Branch and Bound: Eine Einführung

1973 ◽  
Keyword(s):  
Branch And Bound

PENJADWALAN OPTIMAL TIPE PRODUKSI FLOWSHOP DUA TAHAP MENGGUNAKAN METODE BRANCH AND BOUND DENGAN MEMPERHATIKAN WAKTU TRANSPORTASI

2017 ◽  
Vol 2 (1) ◽  
pp. 1-8
Author(s):  
Marie Muhammad ◽  
Elis Ratna Wulan
Keyword(s):  
Branch And Bound

Penjadwalan produksi dapat dibagi menjadi dua jenis, yaitu penjadwalan produksi tipe jobshop dan penjadwalan produksi tipe flowshop. Penjadwalan produksi tipe flowshop adalah sebuah penjadwalan sebuah produk yang sedemikian rupa sehingga setiap produk diproduksi melalui mesin yang sama dengan alur produksi yang sama. Terdapat beberapa masalah flowshop, salah satunya adalah dengan memperhatikan waktu transportasi. Dan metode Branch and Bound adalah solusi yang tepat untuk memecahkan masalah penjadwalan produksi dengan memperhatikan waktu transportasi untuk meminimalisir waktu yang terlewati. Pada penulisan Studi Literatur ini, Penjadwalan optimal dari 4 buah job dan 2 buah mesin dengan memperhatikan waktu transportasi adalah 1, 2, 4, dan 3 dengan waktu yang terlewati adalah 59 unit satuan waktu.

Unit Commitment Solution by Branch and Bound Algorithm

2020 ◽  
Author(s):  
Bishaljit Paul ◽  
Sushovan Goswami ◽  
Dipu Mistry ◽  
Chandan Kumar Chanda
Keyword(s):  
Branch And Bound ◽  
Unit Commitment ◽  
Branch And Bound Algorithm

scholarly journals Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-22
Author(s):  
Jing Tang ◽  
Xueyan Tang ◽  
Andrew Lim ◽  
Kai Han ◽  
Chongshou Li ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Greedy Algorithm ◽  
Branch And Bound ◽  
Upper Bound ◽  
Optimization Problem ◽  
Approximation Factor ◽  
Real World Application ◽  
Efficiency Of Algorithms ◽  
Knapsack Constraint ◽  
Submodular Maximization

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we show that this algorithm can achieve an approximation factor of 0.405, which significantly improves the known factors of 0.357 given by Wolsey and (1-1/e)/2\approx 0.316 given by Khuller et al. More importantly, our analysis closes a gap in Khuller et al.'s proof for the extensively mentioned approximation factor of (1-1/\sqrte )\approx 0.393 in the literature to clarify a long-standing misconception on this issue. Second, we enhance the modified greedy algorithm to derive a data-dependent upper bound on the optimum. We empirically demonstrate the tightness of our upper bound with a real-world application. The bound enables us to obtain a data-dependent ratio typically much higher than 0.405 between the solution value of the modified greedy algorithm and the optimum. It can also be used to significantly improve the efficiency of algorithms such as branch and bound.

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