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Questions tagged [network-flow]

For questions related to the formulation or solution methodologies of network flow problems. Some of the well-known network flow problems are maximum flow problem, minimum-cost flow problem, and multi-commodity flow problem.

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Solver for Go Programming Laguage

Has anyone used MIP solvers (open source or commercial) with Go language https://golang.org/? I am looking for a solver for simple linear MIPs for network flows and set cover types of problems.
Alexey Sorokin's user avatar
6 votes
0 answers
105 views

Demonstrating a given solution is basic for a MCFP?

Given a minimum-cost flow problem, how could I go about demonstrating that a specific solution (as sets of basic and non-basic (!) arcs that build a rooted spanning tree for a given graph) is basic ...
Johnny Bueti's user avatar
5 votes
0 answers
63 views

Complexity of solving a certain commodity flow problem

Does anyone know the complexity of obtaining the optimal solution to the integral multi-commodity network flow problem with unit demands, integral capacities, but the cost of using an arc varies ...
batwing's user avatar
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4 votes
0 answers
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Google-OR tools vs Pyomo and other commercial Solvers for solving a simple maximum flow problem

I have implemented a Pyomo model for solving maximum flow problem as a subroutine of an algorithm. However, the approach does not scale very well because Pyomo does not provide a very good way to re-...
Pia MiA's user avatar
  • 390
3 votes
0 answers
77 views

Flow problem with flow demands

Recently I found a subproblem in a project I am working with. This problem is a sort of flow variant, as you will see. And I am looking for literature-related articles and also fast approaches for ...
Matheus Diógenes Andrade's user avatar
3 votes
0 answers
142 views

Sources of Min-Cost Flow Models That Utilize Binary Variables for Transportation Networks

I am looking for articles that include min-cost flow models with binary variables for flow transportation like gas networks, traffic systems, heating systems. Is there any specific place(like OR ...
asdf's user avatar
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3 votes
0 answers
118 views

Availability of library for solving generalized network flow problems

I need to solve a large-scale generalized network flow problem. For reference, it is a pure network-flow model with the exception that arcs have a positive coefficient applied to flow on them. In my ...
Suleyman Karabuk's user avatar
3 votes
0 answers
196 views

Multi-commodity (Integral) flow problem with unit demand; complexity

It seems to me that a multi-commodity flow problem should be treated differently when the commodity demand constraint is an equivalence and not a lower-bound. Consider a unit demand. Apparently, in ...
Daniele Cuomo's user avatar
3 votes
0 answers
152 views

Simplex method on graphs: How do I find a basic solution using the Ford-Fulkerson algorithm?

I'm tasked with solving a minimal cost flow problem. I'm asked to first use the Ford-Fulkerson algorithm on my graph to find a basic solution that will then be used to do the simplex method on that ...
WindBreeze's user avatar
2 votes
0 answers
31 views

How to formulate / solve a multi-commodity flow problem with dependent flow between commodities to plan harvesting operations

I am working on a multi-commodity flow problem to conduct tactical harvesting planning. The idea is to model the crop and the machinery as commodities. Crop move from field to being harvested and ...
Ludwig B's user avatar
2 votes
0 answers
42 views

Lexicographic flow property and consequences

I am struggling with the understanding of the (quite famous) paper on lexicographical flows: Maximal, Lexicographic, and Dynamic Network Flows - by Edward Minieka ...
Daniele Cuomo's user avatar
2 votes
0 answers
286 views

Solving transportation problem by the Network Simplex

I am trying to solve the following problem using Network Simplex method. But I have questions. My attempt: Basis Matrix$(B)$ Rows: 1, 2, 3, 4, 5 Column: (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) $$ \...
diabolik's user avatar
2 votes
0 answers
162 views

Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
JirenOppaik's user avatar
1 vote
1 answer
58 views

Reference request for different network types

I am trying to understand the mathematical models used in airline revenue management when a disruption occurs. The researchers are re-scheduling the resources(aircraft, flights etc.) in recovery ...
Learning's user avatar
1 vote
0 answers
43 views

Network flow problem to minimize differences between nodes

What type of algorithm should I be researching to solve the following problem? Each node has a potential that is a function (linear or non linear) of the net flow in/out of that node. Nodes are ...
granddejeuner's user avatar
1 vote
0 answers
37 views

How to convert unit-capacity network flow into transportation problems?

I am working on a problem that can be modeled as a minimum-cost network flow problem where the capacity of edges is 1. I found Exercise 3.8, Chapter 5 of Parallel and Distributed Computation: ...
Recursion's user avatar
1 vote
1 answer
68 views

Fast Algorithms for Min-cost Multicommodity Flow Problem with Most Arcs Having 0 cost

I have a min-cost multicommodity flow problem with the following characteristics: Flows can be fractional (integer flows not required) Set of commodity types is $K$, set of demand nodes is $\\{ d_k : ...
graphtheory123's user avatar
1 vote
0 answers
94 views

Numerical infeasibility for moving numbers along some specific conversion edges to get maximal number on target node from some starter node

I have a problem that can be represented as an optimization problem. Sometimes, solver engines report infeasible depending on the parameters I have at hand. The root cause is numeric ranges. ...
Dzmitry Lahoda's user avatar
1 vote
0 answers
79 views

Resources about Busacker & Gowen algorithm

I have a relatively hard time understanding the Busacker & Gowen algorithm. I could not find any resources on it, contrary to Ford-Fulkerson method that is described in Comen's "Introduction ...
satk0's user avatar
  • 123
1 vote
0 answers
117 views

Assignment problem with continuous constraints

I am trying to solve an assignment problem where all the variables are continuous. I have a set of sources S, and another set of destinations D. Each source and destination have capacity/demand ...
PrashanthVajjhala's user avatar
1 vote
0 answers
155 views

How to see fix constraint violations found with IIS

I'm running a simple MCNF model to see if my network is balanced. I'm using Gurboi in Python and with the IIS I can see that there are 2 constraint violations making it infeasible. How do I fix these ...
Emma Kuttler's user avatar
1 vote
0 answers
766 views

How to eliminate large matrix coefficients and large RHS warning in Gurobi

I'm solving a large network flow problem using Gurobi to do Benders decomposition in Python. The imported .csvs contain values that typically fall in either zero, the range of [20,200], or with a ...
Emma Kuttler's user avatar
1 vote
0 answers
22 views

Asserting solution existence via approximation of multi-commodity integral flow

Consider a polynomial $\epsilon$-approximation for MCF with integral flow (like the one based on LP relaxation). Can I (in general) use this algorithm as a predicate, asserting whether a solution ...
Daniele Cuomo's user avatar
1 vote
0 answers
70 views

Multi-commodity flow problem reduction

Assume to tackle a particular group of instances for the integral multi-commodity flow problem. Particularly, given a digraph $G = (V \cup S \cup T,E)$, such that $S, T, V$ are all disjoint. ...
Daniele Cuomo's user avatar
1 vote
0 answers
51 views

Solving a max-flow problem through lex-max flow problem

Assume that, for a given network, its multi-sink multi-source max-flow satisfies a lexicographic order. Is this enough to state that I can solve the max-flow problem, by using a lex-max solver (i.e. a ...
Daniele Cuomo's user avatar
1 vote
0 answers
22 views

Complexity of lexicographic integral flow

I read that the lexicographic flow problem is polynomially solvable. However it allows for continuous flow values. Is there any reference about the problem with integral flow (and its complexity)?
Daniele Cuomo's user avatar
1 vote
0 answers
29 views

Is there a difference between "Integral Quickest Transshipment" and "Integral Quickest Multicommodity flow"?

I can't get the difference between this two problems, which seem equal to me. But, for the former, a polynomial solver is known, while, for the latter, it is not. EDIT - References: ...
Daniele Cuomo's user avatar
0 votes
0 answers
29 views

Spectral clustering with laplacian matrix eigenvector

I want to separate a given graph in $k$ clusters with the laplacian matrix ($L = D-A$ where $D$ is the degree matrix and $A$ the adjacency matrix). How can the eigenvectors of $L$ be used, along with ...
Sham's user avatar
  • 1
0 votes
0 answers
40 views

Network formulation based side constraints for a workforce scheduling problem

For a workforce scheduling problem, I have formulated the "at most one shift per day" constraint as a network formulation based side constraint (with other constraints like demand coverage, ...
SDC's user avatar
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