An enhanced branch-and-bound algorithm for bilevel integer linear programming

2020 ◽  
Author(s):  
Shaonan Liu ◽  
Mingzheng Wang ◽  
Nan Kong ◽  
Xiangpei Hu
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Integer Linear Programming ◽  
Branch And Bound Algorithm

scholarly journals A Note on Branch and Bound Algorithm for Integer Linear Programming

2019 ◽  
pp. 1-6
Author(s):  
Syed Inayatullah ◽  
Wajiha Riaz ◽  
Hafsa Athar Jafree ◽  
Tanveer Ahmed Siddiqi ◽  
Muhammad Imtiaz ◽  
...  
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Integer Linear Programming ◽  
Simplex Method ◽  
Phase 1 ◽  
Branch And Bound Algorithm ◽  
Dual Simplex Method ◽  
Dual Simplex ◽  
Efficient Alternative ◽  
A New Technique

In branch and bound algorithm for integer linear programming the usual approach is incorporating dual simplex method to achieve feasibility for each sub-problem. Although one can also employ the phase 1 simplex method but the simplicity and easy implementation of the dual simplex method bounds the users to use it. In this paper a new technique for handling sub-problems in branch and bound method has been presented, which is an efficient alternative of dual simplex method.

scholarly journals Penjadwalan Integer Linear Programming pada Penjadwalan Produksi Tipe Flowshop dan Program Optimasi Waktu dengan Metode Branch and Bound

2021 ◽  
Vol 3 (1) ◽  
pp. 44-51
Author(s):  
Ismawati Khotimah ◽  
Hagni Wijayanti ◽  
Sri Setyaningsih
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Integer Linear Programming

Penjadwalan merupakan pengalokasian sumber daya yang tersedia untuk menyelesaikan sejumlah pekerjaan dengan mempertimbangkan batasan yang ada. Hal yang cukup penting dalam perusahaan adalah menentukan penjadwalan yang optimal agar kegiatan produksi dapat berjalan dengan lancar, efisien, dan sistematis. PT Unitex merupakan perusahaan yang bergerak dalam bidang tekstil. Perusahaan ini menerapkan penjadwalan yang kurang efisien sehingga menyebabkan permasalahan seperti keterlambatan waktu dalam penyelesaian produksi akibat terlalu banyaknya permintaan konsumen yang tidak menentu. Perusahaan melakukan penjadwalan hanya diperkirakan saja dan tidak menggunakan metode ilmiah. Metode Branch and Bound dapat diterapkan pada permasalahan tersebut karena dapat menentukan penjadwalan yang tepat dengan waktu optimal. Metode Branch and Bound adalah metode pencarian dalam menentukan solusi optimal pada penjadwalan dengan menentukan nilai batas atas dan nilai  batas bawah untuk menghasilkan nilai makespan dari tiap job yang dikerjakan. Penjadwalan menggunakan Metode Branch and Bound menghasilkan urutan penjadwalan produksi dengan job 1-5-3-6-7-2-4 dengan makespan sebesar 17290.73 menit. Nilai ini lebih kecil dibandingkan hasil makespan perusahaan yaitu 19278.13 menit. Hal tersebut meminimumkan makespan sebesar 10.31%.

scholarly journals A Deterministic Method for Solving the Sum of Linear Ratios Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhenping Wang ◽  
Yonghong Zhang ◽  
Paolo Manfredi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Branch And Bound ◽  
Nonconvex Programming ◽  
Real Life ◽  
Branch And Bound Algorithm ◽  
Separation Technique ◽  
Linear Programming Relaxation ◽  
Deterministic Method ◽  
Linearization Technique

Since the sum of linear ratios problem (SLRP) has many applications in real life, for globally solving it, an efficient branch and bound algorithm is presented in this paper. By utilizing the characteristic of the problem (SLRP), we propose a convex separation technique and a two-part linearization technique, which can be used to generate a sequence of linear programming relaxation of the initial nonconvex programming problem. For improving the convergence speed of this algorithm, a deleting rule is presented. The convergence of this algorithm is established, and some experiments are reported to show the feasibility and efficiency of the proposed algorithm.

scholarly journals Historical Load Balance in Distribution Systems Using the Branch and Bound Algorithm

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1219 ◽  
Author(s):  
Jorge Arias ◽  
Maria Calle ◽  
Daniel Turizo ◽  
Javier Guerrero ◽  
John Candelo-Becerra
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Distribution System ◽  
Load Balance ◽  
Distribution Systems ◽  
Branch And Bound Algorithm ◽  
Power Demand ◽  
Planning Tool ◽  
Time Intervals ◽  
Processing Technologies

One of the biggest problems with distribution systems correspond to the load unbalance created by power demand of customers. This becomes a difficult task to solve with conventional methods. Therefore, this paper uses integer linear programming and Branch and Bound algorithm to balance the loads in the three phases of the distribution system, employing stored data of power demand. Results show that the method helps to decrease the unbalance factor in more than 10%, by selecting the phase where a load should be connected. The solution may be used as a planning tool in distribution systems applied to installations with systems for measuring power consumption in different time intervals. Furthermore, in conjunction with communications and processing technologies, the solution could be useful to implement with a smart grid.

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