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Integer Linear Programming In Production Profit Optimization Problems Using Branch And Bound Methods & Gomory Cutting Plane

Jurnal Matematika, Statistika dan Komputasi · Vol. 20 No. 3 (2024) · pp. 552–567

DOI
10.20956/j.v20i3.32888
ISSN
2614-8811, 1858-1382
Published
2024-05-15
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Integer Linear Programming is a mathematical model that allows the results of solving cases in linear programming in the form of integers. Methods to solve Integer Programming problems include the Branch and Bound Method and the Gomory Cutting Plane Method. Both of these methods have certain rules for adding new constraint functions until an optimal solution to an integer is obtained. The purpose of this study is to optimize the profits of the production of UMKM Capal Classic Shoes Kab. Agam by using the Branch and Bound method and the Gomory Cutting Plane method and analyzing the comparison of optimal results resulting from the two methods. The data used in the study are data on raw materials for making classic sandals and profit data. The results obtained by these two methods produce the same maximum profit, namely RP. 664,000 with each producing 15 pairs of men's sandals and 13 pairs of women's sandals. But in its completion, the Branch and Bound method requires many iterations and a longer time compared to the Gumory Cutting plane method.

Bahasa Indonesia

Integer Linear Programming adalah sebuah model matematis yang memungkinkan hasil penyelesaian kasus pada pemrograman linier yang berupa bilangan bulat. Metode untuk menyelesaikan persoalan Integer Programming diantaranya adalah Metode Branch and Bound dan Metode Gomory Cutting Plane. Kedua metode ini memiliki aturan tertentu dalam menambahkan fungsi batasan baru hingga diperoleh solusi optimal bilangan bulat. Tujuan dari penelitian ini adalah mengoptimalkan keuntungan dari produksi UMKM Capal Classic Shoes Kabupaten Agam dengan menggunakan metode Branch and Bound dan metode Gomory Cutting Plane serta menganalisis perbandingan terhadap hasil optimal yang dihasilkan dari kedua metode tersebut. Hasil yang diperoleh kedua metode tersebut menghasilkan keuntungan optimal yang sama yaitu Rp. 664.000

Keywords

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7 authors · 8 co-authorship links

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Muhafzan MuhafzanAffiliation unknown1
DWI SULISTIOWATIAffiliation unknown1
Ilham Dangu RianjayaAffiliation unknown1
Iswan RinaAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Integer Linear Programming In Production Profit Optimization Problems Using Branch And Bound Methods &amp; Gomory Cutting Plane</dc:title>
	<dc:creator xml:lang="en">putri, Nurweni</dc:creator>
	<dc:creator xml:lang="en">Syahrul, Maya Sari </dc:creator>
	<dc:creator xml:lang="en">Ramayanti, Rosi </dc:creator>
	<dc:subject xml:lang="en"> Linear Programming</dc:subject>
	<dc:subject xml:lang="en"> Integer Programming</dc:subject>
	<dc:subject xml:lang="en">Branch and Bound</dc:subject>
	<dc:subject xml:lang="en">Gomory Cutting Plane</dc:subject>
	<dc:description xml:lang="en">Integer Linear Programming is a mathematical model that allows the results of solving cases in linear programming in the form of integers. Methods to solve Integer Programming problems include the Branch and Bound Method and the Gomory Cutting Plane Method. Both of these methods have certain rules for adding new constraint functions until an optimal solution to an integer is obtained. The purpose of this study is to optimize the profits of the production of UMKM Capal Classic Shoes Kab. Agam  by using the Branch and Bound method and the Gomory Cutting Plane method and analyzing the comparison of optimal results resulting from the two methods. The data used in the study are data on raw materials for making classic sandals and profit data. The results obtained by these two methods produce the same maximum profit, namely RP. 664,000 with each producing 15 pairs of men's sandals and 13 pairs of women's sandals. But in its completion, the Branch and Bound method requires many iterations and a longer time compared to the Gumory Cutting plane method.</dc:description>
	<dc:description xml:lang="id">Integer Linear Programming adalah sebuah model matematis yang memungkinkan hasil penyelesaian kasus pada pemrograman linier yang berupa bilangan bulat. Metode untuk menyelesaikan persoalan Integer Programming diantaranya adalah Metode Branch and Bound dan Metode Gomory Cutting Plane. Kedua metode ini memiliki aturan tertentu dalam menambahkan fungsi batasan baru hingga diperoleh solusi optimal bilangan bulat. Tujuan dari penelitian ini adalah mengoptimalkan keuntungan dari produksi UMKM Capal Classic Shoes Kabupaten Agam dengan menggunakan metode Branch and Bound dan metode Gomory Cutting Plane serta menganalisis perbandingan terhadap hasil optimal yang dihasilkan dari kedua metode tersebut. Hasil yang diperoleh kedua metode tersebut menghasilkan keuntungan optimal yang sama yaitu Rp. 664.000</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2024-05-15</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/32888</dc:identifier>
	<dc:identifier>10.20956/j.v20i3.32888</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 20 No. 3 (2024): May 2024; 552-567</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/32888/11487</dc:relation>
	<dc:relation>10.20956/j.v20i3.32888.g11487</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2024 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>