The number of transaction requests received by a bank peaks around 1 PM. For efficient use of resources, the personnel available should therefore vary correspondingly. A variable capacity could be achieved by employing part-time personnel.

The problem is to find the optimal workforce schedule that would meet the personnel requirements at any given time and also be economical.

By corporate policy part-time personnel hours are limited to a maximum of 40% of the day's total requirement.

Full-time employees work for 8 hours (1 hour for lunch included) per day. Thus their productive time is 35 hours per week.

Part-timers work for at least 4 hours per day but less than 8 hours, and are not allowed lunch break.

50% of full-timers go to lunch between 11 am and noon and the remaining 50% go between noon and 1 PM.

The shift starts at 9 AM and ends at 7 PM (overtime is limited to 2 hours). Any work left over at 7 PM is considered holdover for the next day.

A full time employee is not allowed to work more than 5 hours overtime per week. He is paid at normal rate for over time hours; no lunch hours are applicable during over time hours.

The following are the costs:

The average cost per full-time personnel hour (fringe benefits included) is $10.11 .

The average cost per overtime personnel hour (for full timers), starting rate excluding fringe benefits is $8.08 .

The average cost per part-time personnel hour is $7.82 .

Personnel hours required by hour of day are as given below:

9 AM -10 AM - 14
10 AM -11 AM - 25
11 AM -12 PM - 26
12 PM -1 PM - 38
1 PM -2 PM - 55
2 PM -3 PM - 60
3 PM -4 PM - 51
4 PM -5 PM - 29
5 PM -6 PM - 14
6 PM -7 PM - 9

The bank's goal is to achieve minimum possible personnel cost subject to meeting or exceeding the hourly workforce requirements as well as the constraints on the workers listed above.