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Introduction
This is a case study of chase bank Manhattan bank which is suffering from tasking workload in many
areas of bank operations which has the characteristics of non-uniform distribution of domestic
money transfer requests received from customers and if plotted against time of day it would appear
to have the shape of an inverted U curve with the peak around 1 P.M.
Consistently. Chase bank manhating is facing with efficient use of resources and personnel
availability which supposed to vary correspondingly in other to balance workload factors. This
variable requirement resulted in employee schedule problem due to insufficient manpower in pick
hours balance the job demand. To meet the goal of solving this problem during peak period.
Scheduling of sufficient personnel in every hour is th most cost-effective way and this require having
some part time personnel in different hours as per demand.
In this case study, we will utilize linear programing model to review, analysis, identify the problem,
decision variables, objective function constraints, construct the LP model, Plot the model in a spread
sheet to obtain optimum solution and we will finally focus on discussing questions the bank operation
is struggling with.
LP problem Identification for chase bank operation
• Busy hours resulted from non - uniform distribution of money transfer.
• Number of fulltime personal ˂ required number of personnel
Decision variables and objective function
My Team assumption upheld that we will represent the total number of full time personnel =F
and we proceed that work between 9am – 5pm is considered full time. We also agreed that
work between 5pm - 7pm will be overtime personnel. We also upheld that every part time will
work exactly 4 hours. We proceed that;
• F represent full time personnel, p1 represent part timers that join at 9am.
P2 represent part time that join at 10.00AM, P3 represent is the part time that join at 11am
• P4 represent the part timers that join at 12PM, P4 represent the part timers that join at 1pm
• P5 represent the part time that join at 2p.m, 0T1 represent full timer working 5-6pm as
overtime, 0T2 represent full timer working 6-7pm as over time T
Table 1
Time interval
Full time
Over time
Part timer
Number of
personnel
required
9-10AM
F
0
P1
14
10-11AM
F
0
P1 + P2
25
11-12PM
0.5F
0
P1+P2+P3
26
12-1.00PM
0.5F
0
P1+P2+P3+P4
38
1-2PM
F
0
P2+P3+P4+P5
55
2-3PM
F
0
P3+P4+P5+P6
60
3-4PM
F
0
P4+P5+P6
51
4-5PM
F
0
P5+P6
29
LP model decision variable model equation 1-10
Table 2
Time interval
Equations
Equation number
9-10am
F+P1≥14
1
10-11am
F+P1+P2≥ 25
2
11-12am
0.5F+P1+P2+P3≥ 26
3
12-1pm
0.5F+P1+P2+P3+P4≥38
4
1-2pm
F+P2+P3+P4+P5≥55
5
2-3pm
F+P3+P4+P5+P6 ≥60
6
3-4pm
F+P4+P5+P6 ≥51
7
4-5pm
F+P5+P6≥ 29
8
5-6pm
0T1+P6 ≥14
9
6-7pm
0T2 ≥9
10
5-6PM
0
0T1
P6
14
6-7PM
0
0T2
0
9
Total
321
