Modified Integer Linear Programming Model for Bin-Packing Problems

1
Niluka P. Rodrigo
Niluka P. Rodrigo
2
W. B. Daundasekera
W. B. Daundasekera
3
A. A.I. Perera
A. A.I. Perera
1 University of Peradeniya

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In this paper, our objective is to compare the solutions obtained from develop mathematical model and general model for Two-Dimensional Bin Packing Problem (BPP) with different sizes of boxes. It has become one of the most important mathematical applications throughout the time. In our study, Modified Branch and Bound Algorithm (MBBA) is developed to generate all the feasible packing patterns of given boxes to required containers for Two-Dimensional BPP. A computer program is developed using Matlab software package to generate feasible packing patterns and optimum packing plan. As a case study, three different sizes of rectangular shape packing items are selected with given demand in order to pack into two different sizes of pallets. Applying the proposed algorithm, demand is satisfied and total unused area significantly minimized. Accordingly, proposed mathematical model is more appropriate for medium size two dimensional BPP.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Niluka P. Rodrigo. 2020. \u201cModified Integer Linear Programming Model for Bin-Packing Problems\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F8): .

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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 15A86
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v1.2

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December 15, 2020

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English

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In this paper, our objective is to compare the solutions obtained from develop mathematical model and general model for Two-Dimensional Bin Packing Problem (BPP) with different sizes of boxes. It has become one of the most important mathematical applications throughout the time. In our study, Modified Branch and Bound Algorithm (MBBA) is developed to generate all the feasible packing patterns of given boxes to required containers for Two-Dimensional BPP. A computer program is developed using Matlab software package to generate feasible packing patterns and optimum packing plan. As a case study, three different sizes of rectangular shape packing items are selected with given demand in order to pack into two different sizes of pallets. Applying the proposed algorithm, demand is satisfied and total unused area significantly minimized. Accordingly, proposed mathematical model is more appropriate for medium size two dimensional BPP.

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Modified Integer Linear Programming Model for Bin-Packing Problems

Niluka P. Rodrigo
Niluka P. Rodrigo University of Peradeniya
W. B. Daundasekera
W. B. Daundasekera
A. A.I. Perera
A. A.I. Perera

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