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.
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.
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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.
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