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The workload in many areas of bank operations has the characteristic of being unevenly distributed throughout the day. For example, at Chase Manhattan Bank in New York, the number of domestic money transfer requests received from customers, if plotted against the time of day, would appear according to the workload described in Figure 1 below. For efficient use of resources, the personnel available should therefore vary correspondingly.

Figure 1: A typical workload curve that describes the
corresponding personnel requirements at different hours of the day.

A variable capacity can be achieved effectively by employing part-time personnel in conjunction with full-time personnel. Because part-timers are not entitled to all the fringe benefits, they are often more economical than full-time employees. Other considerations such as consistency and quality control 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 will meet personnel requirements at any given time and also be economical.

Some of the factors affecting personnel assignment for the Chase Manhattan Bank that you are modeling are as follows:

1. Corporate policy mandates that part-time personnel hours are limited to a maximum of 40% of the day’s total requirements.
2. Full-time employees start at 9:00 A.M. and work for 8 hours with one hour for lunch per day. Thus a full-timer’s productive time is 35 hours per week. They are not paid during their lunch break.
3. Part-timers work for at least 4 hours per day but no more than 6 hours and are not allowed a lunch break. A part-timer may start his/her shift anytime between 9:00 A.M. and 3:00 P.M.
4. Fifty percent of the full-timers go to lunch between 11 A.M. and noon and the remaining 50% go betweennoon and 1 P.M.
5. The bank operates from 9 A.M. to 7 P.M. Any work left over at 7 P.M. is considered holdover for the next day.
6. A full-time employee is allowed to work up to 2 hours of overtime per day, but the total overtime hours worked may not exceed more than 5 hours per week per employee. Overtime is worked between the hours of 5:00 P.M. and 7:00 P.M. The employee is paid at the normal rate of $10.85 for overtime hours (not at time and a half). Fringe benefits are not applied to overtime hours. When the fringe benefits are applied to the employee’s 35 hour work week, the average cost per full-time personnel hour is $12.40.
7. Part-time personnel are paid $8.80 per hour.
8. The personnel hours required, by hour of the day, are given in Table 1 below.

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.

Time Period Number of Personnel Required
9-10 A.M. 14
10-11 A.M. 25
11-12 26
12-1 P.M. 38
1-2 55
2-3 60
3-4 51
4-5 29
5-6 14
6-7 9
Table 1: Workforce Requirements

1) What is the minimum schedule for the task? The answer will consist of the total cost to the bank and the number of each type of employee needed and the start times for the employees.
2) What are the limitations of the model used to answer question 1? The answer should include the characteristics that formed the constraints. The answer should also include why this will not always work. Provide the uncertainties that would make this model, at times, not function well.
3) Would changing the 40% part-time to a larger percent reduce the cost? Do not just give “yes” or “no.” Run the model in the modified state and prove the “yes” or “no.”

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