tellers who work 5 hrs from 11am to 4pm P11 = PT tellers who work 6 hrs from 11am to 5pm P12 = PT tellers who work 7 hrs from 11am to 6pm P13 = PT tellers who work 4 hrs from 12pm to 4pm P14 = PT tellers who work 5 hrs from 12pm to 5pm P15 = PT tellers who work 6 hrs from 12pm to 6pm P16 = PT tellers who work 7 hrs from 12pm to 7pm P17 = PT tellers who work 4 hrs from 1pm to 5pm P18 = PT tellers who work 5 hrs from 1pm to 6pm P19 = PT tellers who work 6 hrs from 1pm to 7pm P20 = PT tellers who work 4 hrs from 2pm to 6pm P21 = PT tellers who work 5 hrs from 2pm to 7pm P22 = PT teller who work 4 hrs from 3pm to 7pm 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 +[8.08]F1 $10.11 is the cost per hour for FT, 7 is 1 day of work min 1 hour overtime +[(8.08)(2)]F2 +[(7.82)(4)+[P1+P5+P9+P13+P17+P20+P22] +[(7.82)(5)+[P2+P6+P10+P14+P18+P21] +[(7.82)(6)+[P3+P7+P11+P15+P19] +[(7.82)(7)+[P4+P8+P12+P16] Constraints Workforce Requirements 9-10am = (F) + P1+P2+P3+P4 2 hour overtime $7.82 is the cost/hr for PT, 4=hrs/shif >= 14 10-11 am = (F) + P1+P2+P3+P4+P5+P6+P7+P8 >=25 +P11+P >=26 11-12 pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P 0.59+P reflects lunch time 10 12 12-1pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16 >=38 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 = (F) + P3+P4+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21 >=60 3-4pm = (F) + P4+P7+P8+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >=51 4-5pm = (F) + P8+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >= 29 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. 4(P1+P5+P9+P13+P17+P20+P22) + 5(P2+P6+P10+P14+P18+P21) + 6(P3+P7+P11+P15+P19) + 7(P4+P8+P12+P16) 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 Excel Model F F1 30 9-10am 10-11 am 11-12 pm 12-1pm 1-2 pm 2-3pm 3-4pm 4-5pm 5-6pm F2 1 P1 8 1 1 0.5 0.5 1 1 1 1 1 1 P2 P3 P4 P5 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P6 P7 P8 P9 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P10 P11 9 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6-7pm 1 Additional constraints 25 123 30 128 Objective Function Minimize total Cost = $3,222.32 1. What is the minimum-cost schedule for the bank? 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. 2. What are the limitations of the model used to answer question 1? Limitations: 1) The model doesnot allow different loading for different days in a week. 2) The model doesnot allow flexi timings for full time employees. If say full-time employees are allowed to work from 117pm then the overtime cost could be reduced. 3. Costs might be reduced by relaxing the constraint that no more than 60% of the day's requirement be met by parttimers. Would changing the 60% 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 60 %. The constraint of 60 % has slack and therefore incresing this limit will not reduce cost. FT, 7 is 1 day of work minus lunch hour ay's total requirement. = 14 10-11 am = (F) + P1+P2+P3+P4+P5+P6+P7+P8 >=25 +P11+P >=26 11-12 pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P 10 12 0.59+P reflects lunch time 12-1pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16 >=38 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 = (F) + P3+P4+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21 >=60 3-4pm = (F) + P4+P7+P8+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >=51 4-5pm = (F) + P8+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >= 29 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. 4(P1+P5+P9+P13+P17+P20+P22) + 5(P2+P6+P10+P14+P18+P21) + 6(P3+P7+P11+P15+P19) + 7(P4+P8+P12+P16) 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 hou Excel Model F F1 F2 30 9-10am 10-11 am 11-12 pm 12-1pm 1-2 pm 2-3pm 3-4pm 4-5pm 5-6pm 6-7pm 1 P1 8 1 1 0.5 0.5 1 1 1 1 1 P2 P3 P4 P5 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P6 P7 P8 P9 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P10 P11 9 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Additional constraints 25 123 30 128 Objective Function Minimize total Cost = $3,222.32 1. What is the minimum-cost schedule for the bank? Minimum total cost is $ 3222.32. 2. What are the limitations of the model used to answer question 1? We assume that the variables have linear relationships, which may not be correct. While adding more workers the extra worker added may have diminishing productivity for many reasons. The productivity of full time and part time workers may not be same for reasons such as motivation, benefits 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? Yes. Since part time workers are relatively cheaper as compared to full time workers cost can be reduced by eliminating the constraint. But for the reasons given in above quation, it may not be practicable or there may be other qualitative issues. Mathematically it is possible, if we relax the condition to 50%, the cost can be reduced to 3149.60 .A combination of full time and part time workers would leads to better management of reduced to 3149.60 .A combination of full time and part time workers would leads to better management of workers and would reduce the cost. The costs can be further reduced by relaxing the constraint on part time workers FT, 7 is 1 day of work minus lunch hour y's total requirement. time employees. = 14 10-11 am = (F) + P1+P2+P3+P4+P5+P6+P7+P8 >=25 +P11+P >=26 11-12 pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P 0.59+P reflects lunch time 10 12 12-1pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16 >=38 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 = (F) + P3+P4+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21 >=60 3-4pm = (F) + P4+P7+P8+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >=51 4-5pm = (F) + P8+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >= 29 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. 4(P1+P5+P9+P13+P17+P20+P22) + 5(P2+P6+P10+P14+P18+P21) + 6(P3+P7+P11+P15+P19) + 7(P4+P8+P12+P16) 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 Excel Model F F1 30 9-10am 10-11 am 11-12 pm 12-1pm 1-2 pm 2-3pm 3-4pm 4-5pm 5-6pm F2 1 P1 8 1 1 0.5 0.5 1 1 1 1 1 1 P2 P3 P4 P5 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P6 P7 P8 P9 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P10 P11 9 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6-7pm 1 Additional constraints 25 123 30 128 Objective Function Minimize total Cost = $3,222.32 1. What is the minimum-cost schedule for the bank? 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. 2. What are the limitations of the model used to answer question 1? Limitations: 1) The model doesnot allow different loading for different days in a week. 2) The model doesnot allow flexi timings for full time employees. If say full-time employees are allowed to work from 117pm then the overtime cost could be reduced. 3. Costs might be reduced by relaxing the constraint that no more than 60% of the day's requirement be met by parttimers. Would changing the 60% 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 60 %. The constraint of 60 % has slack and therefore incresing this limit will not reduce cost. FT, 7 is 1 day of work minus lunch hour ay's total requirement. = 14 10-11 am = (F) + P1+P2+P3+P4+P5+P6+P7+P8 >=25 +P11+P >=26 11-12 pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P 10 12 0.59+P reflects lunch time 12-1pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16 >=38 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 = (F) + P3+P4+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21 >=60 3-4pm = (F) + P4+P7+P8+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >=51 4-5pm = (F) + P8+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >= 29 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. 4(P1+P5+P9+P13+P17+P20+P22) + 5(P2+P6+P10+P14+P18+P21) + 6(P3+P7+P11+P15+P19) + 7(P4+P8+P12+P16) 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 hou Excel Model F F1 F2 30 9-10am 10-11 am 11-12 pm 12-1pm 1-2 pm 2-3pm 3-4pm 4-5pm 5-6pm 6-7pm 1 P1 8 1 1 0.5 0.5 1 1 1 1 1 P2 P3 P4 P5 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P6 P7 P8 P9 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P10 P11 9 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Additional constraints 25 123 30 128 Objective Function Minimize total Cost = $3,222.32 1. What is the minimum-cost schedule for the bank? Minimum total cost is $ 3222.32. 2. What are the limitations of the model used to answer question 1? We assume that the variables have linear relationships, which may not be correct. While adding more workers the extra worker added may have diminishing productivity for many reasons. The productivity of full time and part time workers may not be same for reasons such as motivation, benefits 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? Yes. Since part time workers are relatively cheaper as compared to full time workers cost can be reduced by eliminating the constraint. But for the reasons given in above quation, it may not be practicable or there may be other qualitative issues. Mathematically it is possible, if we relax the condition to 50%, the cost can be reduced to 3149.60 .A combination of full time and part time workers would leads to better management of reduced to 3149.60 .A combination of full time and part time workers would leads to better management of workers and would reduce the cost. The costs can be further reduced by relaxing the constraint on part time workers FT, 7 is 1 day of work minus lunch hour y's total requirement. time employees. = 14 10-11 am = (F) + P1+P2+P3+P4+P5+P6+P7+P8 >=25 +P11+P >=26 11-12 pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P 10 12 0.59+P reflects lunch time 12-1pm = 0.5(F) + P1+P2+P3+P4+P5+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16 >=38 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 = (F) + P3+P4+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21 >=60 3-4pm = (F) + P4+P7+P8+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >=51 4-5pm = (F) + P8+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22 >= 29 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. 4(P1+P5+P9+P13+P17+P20+P22) + 5(P2+P6+P10+P14+P18+P21) + 6(P3+P7+P11+P15+P19) + 7(P4+P8+P12+P16) 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 Excel Model F F1 30 9-10am 1 F2 1 P1 8 P2 P3 P4 P5 0 0 0 0 1 1 1 1 P6 0 P7 0 P8 0 P9 0 P10 9 P11 2 0 10-11 am 11-12 pm 12-1pm 1-2 pm 2-3pm 3-4pm 4-5pm 5-6pm 6-7pm 1 0.5 0.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Additional constraints 25 123 30 128 Objective Function Minimize total Cost = $3,222.32 1. What is the minimum-cost schedule for the bank? 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. 2. What are the limitations of the model used to answer question 1? Limitations: a) it does not allow different loading for different days in a week. b) it does not allow flexible timings for full time employees. If say full-time employees are allowed 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? the cost would not reduce . This is because the optimal cost solution requires less number of full timers than 40 %. The constraint of 40 % has slack and therefore increasing this limit will not reduce cost. FT, 7 is 1 day of work minus lunch hour y's total requirement.