Excel Please. The workload of many areas of banking operations varies considerably based on time of day. A variable capacity can be achieved effectively by employing part-time personnel. Because part-timers are not entitled to all the fringe benefits, they are often more economical than full-time employees. Other considerations, however, may limit the extent to which part-time people can be hired in a given department. The problem is to find an optimal workforce schedule that would meet personnel requirements at any given time and also be economical. Some of the factors affecting personnel assignments are listed here: The bank is open from 9:00am to 7:00pm. Full-time employees work for 8 hours (1 hour for lunch included) per day. They do not necessarily have to start their shift when the bank opens. Part-time employees work for at least 4 hours per day, but less than 8 hours per day and do not get a lunch break. By corporate policy, total part-time personnel hours is limited to a maximum of 40% of the day’s total labor requirement. *Only an integer number of people can be employed No more than 60% of the full-timers can be gone to lunch at a given time. Lunch can be taken from 11:00am-12:00pm or from 12:00 – 1:00pm. A full-time employee can work up to one hour of overtime per day (assume that it would come at the end of his/her shift). A full-time employee is paid at the normal rate for overtime hours which excludes fringe benefits. Pay rates are $15.25 per full-time personnel hour (includes fringe benefits), $12.50 per full-time overtime personnel hour (excludes fringe benefits), and $12.00 per part-time personnel hour. The personnel hours required by hour of day are given below. Time Period Hours Required 9-10am 14 10-11am 25 11am-12pm 26 12-1pm 38 1-2pm 55 2-3pm 60 3-4pm 51 4-5pm 29 5-6pm 14 6-7pm 9 Design a single linear programming model that can be used to answer all of the following questions: The bank’s goal is to achieve the minimum possible daily personnel cost while satisfying the hourly labor requirements and other constraints. Use linear programming to determine how to best schedule the personnel. Management is concerned that the requirement that no more than 60% of the full-timers can be gone to lunch at a given time is too lax and would like to tighten it somewhat. Use Solvertable to investigate further restricting the requirement by increments of 5%. By how much could they restrict this requirement before the LP is no longer feasible? To gear up for a busy holiday season, management thinks they may simultaneously need up to 5 more labor hours available in each of the time periods in the workday. Use Solvertable to investigate the consequence of needing from 1 to 5 extra hours by increments of 1 hour. (i.e. 1 extra hour needed in every time period, 2 extra hours needed in every time period, …, 5 extra hours needed in every time period. *With the integer constraints, the model can take a while to solve. You might run it initially without the integer constraints to be sure that your logic is working and then add them at the end.

Excel Please. The workload of many areas of banking operations varies considerably based on time of day. A variable capacity can be achieved effectively by employing part-time personnel. Because part-timers are not entitled to all the fringe benefits, they are often more economical than full-time employees. Other considerations, however, may limit the extent to which part-time people can be hired in a given department. The problem is to find an optimal workforce schedule that would meet personnel requirements at any given time and also be economical. Some of the factors affecting personnel assignments are listed here: The bank is open from 9:00am to 7:00pm. Full-time employees work for 8 hours (1 hour for lunch included) per day. They do not necessarily have to start their shift when the bank opens. Part-time employees work for at least 4 hours per day, but less than 8 hours per day and do not get a lunch break. By corporate policy, total part-time personnel hours is limited to a maximum of 40% of the day’s total labor requirement. Only an integer number of people can be employed No more than 60% of the full-timers can be gone to lunch at a given time. Lunch can be taken from 11:00am-12:00pm or from 12:00 – 1:00pm. A full-time employee can work up to one hour of overtime per day (assume that it would come at the end of his/her shift). A full-time employee is paid at the normal rate for overtime hours which excludes fringe benefits. Pay rates are $15.25 per full-time personnel hour (includes fringe benefits), $12.50 per full-time overtime personnel hour (excludes fringe benefits), and $12.00 per part-time personnel hour. The personnel hours required by hour of day are given below. Time Period Hours Required 9-10am 14 10-11am 25 11am-12pm 26 12-1pm 38 1-2pm 55 2-3pm 60 3-4pm 51 4-5pm 29 5-6pm 14 6-7pm 9 Design a single linear programming model that can be used to answer all of the following questions: The bank’s goal is to achieve the minimum possible daily personnel cost while satisfying the hourly labor requirements and other constraints. Use linear programming to determine how to best schedule the personnel. Management is concerned that the requirement that no more than 60% of the full-timers can be gone to lunch at a given time is too lax and would like to tighten it somewhat. Use Solvertable to investigate further restricting the requirement by increments of 5%. By how much could they restrict this requirement before the LP is no longer feasible? To gear up for a busy holiday season, management thinks they may simultaneously need up to 5 more labor hours available in each of the time periods in the workday. Use Solvertable to investigate the consequence of needing from 1 to 5 extra hours by increments of 1 hour. (i.e. 1 extra hour needed in every time period, 2 extra hours needed in every time period, …, 5 extra hours needed in every time period. With the integer constraints, the model can take a while to solve. You might run it initially without the integer constraints to be sure that your logic is working and then add them at the end.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

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Question

Some of the factors affecting personnel assignments are listed here:

The bank is open from 9:00am to 7:00pm.
Full-time employees work for 8 hours (1 hour for lunch included) per day. They do not necessarily have to start their shift when the bank opens.
Part-time employees work for at least 4 hours per day, but less than 8 hours per day and do not get a lunch break.
By corporate policy, total part-time personnel hours is limited to a maximum of 40% of the day’s total labor requirement.
*Only an integer number of people can be employed
No more than 60% of the full-timers can be gone to lunch at a given time. Lunch can be taken from 11:00am-12:00pm or from 12:00 – 1:00pm.
A full-time employee can work up to one hour of overtime per day (assume that it would come at the end of his/her shift).
A full-time employee is paid at the normal rate for overtime hours which excludes fringe benefits. Pay rates are $15.25 per full-time personnel hour (includes fringe benefits), $12.50 per full-time overtime personnel hour (excludes fringe benefits), and $12.00 per part-time personnel hour.
The personnel hours required by hour of day are given below.

Time Period	Hours Required
9-10am	14
10-11am	25
11am-12pm	26
12-1pm	38
1-2pm	55
2-3pm	60
3-4pm	51
4-5pm	29
5-6pm	14
6-7pm	9

Design a single linear programming model that can be used to answer all of the following questions:

The bank’s goal is to achieve the minimum possible daily personnel cost while satisfying the hourly labor requirements and other constraints. Use linear programming to determine how to best schedule the personnel.
Management is concerned that the requirement that no more than 60% of the full-timers can be gone to lunch at a given time is too lax and would like to tighten it somewhat. Use Solvertable to investigate further restricting the requirement by increments of 5%. By how much could they restrict this requirement before the LP is no longer feasible?
To gear up for a busy holiday season, management thinks they may simultaneously need up to 5 more labor hours available in each of the time periods in the workday. Use Solvertable to investigate the consequence of needing from 1 to 5 extra hours by increments of 1 hour. (i.e. 1 extra hour needed in every time period, 2 extra hours needed in every time period, …, 5 extra hours needed in every time period.

*With the integer constraints, the model can take a while to solve. You might run it initially without the integer constraints to be sure that your logic is working and then add them at the end.

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