Homework Help is Here – Start Your Trial Now!
Business
Operations Management
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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
See similar textbooks
icon
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.

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.
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
steps

Step by step

Solved in 3 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Practical Management Science
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
SEE MORE TEXTBOOKS