scholarly journals Exact and Heuristic Approaches to the Maximum Capacity Representatives Problem

2018 ◽  
Author(s):  
Italos Estilon Da Silva De Souza ◽  
Mauro Roberto Costa Da Silva ◽  
Welverton Rodrigues Da Silva ◽  
Rafael C. S. Schoeury
Keyword(s):  
Integer Programming ◽  
Branch And Bound ◽  
Exact Method ◽  
Branch And Bound Algorithm ◽  
Maximum Capacity ◽  
Heuristic Approaches ◽  
Disjoint Sets

This paper approaches the problem of finding the system of representatives of a family of disjoint sets. To solve this problem, three methods were used: integer programming, branch-and-bound, and the BRKGA metaheuristic. We observed that, in randomly generated instances, the branch-and-bound algorithm was the best exact method but it was surpassed by BRKGA for large instances.

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

2021 ◽  
Vol 5 (1) ◽  
pp. 14-18
Author(s):  
Nintia Litano Buyung ◽  
Endang Suhendar
Keyword(s):  
United States ◽  
Integer Programming ◽  
Production Planning ◽  
Branch And Bound ◽  
Operations Research ◽  
United States Of America ◽  
Applied Mathematics ◽  
Branch And Bound Algorithm ◽  
Theory Of Constraints ◽  
Engineering System

AbstractIn 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.

scholarly journals Estimating the size of search trees by sampling with domain knowledge

2017 ◽  
Author(s):  
Gleb Belov ◽  
Samuel Esler ◽  
Dylan Fernando ◽  
Pierre Le Bodic ◽  
George L. Nemhauser
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Branch And Bound ◽  
Domain Knowledge ◽  
Estimation Error ◽  
Search Tree ◽  
Branch And Bound Algorithm ◽  
Mixed Integer ◽  
Search Trees ◽  
Sampling Algorithm

We show how recently-defined abstract models of the Branch-and-Bound algorithm can be used to obtain information on how the nodes are distributed in B&B search trees. This can be directly exploited in the form of probabilities in a sampling algorithm given by Knuth that estimates the size of a search tree. This method reduces the offline estimation error by a factor of two on search trees from Mixed-Integer Programming instances.

Sign in / Sign up

Export Citation Format

Share Document