Question

WestEast Bank is a busy metropolitan bank open to customers from 9:00 am to 4:00 pm each day. It employs both full-time and part-time tellers. Full-timers work 8 hours/day, from 8:00 am to 5:00 pm, with a 1-hour lunch period beginning at either 11:00 am or 12:00 noon. Part-timers work 4 hours/day with no lunch break. Part-timers report for work at the beginning of the hour for the period they are hired.

Full-time tellers earn P1,000 for an 8-hour workday, including both salary (P600) and benefits (P400). Part-timers earn only P250 in salary for a 4-hour workday, with no benefits. The bank’s busiest times are around noon and during the last business hour of the afternoon. As the table below shows, the need for tellers varies during the day. Because of the work of preparing for and reconciling the day’s activities at the beginning and the end of each day cannot be done by part-timers, the bank requires that at least six of the tellers be full-timers. Also at least four full-timers must be on duty during the bank’s busiest time (12:00 noon to 1:00 pm).

WestEast Bank is a busy metropolitan bank open to customers from 9:00 am to 4:00 pm each day. It employs both full-time and part-time tellers. Full-timers work 8 hours/day, from 8:00 am to 5:00 pm, with a 1-hour lunch period beginning at either 11:00 am or 12:00 noon. Part-timers work 4 hours/day with no lunch break. Part-timers report for work at the beginning of the hour for the period they are hired.

Full-time tellers earn P1,000 for an 8-hour workday, including both salary (P600) and benefits (P400). Part-timers earn only P250 in salary for a 4-hour workday, with no benefits. The bank’s busiest times are around noon and during the last business hour of the afternoon. As the table below shows, the need for tellers varies during the day. Because of the work of preparing for and reconciling the day’s activities at the beginning and the end of each day cannot be done by part-timers, the bank requires that at least six of the tellers be full-timers. Also at least four full-timers must be on duty during the bank’s busiest time (12:00 noon to 1:00 pm).

Time Period	Beginning and Ending Hours	Minimum Number of Tellers Required
1	09:00 am - 10:00 am	8
2	10:00 am - 11:00 am	6
3	11:00 am - 12:00 nn	14
4	12:00 nn - 01:00 pm	15
5	01:00 pm - 02:00 pm	10
6	02:00 pm - 03:00 pm	5
7	03:00 pm - 04:00 pm	12

1. How many full-time and part-time tellers should the bank schedule each day?
2. When should the part-timers report for work?
3. When should the full-time tellers begin their lunch breaks?
4. How do your responses change if, in addition to minimizing the workforce, the bank also wants to minimize the maximum overstaffing during any period?

Answer 1

a)

Let F1 be the number of full-time tellers who take 1-hour lunch break from 11am to 12nn, and

F2 be the number of full-time tellers who take 1-hour lunch break from 12nn to 1pm

P1 be the number of part-time tellers who start work at 9am

P2 be the number of part-time tellers who start work at 10am

P3 be the number of part-time tellers who start work at 11am

P4 be the number of part-time tellers who start work at 12nn

Minimize 1000F1+1000F2+250P1+250P2+250P3+250P4

s.t.

F1+F2 >= 6

F1 >= 4

F1+F2+P1 >= 8

F1+F2+P1+P2 >= 6

F2+P1+P2+P3 >= 14

F1+P1+P2+P3+P4 >= 15

F1+F2+P2+P3+P4 >= 10

F1+F2+P3+P4 >= 5

F1+F2+P4 >= 12

F1, F2, P1, P2, P3, P4 >= 0

Solution using LINGO is following:

Following number of full-time and part-time tellers should be scheduled each day:

Full timers = F1+F2 = 4+2 = 6

Part-timers = P1+P2+P3+P$ = 12+0+0+6 = 18

b)

Part-timers report for work as below:

At 9am, P1 = 12 part-timers

At 10am, P2 = 0 part-timers

At 11am, P3 = 0 part-timers

At 12nn, P4 = 6 part-timers

c)

Full-timers should beging their lunch breaks as per following schedule:

Lunch break at 11am-12nn = 4 full-time tellers

Lunch break at 12nn-1pm = 2 full-time tellers