On dual minimum cost flow algorithms

2002 ◽  
Vol 56 (1) ◽  
pp. 101-126 ◽  
Author(s):  
Jens Vygen
Keyword(s):  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Cost Flow

scholarly journals A Generalized Minimum Cost Flow Model for Multiple Emergency Flow Routing

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jianxun Cui ◽  
Shi An ◽  
Meng Zhao
Keyword(s):  
Flow Model ◽  
Time Window ◽  
Programming Model ◽  
Real Life ◽  
Minimum Cost ◽  
Emergency Evacuation ◽  
Mixed Integer ◽  
Fixed Cost ◽  
Minimum Cost Flow ◽  
Cost Flow

During real-life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict with each other on the same spatial road network and within the same time window. Therefore, we propose a novel generalized minimum cost flow model to optimize the distribution pattern of these two types of flow on the same network by introducing the conflict cost. The travel time on each link is assumed to be subject to a bureau of public road (BPR) function rather than a fixed cost. Additionally, we integrate contraflow operations into this model to redesign the network shared by those two types of flow. A nonconvex mixed-integer nonlinear programming model with bilinear, fractional, and power components is constructed, and GAMS/BARON is used to solve this programming model. A case study is conducted in the downtown area of Harbin city in China to verify the efficiency of proposed model, and several helpful findings and managerial insights are also presented.

Minimum cost flow problem with conflicts

Networks ◽  
2021 ◽  
Author(s):  
Zeynep Şuvak ◽  
İ. Kuban Altınel ◽  
Necati Aras
Keyword(s):  
Flow Problem ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Minimum Cost Flow Problem ◽  
Cost Flow

Inverse Generalized Minimum Cost Flow Problem Under the Hamming Distances

2018 ◽  
Vol 7 (2) ◽  
pp. 355-364 ◽  
Author(s):  
Mobarakeh Karimi ◽  
Massoud Aman ◽  
Ardeshir Dolati
Keyword(s):  
Flow Problem ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Minimum Cost Flow Problem ◽  
Cost Flow

scholarly journals Efficient Algorithms for Identifying Loop Formation and Computing θ Value for Solving Minimum Cost Flow Network Problems

2021 ◽  
Vol 20 ◽  
pp. 107-117
Author(s):  
TIMOTHY MICHAEL CHÁVEZ ◽  
DUC THAI NGUYEN
Keyword(s):  
Real Life ◽  
Minimum Cost ◽  
Simplex Algorithm ◽  
Efficient Algorithms ◽  
Computer Implementation ◽  
Loop Formation ◽  
Minimum Cost Flow ◽  
Flow Network ◽  
Network Problems ◽  
Cost Flow

While the minimum cost flow (MCF) problems have been well documented in many publications, due to its broad applications, little or no effort have been devoted to explaining the algorithms for identifying loop formation and computing the θ value needed to solve MCF network problems. This paper proposes efficient algorithms, and MATLAB computer implementation, for solving MCF problems. Several academic and real-life network problems have been solved to validate the proposed algorithms; the numerical results obtained by the developed MCF code have been compared and matched with the built-in MATLAB function Linprog() (Simplex algorithm) for further validation.

Minimum Cost Flow Problem

2008 ◽  
pp. 2095-2108
Author(s):  
Ravindra K. Ahuja ◽  
Thomas L. Magnanti ◽  
James B. Orlin
Keyword(s):  
Flow Problem ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Minimum Cost Flow Problem ◽  
Cost Flow
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