27. Six Sigma is a well-recognized quality management system that employs improvement projects to improve business processes to reduce product and service defects, reduce costs, and increase profits. Each project has a "champion" from upper management who is responsible for the proj-ect's success. The project leader is known as a "black belt," and project team members are called "green belts." Simsun, a manufacturer of cell phone parts and components, has eight improvement projects under consideration, and six champions, 10 black belts, and 25 green belts available to be assigned to the projects. The following table shows for each of the projects the number of green belts required, the percent reduction in defects expected, the cost savings (in $ millions), and the profit improvement (in $ millions). Green Belts Defect Cost Reduction (%) Savings (SM) Profit Improvements (S M) Project 1 3 0.97 1.32 1.9 2 4 1.35 1.16 2.3 3 7 1.16 0.95 3.6 4 2 0.82 0.88 2.7 5 6 1.02 1.05 4.1 6 5 0.86 1.26 3.8 7 4 1.15 1.13 5.3 8 6 0.96 0.85 4.8 The company wants to select the projects that will result in the greatest profit improvement while achieving a defect reduction of at least 5 percent and cost savings of at least $6.3 million. Formu-late and solve an integer programming model for this problem.

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...
icon
Related questions
Question
Please solve the problem in steps
27. Six Sigma is a well-recognized quality management system
that employs improvement projects to improve business
processes to reduce product and service defects, reduce costs,
and increase profits. Each project has a “champion" from upper
management who is responsible for the proj-ect's success. The
project leader is known as a "black belt," and project team
members are called "green belts." Simsun, a manufacturer of
cell phone parts and components, has eight improvement
projects under consideration, and six champions, 10 black belts,
and 25 green belts available to be assigned to the projects. The
following table shows for each of the projects the number of
green belts required, the percent reduction in defects expected,
the cost savings (in $ millions), and the profit improvement (in $
millions).
Green
Defect
Cost
Reduction (%) Savings ($ M)
Profit
Improvements ($ M)
Project
Belts
1
3
0.97
1.32
1.9
2
4
1.35
1.16
2.3
3
7
1.16
0.95
3.6
4
2
0.82
0.88
2.7
5
6
1.02
1.05
4.1
6
5
0.86
1.26
3.8
7
4
1.15
1.13
5.3
8
6
0.96
0.85
4.8
The company wants to select the projects that will result in the
greatest profit improvement while achieving a defect reduction
of at least 5 percent and cost savings of at least $6.3 million.
Formu-late and solve an integer programming model for this
problem.
Transcribed Image Text:27. Six Sigma is a well-recognized quality management system that employs improvement projects to improve business processes to reduce product and service defects, reduce costs, and increase profits. Each project has a “champion" from upper management who is responsible for the proj-ect's success. The project leader is known as a "black belt," and project team members are called "green belts." Simsun, a manufacturer of cell phone parts and components, has eight improvement projects under consideration, and six champions, 10 black belts, and 25 green belts available to be assigned to the projects. The following table shows for each of the projects the number of green belts required, the percent reduction in defects expected, the cost savings (in $ millions), and the profit improvement (in $ millions). Green Defect Cost Reduction (%) Savings ($ M) Profit Improvements ($ M) Project Belts 1 3 0.97 1.32 1.9 2 4 1.35 1.16 2.3 3 7 1.16 0.95 3.6 4 2 0.82 0.88 2.7 5 6 1.02 1.05 4.1 6 5 0.86 1.26 3.8 7 4 1.15 1.13 5.3 8 6 0.96 0.85 4.8 The company wants to select the projects that will result in the greatest profit improvement while achieving a defect reduction of at least 5 percent and cost savings of at least $6.3 million. Formu-late and solve an integer programming model for this problem.
Expert Solution
steps

Step by step

Solved in 5 steps with 4 images

Blurred answer
Similar questions
Recommended textbooks for you
Practical Management Science
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Business in Action
Business in Action
Operations Management
ISBN:
9780135198100
Author:
BOVEE
Publisher:
PEARSON CO
Purchasing and Supply Chain Management
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…
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.