Question

The workload in many areas of bank operations has the characteristics of a nonuniform 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 customers, 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 the fringe benefits, they are often more economical than full-time employees. Other considerations, 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 of the 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 8 hours and are not allowed a lunch break.
4. Fifty percent of the full-timers go to lunch between 11 A.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 7 P.M. (i.e., overtime is limited to 2 hours). Any work left over at 7 P.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 benefits included) is $10.11.
2. The average cost per overtime personnel hour for full-timers (straight rate excluding fringe benefits) is $8.08.
3. The average cost per part-time personnel hour is $7.82.

The personnel hours required, by hour of day, are given in the following Table.

TABLE: Workforce Requirements

NUMBER OF PERSONNEL	TIME PERIOD REQUIRED
9–10 A.M.	14
10–11	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

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 earlier.

Discussion Questions:
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?

Source: Adapted from Shyam L. Moondra. “An L. P. Model for Work Force Scheduling for Banks,” Journal of Bank Research (Winter 1976): 299–301.

Label your completed file CS1 - Your Team's Name (Team A, B, or C) and upload it to Case Study 2 assignment. You do not need to write many words, but you do need to answer all the questions above. If you do not address those three questions in particular, points will be deducted. Question 1 has 50 points, Question 2 has 20 points and Question 3 has 30 points. Upload your file to this Case Study assignment.

Hint: For Question 3, please choose a hypothetical higher number, say 45% or 50%, to illustrate your analysis and conclusion. You also need to explain why. In some cases, you may use the "QM for Windows" software (rather than Excel QM) to obtain the LP diagram to support your finding. After solving your LP program, you may click on "Windows" and the select "Graphs" to get to the graph output. You may then copy and paste any graph into your word document. However, this option may not work in all cases. Please discuss why.

Answer 1

Now we can answer these question from the excel output as follows:

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

Answer: Minimum Cost = $3222.32

16 Employees do 2Hrs of OT for 2 days, 8 Employees do 2Hrs of OT once a week and 1 Employee do 1Hr of OT for 5 days a week.

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

Answer: It does not allowdifferent loading for different days in a week.

It does not provide the flexible timings to full time employees.

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?

No, the cost would not reduce because optimal cost requires less number of full timers than 40%. The constraint that no more than 40% is a slack and therefore increasing this limit won't reduce the cost.