the bank teller scheduling problem

7/27/2019 The Bank Teller Scheduling Problem

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Linear Programming Exercise 1Employee Scheduling Problem (due 9/26)

A bank manager has 4 full time tellers that must be scheduled for six consecutive hours. Theseindividuals are paid $12.00 per hour. Full time tellers can work up to one hour of overtime pershift at $15.00 per hour. Part time tellers can be scheduled in two or three consecutive hour

shifts. The hourly wages that must be paid to part time tellers working two or three hour shiftsare $10.00 and $9.00, respectively. There are no restrictions on the number of part time shiftsused. The minimum number of tellers needed to meet customer service requirements during eachhour of the day is summarized below:

Hour:

8-9 am 69-10 am 510-11 am 411-12 pm 7

12-1 pm 81-2 pm 62-3 pm 33-4 pm 24-5 pm 3

Document a solution for assigning starting hours to different types of shifts that will minimizetotal labor costs.


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Eric Acchitelli

ISYE-1100

Prof. Malmborg

14 September 2012

The Employee Scheduling Problem Solution, or How to Not Break the Bank

In this situation, the objective is to create a work schedule that will minimize the total

labor costs for the day. There are 36 possible variables to consider in this equation. However,

this task has three constraints. The first of these constraints is that all four full-time workers

(whether they work overtime or not) must be scheduled at some point during the day. The

second constraint is the minimum number of tellers that must be on duty for any given hour of

work. The third and final constraint is that the workers must work for the entire specified

amount of time.

Before attempting to solve the scheduling dilemma, it is a very good idea to eliminate

unnecessary variables. However, because of the final constraint, there are a few variables that

can be immediately eliminated from the equation. Because full-time workers who do not work

an overtime shift must work for a full six-hour shift, none can be assigned beyond the fourth

hour. Therefore, all variables from Xfn5 to Xfn9 are no longer considered. Due to similar time

constraints, the variables from Xfo4 to Xfo9, XP2-9, and from XP3-8 to XP3-9 are all moot,

leaving a total count of 22 variables

In order to have the lowest possible labor cost, this is what the final schedule should

include:

During the first hour (8-9 am), three of the full-time tellers (who will not work overtime)and three two-hour part-time tellers should be assigned. This fulfills our requirement that

there must be at least 6 workers during this hour.

During the second hour (9-10 am), no other tellers need to be scheduled. The six tellersthat started their shift in the first hour are still on duty and fulfill the requirement that

there must be at least 5 workers during this hour.

At the beginning of the third hour (10-11 am), the three two-hour part-time tellers finishtheir shift. To offset this, a three-hour part-time teller should be scheduled to start at thishour, meeting the requirement of 4 tellers for this hour.

For the fourth hour (11 am-12 pm), one full-time teller (not working overtime), one two-hour part-time teller, and one three-hour part-time teller should be scheduled in order to

have 7 tellers working the bank.

During the fifth hour (12-1 pm), one three-hour part-time teller should be scheduled tofulfill the eight-teller requirement.


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At the start of the sixth hour (1-2 pm), two members of the staff end their shift.However, the requirement of six tellers for this hour is still fulfilled, so none need to be

scheduled.

For the seventh hour (2-3 pm), however, the first three full-time tellers as well as one ofthe part-time workers have finished their shifts. In order to meet the requirement that

three tellers be working this hour, another three-hour part-time teller must be scheduled.

At the beginning of the eighth hour (3-4 pm), the part-time teller who started at noon hasfinished his or her shift. While no teller needs to be added to fulfill the minimum teller

requirement of two for this hour, schedule a part-time two-hour teller to fulfill the last

hours requirement. This is because a teller cannot be scheduled during the last hour

because of the lack of available hours.

Because of the foresight in the previous hour, this hour (4-5 pm) meets the minimumrequirements of three tellers on duty. And at the end of this hour, all members of staff

have completed a full shift, closing the bank for the day.

At the end of this schedule, the total labor cost is calculated to be $496.

Overview:

Hour 1. Bank opens; 3 full-time tellers with no OT + 3 two-hour part-time tellersHour 2. No additionsHour 3. 1 three-hour part-time tellerHour 4. 1 full-time teller with no OT + 1 two-hour part-time teller + 1 three-hour

part-time teller

Hour 5. 1 three-hour part-time tellerHour 6. No additionsHour 7. 1 three-hour part-time tellerHour 8. 1 two-hour part-time tellerHour 9. No additions; Bank closes

the bank teller scheduling problem

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