Implementasi Integer Programming dengan Algoritma Branch and Bound Menggunakan QM for Windows dalam Memaksimalkan Keuntungan di PT XYZ

Abstract

In maximizing the profits to be obtained the company needs optimal production planning. The plan considers the resources of the company. PT XYZ is a furniture company. This research focuses on optimizing production planning on the manufacture of door products at PT. XYZ. There are several types of products issued in: D1 type door, D2 type door, D3 type door, and D4 type door. Production planning at PT. XYZ can be seen as an integer program model, which is a method related to optimizing resources to increase profits. Optimization is done by determining the amount of production for each type and each calculating existing resources. The solution search for this model is done by the Branch and Bound algorithm. Based on the calculation results using QM software for Windows, the amount corresponding to production is obtained by using Branches and Bound giving an increase of 36.5% compared to the acquisition of PT. XYZ before. Keywords: Branch and Bound Algorithms, Integer Programming,Optimization AbstrakDalam memaksimalkan keuntungan yang akan diperoleh perusahaan perlu adanya perencanaan produksi yang optimal. Perencanaan tersebut mempertimbangkan ketersediaan sumber daya pada perusahaan. PT XYZ merupakan perusahaan yang bergerak di bidang furniture. Penelitian ini fokus kepada pengoptimalan perencanaan produksi pada pembuatan produk pintu di PT.XYZ. Terdapat beberapa jenis produk yang diproduksi di antaranya: Pintu tipe D1, Pintu tipe D2, Pintu tipe D3, dan Pintu tipe D4. Perencanaan produksi di PT.XYZ ini dapat dikatakan sebagai model program integer, karena semua variabel menghendaki hasilnya berupa bilangan bulat. Program tersebut berhubungan dengan pengoptimalan ketersediaan sumber daya bertujuan untuk memaksimalkan keuntungan. Pengoptimalan yang dilakukan yaitu dengan menentukan jumlah produksi untuk masing-masing tipe serta mempertimbangkan semua ketersediaan sumber daya yang ada. Pencarian solusi untuk model ini dilakukan dengan algoritma Branch and Bound. Berdasarkan hasil perhitungan menggunakan software QM for Windows, diketahui bahwa penentuan jumlah produksi dengan menggunakan algoritma Branch and Bound memberikan peningkatan keuntungan sebesar 36.5% dibandingkan dengan keuntungan PT.XYZ sebelumnya. Kata kunci: Optimasi, program integer, algoritma Branch and BoundReferensi[1] Sofyan Assauri. Manajemen Produksi dan Operasi. Lembaga Penerbit FakultasEkonomi Universitas Indonesia. Jakarta. 2008.[2] Winston, W. L. Operations Research: Applications and Algorithms. Edisi Keempat.Canada: Brooks/Cole-Thomson Learning. 2004.[3] Akram, S. A., dan Jaya, A. I. Optimalisasi Produksi Roti dengan Menggunakan Metode Branch and Bound (Studi Kasus Pada Pabrik Roti Syariah Bakery, Jl. Maleo, Lrg.VIII No. 68 Palu). Jurnal Ilmiah Matematika dan Terapan, 13(2): 98-107. 2016.[4] Jiao, H. W., dkk. An Effective Branch and Bound Algorithm for MinimaxLinear Fractional Programming. Journal of Applied Mathematics, Volume 2014: 8. 2014.[5] Williams, H. P. The Problem with Integer Programming. Journal of Management Mathematics, 22(3): 213-230. 2011.[6] Falani, I. Penentuan Nilai Parameter Metode Exponential Smoothing dengan Algoritma Genetik dalam Meningkatkan Akurasi Forecasting. Journal of Computer Engineering System and Science, 3(1): 14–16. 2018.[7] Mehdizadeh, E., dan Jalili, S. An Algorithm Based on Theory of Constraints and Branch and Bound for Solving Integrated Product-Mix-Outsourcing Problem. Journal of Optimization in Industrial Engineering, 12(1): 167-172. 2019.[8] Taylor, B. W. Introduction to Management Science. Edisi ke-11. United States of America: Prentice-Hall International, INC. 2013[9] Puryani., dan Ristono, A. Penelitian Operasional. Yogyakarta: Graha Ilmu. 2012.[10] Yusrah N. dkk. Implementasi Algoritma Branch and Bound Dalam Penentuan Jumlah Produksi Untuk Memaksimalkan Keuntungan. Jurnal String Vol. 3 No. 1 Agustus 2018. ISSN: 2527-9661[11] Taha, H. A. Operations Research: An Introduction. Edisi ke-8. United States of America: Prentice-Hall International, INC. 2007.

Application of integer linear program in optimizing convection sector production results using branch and bound method

“…Thus, the optimal amount of daily production at Ayyumnah store is 1 pcs of long shirt and 9 pcs of tunics with maximum profit of Rp 310.000,00. The results of this study are in line with previous studies, namely (Buyung & Suhendar, 2020), (Buyung & Suhendar, 2021), (Jannah A.M et al, 2018), (Purba & Ahyaningsih, 2020) and (Liu & Gao, 2015). The novelty value of this study is the development of an integer linear program application using the branch and bound method in the convection sector, where this has not been discussed in previous studies.…”

“…While Buyung and Suhendar, in 2020, used the branch and bound method to optimize profits (Buyung & Suhendar, 2020). In another article, Buyung and Suhendar, in 2021, implemented an integer program with a branch and bound algorithm using QM for Windows. (Buyung & Suhendar, 2021).…”

“…In another article, Buyung and Suhendar, in 2021, implemented an integer program with a branch and bound algorithm using QM for Windows. (Buyung & Suhendar, 2021).…”