AN ANALYSIS OF GOMORY CUTTING PLANE METHOD APPLICATION IN THE OPTIMIZATION OF PRODUCTION PROFIT: A CASE STUDY OF GRIYA BATIK NOTONEGORO JEMBER

  • Girlyas Rasta Yunta Department of Mathematics Education, FKIP, University of Jember, Indonesia
  • Susi Setiawani Department of Mathematics Education, FKIP, University of Jember, Indonesia
  • Rafiantika Megahnia Prihandini Department of Mathematics Education, FKIP, University of Jember, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss1pp0053-0064
Keywords: optimization, integer programming, gomory cutting plane method, dual simplex method

Abstract

Gomory cutting plane method is one of the methods in linear programming that is needed to solve integer programming when the decision obtained is in the form of fractions with the addition of constraint known as gomory constraint. The purpose of this research is to determine the best optimum solution by maximizing the profit of batik production using the gomory cutting plane method. This type of research is applied research using a quantitative approach. Data collection methods used are interviews and documentation. This research is focused on four kinds of Jember batik motifs which are the best-selling, namely  mbako semak batik cloth;   sekar jagad batik cloth;  kopi daun batik cloth; and  parakopi batik cloth. The results showed that there was an increase in profit of  or  per production when using the simplex method assisted by QM for Windows V5 software. Meanwhile, to make batik cloth, integer values are needed in the form of integers. Therefore, the application of gomory cutting plane method in optimizing the profit of batik production is very appropriate to use with the obtained maximum settlement of   which occurs when  sheets,  sheets,  sheets, and  sheets.

Downloads

Download data is not yet available.

References

A. I. Iheagwara, J. Opara, P. A. Esemokumo, and J. I. Lebechi, “Application of Linear Programming Problem on Niger Mills Company PLC Calabar,” Int. J. Innov. Res. Educ. Sci., vol. 1, no. 2, pp. 2349–5219, 2014.

A. Kumar and J. Kaur, “A New Method for Solving Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers,” J. Fuzzy Set Valued Anal., vol. 2011, pp. 1–12, 2011, doi: 10.5899/2011/jfsva-00102.

H. Palayukan, “Optimization of Production Benefits Through the Linear Program Graph Method: A Case Study Zentha Meubel Hersiyati,” Math. Educ. Journals, vol. 5, no. 1, pp. 66–74, 2021, doi: https://doi.org/10.22219/mej.v5i1.15055.

F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, Seventh Edition. New York: The McGraw-Hill Companies, Inc.: New York: The McGraw-Hill Companies, Inc., 1990.

H. Suwardana, “Revolusi Industri 4. 0 Berbasis Revolusi Mental,” JATI UNIK J. Ilm. Tek. dan Manaj. Ind., vol. 1, no. 2, pp. 109–118, 2018, doi: 10.30737/jatiunik.v1i2.117.

I. R. Salma, A. A. Wibowo, and Y. Satria, “Kopi dan Kakao dalam Kreasi Motif Batik Khas Jember,” Din. Kerajinan dan Batik, vol. 32, no. 7, pp. 63–72, 2015.

P. R. Sinaga, “Perencanaan Optimasi Produksi Sarung Tangan Menggunakan Linear Programing Pada PT. Smart Glove Indonesia,” Maj. Ilm. Inf. dan Teknol. Ilm., vol. 4, no. 1, pp. 44–50, 2016.

I. K. Juliantara and K. Mandala, “Perencanaan dan Pengendalian Produksi Agregat Pada Usaha Tedung UD Dwi Putri di Klungkung,” E-Jurnal Manaj. Univ. Udayana, vol. 9, no. 1, p. 99, 2020, doi: 10.24843/ejmunud.2020.v09.i01.p06.

E. Adriantantri and S. Indriani, “Optimization of Production Planning Using Linear Programming,” Int. J. Softw. Hardw. Res. Eng. Emmalia Adriantantri; Sri Indriani, vol. 9, no. 11, pp. 41–46, 2021, doi: 10.26821/IJSHRE.9.11.2021.91116.

Y. Ba’ru and B. V. Remme, “Penerapan Metode Grafik dalam Merencanakan Produksi Kue Ibu Patrisia di Rantelemo,” J. KIP, vol. 8, no. 1, pp. 21–25, 2019, [Online]. Available: http://scholar.googleusercontent.com/scholar?q=cache:AjOiGSv6M6MJ:scholar.google.com/+4.%09Yusem+Ba%27ru+dan+Beatric+Videlia+Remme,+(2019)+penelitian+ini+tentang+“Penerapan+Metode+Grafik+dalam+Merencanakan+Produksi+Kue+Ibu+Patrisia+di+Rantelemo&hl=id&as_s.

S. Setiawani, “Metode Relaksasi Lagrange untuk Menentukan Solusi Program Bilangan Cacah,” Maj. Ilm. Mat. dan Stat., vol. 17, no. 2, pp. 49–60, 2017.

K. Genova and V. Guliashki, “Linear Integer Programming Methods and Approaches - A Survey,” Cybern. Inf. Technol., vol. 11, no. 1, pp. 3–25, 2011.

Nico, Iryanto, and G. Tarigan, “Aplikasi Metode Cutting Plane Produksi Tahunan,” saintia Mat., vol. 2, no. 2, pp. 127–136, 2014.

F. Firmansah and F. Wulandari, “Integer Linear Programming Application in Production Results Optimization Using Cutting Plane Method,” Desimal J. Mat., vol. 4, no. 1, pp. 57–66, 2021, doi: 10.24042/djm.

F. Wesselmann, A. Koberstein, and U. H. Suhl, “Pivot-and-reduce Cuts: An Approach for Improving Gomory Mixed-integer Cuts,” Eur. J. Oper. Res., vol. 214, no. 1, pp. 15–26, 2011, doi: 10.1016/j.ejor.2011.04.009.

Published
2023-04-15
How to Cite
[1]
G. Yunta, S. Setiawani, and R. Prihandini, “AN ANALYSIS OF GOMORY CUTTING PLANE METHOD APPLICATION IN THE OPTIMIZATION OF PRODUCTION PROFIT: A CASE STUDY OF GRIYA BATIK NOTONEGORO JEMBER”, BAREKENG: J. Math. & App., vol. 17, no. 1, pp. 0053-0064, Apr. 2023.
Issue
Vol 17 No 1 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Girlyas Rasta Yunta, Susi Setiawani, Rafiantika Megahnia Prihandini

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Authors who publish with this Journal agree to the following terms:

  1. Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
  2. Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
  3. Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.