Integer Programming Formulations for Approximate Packing Circles in a Rectangular Container
Joint Authors
Litvinchev, Igor
Ozuna Espinosa, Edith Lucero
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-25
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
A problem of packing a limited number of unequal circles in a fixed size rectangular container is considered.
The aim is to maximize the (weighted) number of circles placed into the container or minimize the waste.
This problem has numerous applications in logistics, including production and packing for the textile, apparel, naval, automobile, aerospace, and food industries.
Frequently the problem is formulated as a nonconvex continuous optimization problem which is solved by heuristic techniques combined with local search procedures.
New formulations are proposed for approximate solution of packing problem.
The container is approximated by a regular grid and the nodes of the grid are considered as potential positions for assigning centers of the circles.
The packing problem is then stated as a large scale linear 0-1 optimization problem.
The binary variables represent the assignment of centers to the nodes of the grid.
Nesting circles inside one another is also considered.
The resulting binary problem is then solved by commercial software.
Numerical results are presented to demonstrate the efficiency of the proposed approach and compared with known results.
American Psychological Association (APA)
Litvinchev, Igor& Ozuna Espinosa, Edith Lucero. 2014. Integer Programming Formulations for Approximate Packing Circles in a Rectangular Container. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-463038
Modern Language Association (MLA)
Litvinchev, Igor& Ozuna Espinosa, Edith Lucero. Integer Programming Formulations for Approximate Packing Circles in a Rectangular Container. Mathematical Problems in Engineering No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-463038
American Medical Association (AMA)
Litvinchev, Igor& Ozuna Espinosa, Edith Lucero. Integer Programming Formulations for Approximate Packing Circles in a Rectangular Container. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-463038
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463038