scholarly journals Efficient algorithm for Minimum cost flow problem with partial lane reversals

2019 ◽  
Vol 36 (1-2) ◽  
pp. 51-59
Author(s):  
Urmila Pyakurel
Keyword(s):  
Polynomial Time ◽  
Flow Problem ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Strongly Polynomial Time ◽  
Parallel Networks ◽  
Minimum Cost Flow Problem ◽  
Parallel Network ◽  
Cost Flow ◽  
Strongly Polynomial

In this paper, we investigate the minimum cost flow problem in two terminal series parallel network. We present modified minimum cost flow algorithm that computes the maximum dynamic and the earliest arrival flows in strongly polynomial time and also preserves all unused arc capacities. We also present strongly polynomial time minimum cost partial contraflow algorithm that solves both problems with partial reversals of arc capacities on two terminal series parallel networks.

scholarly journals Robust minimum cost flow problem under consistent flow constraints

2021 ◽  
Author(s):  
Christina Büsing ◽  
Arie M. C. A. Koster ◽  
Sabrina Schmitz
Keyword(s):  
Polynomial Time ◽  
Polynomial Algorithm ◽  
Flow Problem ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Demand And Supply ◽  
Minimum Cost Flow Problem ◽  
Cost Flow ◽  
Special Case ◽  
Flow Constraints

AbstractThe robust minimum cost flow problem under consistent flow constraints (RobMCF$$\equiv $$ ≡ ) is a new extension of the minimum cost flow (MCF) problem. In the RobMCF$$\equiv $$ ≡ problem, we consider demand and supply that are subject to uncertainty. For all demand realizations, however, we require that the flow value on an arc needs to be equal if it is included in the predetermined arc set given. The objective is to find feasible flows that satisfy the equal flow requirements while minimizing the maximum occurring cost among all demand realizations. In the case of a finite discrete set of scenarios, we derive structural results which point out the differences with the polynomial time solvable MCF problem in networks with integral demands, supplies, and capacities. In particular, the Integral Flow Theorem of Dantzig and Fulkerson does not hold. For this reason, we require integral flows in the entire paper. We show that the RobMCF$$\equiv $$ ≡ problem is strongly $$\mathcal {NP}$$ NP -hard on acyclic digraphs by a reduction from the (3, B2)-Sat problem. Further, we demonstrate that the RobMCF$$\equiv $$ ≡ problem is weakly $$\mathcal {NP}$$ NP -hard on series-parallel digraphs by providing a reduction from Partition. If in addition the number of scenarios is constant, we propose a pseudo-polynomial algorithm based on dynamic programming. Finally, we present a special case on series-parallel digraphs for which we can solve the RobMCF$$\equiv $$ ≡ problem in polynomial time.

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

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

The Minimum Cost Flow Problem of Uncertain Random Network

2018 ◽  
Vol 35 (03) ◽  
pp. 1850016
Author(s):  
Soheila Abdi ◽  
Fahimeh Baroughi ◽  
Behrooz Alizadeh
Keyword(s):  
Flow Model ◽  
Flow Problem ◽  
Random Network ◽  
Minimum Cost ◽  
Random Variable ◽  
Minimum Cost Flow ◽  
Feasible Set ◽  
Uncertain Random Network ◽  
Minimum Cost Flow Problem ◽  
Cost Flow

The aim of this paper is to present a novel method for solving the minimum cost flow problem on networks with uncertain-random capacities and costs. The objective function of this problem is an uncertain random variable and the constraints of the problem do not make a deterministic feasible set. Under the framework of uncertain random programming, a corresponding [Formula: see text]-minimum cost flow model with a prespecified confidence level [Formula: see text], is formulated and its main properties are analyzed. It is proven that there exists an equivalence relationship between this model and the classical deterministic minimum cost flow model. Then an algorithm is proposed to find the maximum amount of [Formula: see text] such that for it, the feasible set of [Formula: see text]-minimum cost flow model is nonempty. Finally, a numerical example is presented to illustrate the efficiency of our proposed method.

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