The workload in many areas of bank operations has thecharacteristics of a nonuniform distribution with respect to timeof day. For example, at Chase Manhattan Bank in New York, thenumber of domestic money transfer requests received from customers,if plotted against time of day, would appear to have the shape ofan inverted U curve with the peak around 1 P.M. For efficient useof resources, the personnel available should, therefore, varycorrespondingly. A variable capacity can be achieved effectively byemploying part-time personnel. Because part-timers are not entitledto all the fringe benefits, they are often more economical thanfull-time employees. Other considerations, however, may limit theextent to which part-time people can be hired in a givendepartment. The problem is to find an optimum workforce schedulethat would meet personnel requirements at any given time and alsobe economical. Some of the factors affecting personnel assignmentare listed here:

1. By corporate policy, part-time personnel hours are limited to amaximum of 40% of the day’s total requirement.
2. Full-time employees work for 8 hours (1 hour for lunchincluded) per day. Thus, a full-timer’s productive time is 35 hoursper week.
3. Part-timers work for at least 4 hours per day but less than 8hours 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., overtimeis limited to 2 hours). Any work left over at 7 P.M. is consideredholdover for the next day.
6. A full-time employee is not allowed to work more than 5 hoursovertime per week. He or she is paid at the normal rate forovertime hours—not at one-and-a-half times the normal rateapplicable to hours in excess of 40 per week. Fringe benefits arenot applied to overtime hours.

In addition, the following costs are pertinent:
1. The average cost per full-time personnel hour (fringe benefitsincluded) 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 thefollowing 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 costsubject to meeting or exceeding the hourly workforce requirementsas 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 question1?
3. Costs might be reduced by relaxing the constraint that no morethan 40% of the day’s requirement be met by part-timers. Wouldchanging the 40% to a higher value significantly reduce costs?

Source: Adapted from Shyam L. Moondra. “An L. P. Model for WorkForce Scheduling for Banks,” Journal of Bank Research (Winter1976): 299–301.

Label your completed file CS1 - Your Team's Name (Team A, B, orC) and upload it to Case Study 2 assignment. You do not need towrite many words, but you do need to answer all the questionsabove. If you do not address those three questions in particular,points will be deducted. Question 1 has 50 points, Question 2 has20 points and Question 3 has 30 points. Upload your file to thisCase Study assignment.

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