1. Chase Manhattan Bank By 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

2. Chase Manhattan Bank By 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

3. Chase Manhattan Bank By 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

4. Chase Manhattan Bank By 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

5. Chase Manhattan Bank By 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]

6. Chase Manhattan Bank By 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

7. Chase Manhattan Bank By 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)

8. Chase Manhattan Bank By South Group
Start QM for Windows
Select Module Menu
Select Linear Programming Menu
Select File Menu
Select New
Define Data set for Linear Program

9. Chase Manhattan Bank By South Group
Fill in data grid with problem data
Solve the problem by clicking the solve button

10. Chase Manhattan Bank By South Group
The solution can be viewed in the data grid

11. Chase Manhattan Bank By South Group
Use Excel Solver to solve the question
Step 1
Start Excel and create a new worksheet
Step 2
Enter Headings, variables, and coefficients for the objective function
Step 3
Enter cells where values of variables will be located, this is where solver will put the solution
Step 4
Write formula to compute left side constraints

12. Chase Manhattan Bank By South Group
Step 5
Enter right side constraints
The spread Sheet is now ready to run solver

13. Chase Manhattan Bank By South Group
Step 6
Click on Tools
then Solver
Step 7
Fill in Solver Parameters to match your Spread Sheet layout

14. Chase Manhattan Bank By South Group
Step 8
Set Solver Options as follows
Step 9
Solve the problem and Keep solver Values

15. Chase Manhattan Bank By South Group
Step 10
Review answer

16. Chase Manhattan Bank By South Group
DISCUSSION QUESTION
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

17. Chase Manhattan Bank By 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.

18. Chase Manhattan Bank By 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:

19. Chase Manhattan Bank By South Group
Changing to 60%
Cost: $2,485.83
Changing to 80%
Cost: $2,382.08
As the percentage
increases, the cost
decreases.