Chase Manhattan Bank By South Group Case: Chase has labor planning problems that address staffing needs over a specific time period. Goals: To minimize.

Chase Manhattan BankBy South Group

Case: Chase has labor planning problems that address staffing needs over a specific time period.

Goals: To minimize total daily personal cost within the corporate policies and constrains

Chase Manhattan BankBy South Group

To solve the issues, we let:

F0 = Number of full-time tellers who don’t work over time

F1 = Number of full-time tellers who work 1 hr over time

F2 = Number of full-time tellers who work 2 hr over time

A = PT tellers who work 4 hrs from 9am to 1pm

B = PT tellers who work 5 hrs from 9am to 2 pm

C = PT tellers who work 6 hrs from 9am to 3 pm

D = PT tellers who work 6 hrs from 9am to 4 pm

Chase Manhattan BankBy South Group

E = PT tellers who work 4 hrs from 10 am to 2 pm

F = PT tellers who work 5 hrs from 10 am to 3 pm

G = PT tellers who work 6 hrs from 10 am to 4 pm

H = PT tellers who work 7 hrs from 10 am to 5 pm

I = PT tellers who work 4 hrs from 11 am to 3 pm

J = PT tellers who work 5 hrs from 11 am to 4 pm

K = PT tellers who work 6 hrs from 11 am to 5 pm

L = PT tellers who work 7 hrs from 11 am to 6 pm

M = PT tellers who work 4 hrs from 12 pm to 4 pm

Chase Manhattan BankBy South Group

N = PT tellers who work 5 hrs from 12 pm to 5 pm

O = PT tellers who work 6 hrs from 12 pm to 6 pm

P = PT tellers who work 7 hrs from 12 pm to 7 pm

Q = PT tellers who work 4 hrs from 1 pm to 5 pm

R = PT tellers who work 5 hrs from 1 pm to 6 pm

S = PT tellers who work 6 hrs from 1 pm to 7 pm

T = PT tellers who work 4 hrs from 2 pm to 6 pm

U = PT tellers who work 5 hrs from 2 pm to 7 pm

V = PT tellers who work 4 hrs from 3 pm to 7 pm

Chase Manhattan BankBy South Group

Objective:

Minimize = (10.11)(7)F0

+[(10.11)(7)+8.08]F1+[(10.11)(7)+(8.08)(2)]F2+[(7.82)(4)][A+E+I+M+Q+T+V]+[(7.82)(5)][B+E+J+N+R+U]+[(7.82)(6)][C+G+K+O+S]+[(7.82)(7)][D+H+L+P]

Chase Manhattan BankBy South Group

Subjects:9-10am (F0+F1+F2)+A+B+C+D >=14

10-11am (F0+F1+F2)+A+B+C+D+E+F+G+H >=25

11-12pm 0.5(F0+F1+F2)+A+B+C+D+E+F+G+H+I+J+K+L >=26

12-1pm 0.5(F0+F1+F2)+A+B+C+D+E+F+G+H+I+J+K+L+M+O+N+P>=38

1-2pm (F0+F1+F2)+B+C+D+E+F+G+H+I+J+K+L+M+N+O+P+Q+R+S >=55

Chase Manhattan BankBy South Group

2-3pm

(F0+F1+F2)+C+D+F+G+H+I+J+K+L+M+N+O+P+Q+R+S+T+U >=60

3-4pm

(F0+F1+F2)+D+G+H+J+K+L+M+N+O+P+Q+R+S+T+U+V >=51

4-5pm

(F0+F1+F2)+H+K+L+M+N+O+P+Q+R+S+T+U+V >=29

5-6pm ( F1+F2)+L+O+P+S+T+U+V >=14

6-7pm ( F1+F2)+P+S+U+V >=9

4(A+E+I+M+Q+T+V)+5(B+F+J+N+R+U)+6(C+G+K+O+S)+7(D+H+L+P)

<= 40%(321)

Chase Manhattan BankBy South Group

Start QM for Windows

Select Module Menu

Select Linear Programming Menu

Select File Menu

Select New

Define Data set for Linear Program

Chase Manhattan BankBy South Group

Fill in data grid with problem data

Solve the problem by clicking the solve button

Chase Manhattan BankBy South Group

The solution can be viewed in the data grid

Chase Manhattan BankBy South Group

Use Excel Solver to solve the questionStep 1

Start Excel and create a new worksheet

Step 2 Enter Headings, variables, and coefficients for the objective function

Step 3Enter cells where values of variables will be located, this is where solver will put the solution

Step 4Write formula to compute left side constraints

Chase Manhattan BankBy South Group

Step 5

Enter right side constraints

The spread Sheet is now ready to run solver

Chase Manhattan BankBy South Group

Step 6

Click on Tools

then Solver

Step 7

Fill in Solver Parameters to match your Spread Sheet layout

Chase Manhattan BankBy South Group

Step 8Set Solver Options as follows

Step 9Solve the problem and Keep solver Values

Chase Manhattan BankBy South Group

Step 10

Review answer

Chase Manhattan BankBy South Group

DISCUSSION QUESTION

1. What is the minimum-cost schedule for the bank?

By utilizing QM for Windows and Excel Solver, we obtain the minimum-cost schedule for the bank is $3,026.65

Chase Manhattan BankBy South Group

DISCUSSION QUESTION

2. What are the limitations of the model used to answer question 1?

The model used to solve the problem suffers from the limitation that there are several optimal outcomes and a different answer may be obtained depending on the sequence in which the constraints are answered.

Chase Manhattan BankBy South Group

DISCUSSION QUESTION

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?

Yes, changing the 40% to a higher value would significantly reduce costs. We provide the sensitivity analysis as follows:

Chase Manhattan BankBy South Group

Changing to 60%Cost: $2,485.83

Changing to 80%Cost: $2,382.08

As the percentageincreases, the cost decreases.