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The workload in many areas of bank operations has the characteristics of a non-uniform distribution with respect to time of day

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The workload in many areas of bank operations has the characteristics of a non-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 customer, 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 of the fringe benefits, they are often more economical than full time employees. Other consideration, 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 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 8m hours and are not allowed a lunch break.
4. 50% of the full timers go to lunch between 11a.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 7p.m. (i.e., over-time is limited to 2 hours). Any work left over at 7p.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 hours-not 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 benefit included) is $10.00
2. The average cost per overtime personnel hours for full timers (straight rate excluding fringe benefits) is $8.08.
3. The aver cost per part time personnel hours is $7.82.

The personnel hours required, by hour of day, are given in the following table. The bank's goal is to achieve the minimum possible personnel cost subject to meeting or exceeding the hourly work-force requirements as well as the constraints on the workers listed earlier.

WORK FORCE REQUIREMENTS
Time Period Number of Personnel Required
9-10 am 14 people
10-11 am 25 people
11-12 am 26 people
12-1pm 38 people
1-2 pm 55 people
2-3 pm 60 people
3-4 pm 51 people
4-5 pm 29 people
5-6 pm 14 people
6-7 pm 9 people

Discussion questions with Excel:
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?
4. What's you conclusion and recommendation for the overall case study?