Penerapan algoritma Dinkelbach dan transformasi Charnes Cooper pada pemrograman fraksional linear di UD Bintang Furniture

  • Muhammad Wakhid Musthofa Program Studi Matematika UIN Sunan Kalijaga Yogyakarta
  • Evira Dian Safitri Program Studi Matematika UIN Sunan Kalijaga Yogyakarta

Abstract

Linear fractional programming is a special case of non-linear programming with an objective function consisting of the ratio of two linear functions. The problem can be solved using the Dinkelbach algorithm and the Charnes Cooper transformation. The essence of these two methods is to convert the problem of linear fractional programming into a linear programming problem which then provides an optimal value of each variable in its objective function. In this study, we will solve the problem of linear fractional programming at UD Bintang Furniture, that is to determine the optimal value of the comparison between profits and production costs of the company. The results show that the Dinkelbach algorithm method requires more iterations than Charnes Cooper's transformation. Despite this, both methods produce the same optimal value. 


Keywords: Linear fractional programming, Dinkelbach algorithm, Charnes Cooper  transformation.
MSC2020: 90C32

Published
2022-09-28
How to Cite
MUSTHOFA, Muhammad Wakhid; SAFITRI, Evira Dian. Penerapan algoritma Dinkelbach dan transformasi Charnes Cooper pada pemrograman fraksional linear di UD Bintang Furniture. Majalah Ilmiah Matematika dan Statistika, [S.l.], v. 22, n. 2, p. 161-176, sep. 2022. ISSN 2722-9866. Available at: <https://jurnal.unej.ac.id/index.php/MIMS/article/view/31615>. Date accessed: 09 feb. 2023. doi: https://doi.org/10.19184/mims.v22i2.31615.