The workload in many areas of banking 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 customers, when compared to the time of day, would appear to be shaped like an inverted U curve with the peak around 1 pm For efficient use of resources, the available staff should therefore vary accordingly. Variable capacity can be achieved effectively by employing part-time staff. Because part-time workers are not entitled to all fringe benefits, they are often cheaper than full-time employees. However, other considerations may limit the extent to which part-time people can be hired in a given department. The problem is to find an optimal work schedule that satisfies the staffing requirements at a given time and is also economical. Some of the factors that affect staff allocation are listed below: By corporate policy, part-time staff hours are limited to a maximum of 40% of the total requirement for the day. Full-time employees work 8 hours (1 hour for lunch included) per day. Therefore, the productive time of a full-time worker is 35 hours per week. Part-time workers work at least 4 hours a day, but less than 8 hours, and are not allowed lunch breaks. Fifty percent of full-time employees go to lunch between 11 a.m. and noon, and the remaining 50% go between noon and 1 p.m. The shift starts at 9 a.m. Any work left at 7 pm is considered carryover for the next day. A full-time employee cannot work more than 5 hours of overtime per week. You are paid at the regular rate for overtime, not one and a half times the regular rate applicable for hours in excess of 40 per week. Fringe benefits do not apply to overtime. Additionally, the following costs are relevant: 1. The average hourly cost for full-time staff (including fringe benefits) is $10.11. 2. The average cost per hour of staff overtime for full-time workers (flat rate not including fringe benefits) is $8.08. 3. The average cost per hour for part-time staff is $7.82. The staff hours required, by time of day, are given in the following Table.

TABLE: Labor requirements NUMBER OF STAFF TIME PERIOD REQUIRED 9–10 AM 14 10–11 25 11–12 26 12–1 PM 38 1–2 55 2–3 60 3–4 51 4-5 29 5- 6 14 6- 7 9 The bank's objective is to achieve the minimum possible staff cost subject to meeting or exceeding the hourly labor requirements as well as the restrictions on workers mentioned above.

STAFF NUMBER	REQUIRED TIME PERIOD
9–10 a. m.	14
10–11	25
11–12	26
12:00 a 13:00	38
1–2	55
2–3	60
3–4	51
4-5	29
5-6	14
6-7	9

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 could be reduced by relaxing the restriction that no more than 40% of the day's requirement be covered by part-time workers. Would changing the 40% to a higher value significantly reduce costs? Source: Adapted from Shyam L. Moondra. “An LP Model for Work Force Scheduling for Banks,” Journal of Bank Research (Winter 1976): 299–301. Label your completed file CS1 – Your Team Name (Team A, B, or C) and upload it to the Case Study 2 assignment. You don't need to write many words, but you do need to answer all of the questions above. If you don't 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. Tip: For question 3, choose a higher hypothetical number, say 45% or 50%, to illustrate your analysis and conclusion. You also need to explain why. In some cases, you can use "QM for Windows" software (instead of Excel QM) to obtain the LP diagram to support your finding. After solving your LP program, you can click "Windows" and select "Charts" to get the graph output. You can then copy and paste any chart into your Word document. However, this option may not work in all cases. Please discuss why. Please include the Excel document.