Question 1 A department store manager is assigning the tasks for a Saturday morning shift. Typically, about 500 shoppers visit the store during this shift. The total working hours available to the manager during the shift are 240 hours. Employees will be assigned to four different tasks: cashiers, customer service employees, operators of the special departments (such as the bakery and the meat departments), and storage management workers. The manager must assign at least 8 working hours for cashiers, 8 working hours for customer service employees, 24 working hours for special departments operators, and 24 working hours to storage management workers. Also, the manager cannot allocate more than 96 and 48 working hours for the cashiers and customer services employees, respectively, due to the limited number of cash registers and customer service desks. The hourly rates for the employees in different departments are given in the table below. The manager wants to limit the total employees' compensation during the shift to a maximum of S 4,800. Moreover, the store has a measure of efficiency (ME) for each task, expressed as follows: No. of hours allocated to the task МЕ No.of shoppers in shift Where y is a variable that depends on the task, as shown in the table below. The higher the value of ME, the better the task performance. The overall efficiency of the shift can be determined as the summation of the (ME) indices of the four tasks. са Task Hourly rate Variable (y) Cashier 18 172 Customer service employee Special departments' operators Storage management workers 21 144 208 152 24 16 Based on the provided information: a) Develop an optimization model to help the manager allocate the optimal number of hours for each task. b) Express the developed model in its standard form.
Question 1 A department store manager is assigning the tasks for a Saturday morning shift. Typically, about 500 shoppers visit the store during this shift. The total working hours available to the manager during the shift are 240 hours. Employees will be assigned to four different tasks: cashiers, customer service employees, operators of the special departments (such as the bakery and the meat departments), and storage management workers. The manager must assign at least 8 working hours for cashiers, 8 working hours for customer service employees, 24 working hours for special departments operators, and 24 working hours to storage management workers. Also, the manager cannot allocate more than 96 and 48 working hours for the cashiers and customer services employees, respectively, due to the limited number of cash registers and customer service desks. The hourly rates for the employees in different departments are given in the table below. The manager wants to limit the total employees' compensation during the shift to a maximum of S 4,800. Moreover, the store has a measure of efficiency (ME) for each task, expressed as follows: No. of hours allocated to the task МЕ No.of shoppers in shift Where y is a variable that depends on the task, as shown in the table below. The higher the value of ME, the better the task performance. The overall efficiency of the shift can be determined as the summation of the (ME) indices of the four tasks. са Task Hourly rate Variable (y) Cashier 18 172 Customer service employee Special departments' operators Storage management workers 21 144 208 152 24 16 Based on the provided information: a) Develop an optimization model to help the manager allocate the optimal number of hours for each task. b) Express the developed model in its standard form.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
Based on the provided information:
a) Develop an optimization model to help the manager allocate the optimal number of hours for each task.
b) Express the developed model in its standard form.
Transcribed Image Text:Question 1
A department store manager is assigning the tasks for a Saturday morning shift. Typically, about
500 shoppers visit the store during this shift. The total working hours available to the manager
during the shift are 240 hours.
Employees will be assigned to four different tasks: cashiers, customer service employees,
operators of the special departments (such as the bakery and the meat departments), and storage
management workers. The manager must assign at least 8 working hours for cashiers, 8 working
hours for customer service employees, 24 working hours for special departments operators, and
24 working hours to storage management workers. Also, the manager cannot allocate more than
96 and 48 working hours for the cashiers and customer services employees, respectively, due to
the limited number of cash registers and customer service desks.
The hourly rates for the employees in different departments are given in the table below. The
manager wants to limit the total employees' compensation during the shift to a maximum of $
4,800. Moreover, the store has a measure of efficiency (ME) for each task, expressed as follows:
No. of hours allocated to the task
МЕ
No.of shoppers in shift
Where y is a variable that depends on the task, as shown in the table below. The higher the value
of ME, the better the task performance. The overall efficiency of the shift can be determined as the
summation of the (ME) indices of the four tasks.
Task
Hourly rate
Variable (y)
Cashier
Customer service employee
Special departments' operators
Storage management workers
18
172
21
144
24
208
16
152
Based on the provided information:
a) Develop an optimization model to help the manager allocate the optimal number of hours
for each task.
b) Express the developed model in its standard form.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.