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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1answer
13 views

Constraining flow into a node and out of a node using Min Cost Flow input

Let's say I have a graph $G=(V,E)$ where each vertex has an edge going both into and out of it (i.e. cyclic, akin to the kidney donor pair problem). Now suppose we have a capacity $u_{ij} = 1 \forall(...
2
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1answer
22 views

Min Cost Flow with lower bound reduction to MCF algorithm

We define the Min Cost Flow Problem with Lower Bounds (MCFPLB) as a generalization of the usual Min Cost Flow. The input consists of: a directed graph $G=(V,E)$ capacities $u_{ij} \geq 0$ for each ...
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1answer
90 views

Solving general minimum cost flow problems using only one demand and one supply node

This is a practice in using reduction. Suppose I have a solver that only allows input to a MCF that specifies only one demand and one supply node. How could I use this solver to solve general MCF ...
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1answer
27 views

Python Gurobipy Maximum Flow: How to model “source” and “sink” in constraints

I am attempting to capture the nature of a "source" node as well as a "sink" node where the net flow for each node aside from the source and sink is zero. Here is my code so far: <...
0
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1answer
42 views

Adding slack nodes to min cost network flows

I have the following question. I want to clarify couple of points. As you can see, total demand and total supply does not match, we do not have enough demand. What I want to ask is: Do we need to ...
2
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0answers
71 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) $$ \...
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1answer
39 views

Maximum flow minimum cut

For the following problem I am trying to find maximum flow and minimum cut: I found the maximum flow as 6 like this: $1-3-7-8:2 flows$ $1-2-5-8: 2 flows$ $1-3-4-5-8:1 flow$ $1-3-4-6-5-8:1 flow$ But I ...
0
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1answer
51 views

Minimum cost flow problem with negative cost arcs

As far as I know, if there is a directed arc with a negative cost, we change its direction to its opposite and get a positive cost. But in the following question, if we change the direction of the arc ...
6
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1answer
187 views

Extreme point and extreme ray of a network flow problem

"It is a well-known result in network flow theory that an extreme point and an extreme ray of the polyhedron defined by the convex hull of feasible region corresponds to a path and cycle (resp.) ...
4
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1answer
54 views

splittable multicommodity problem with CPLEX

I am working on a splittable multicommodity flow problem, where each commodity can be split into k orders. However, I don't know the value of k in advance. Here is my code. ...
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1answer
623 views

How to describe the traveling salesman problem with an integer programming model?

I'm trying to describe the travelling salesman problem as an integer programming model. I'm interested in the asymmetric version of the problem. The problem can be summarized as finding the optimal ...
3
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1answer
55 views

What is the difference between min- cut formulation and (bi) partitioning formulation?

I have a min-cut formulation and a bi-partitioning problem. The two problems focus on finding the minimal cut value separating the two partitions? So what are really the differences between the ...
4
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2answers
207 views

How to solve this convex problem heuristically?

I have the following problem $$\max_{X_{i,j},i\in N_{U},j\in N_{B}}\sum_{i=1}^{N_U}\sum_{j=1}^{N_B}R_{i,j}X_{i,j}$$ $$\text{subject to}$$ $$a_{\min}\le\sum_{j=1}^{N_B}X_{i,j}\le a_{\max}, \forall i$$ $...
3
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0answers
47 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 ...
0
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1answer
77 views

How can I find the shortest path for all nodes in a graph from a source $s$?

This is the shortest path problem. I've used a model where we can find the shortest path between the source and a specified destination. The idea behind this model is that we assign a flow of 1 for ...
2
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1answer
48 views

Algorithm / Method for determining N nodes to disconnect group of nodes

Hell everyone I have been trying to read through this forum for the methodology to approach a graph/network problem. The idea is I have an undirected graph, and every node is capable of talking to any ...
5
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1answer
80 views

Combined arc capacity constraints in network flows

Consider the network flow polyhedron for a directed graph $G = (N, A)$. Along with the standard flow-balance and single-arc capacity constraints, we are faced with additional constraints which enforce ...
4
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1answer
82 views

Max flow problem with piece-wise costs

This question is a variant of a question I posted earlier and also fixes some typos in the earlier post (Complexity \ Reference request for variant of max flow problem). Some of the changes are ...
6
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1answer
64 views

Complexity \ Reference request for variant of max flow problem

In the standard max cost flow problem with arc capacities, the cost of using an arc is proportional to the flow through the arc. For example, if $f_{uv}$ is the flow through the arc $(u,v)$, then the ...
5
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1answer
54 views

Min-cost flow with per-edge flow conservation

I am trying to solve a linear program that is identical to a min-cost flow problem, except for a difference in the flow-conservation constraint. Instead of the summed outgoing flow equaling the summed ...
4
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0answers
48 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 ...
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1answer
70 views

Find minimum cost problem

The problem below aims to find the minimum cost for the network architecture: We want to build a network where client terminals are connected to servers by cabling which is very expensive. The network ...
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0answers
82 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} ...
2
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1answer
126 views

shortest path problem,I want to write constraints in closed form

the constraints in the photo ,I need to translate to the closed-form I don't know how can I do this. Can you help? I need to write the mod file and dat file in Cplex for this problem
4
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2answers
138 views

Maximum Flow Problem : Can someone refer me to accessible valuable resources

Can anyone please refer/suggest me some accessible papers, works, books, websites, documentation related to The Maximum Flow Problem.
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0answers
100 views

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.
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1answer
1k views

How do we call this problem in literature and how to model it?

I have a set of sources and a set of sinks. Each source $s$ can produce a set of different products $P_s$. The transportation inter-sources and inter-sinks are allowed. The sources do not ...
6
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0answers
55 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 ...
7
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2answers
269 views

Max flow problem without splitting the flow from the supply nodes - LP formulation help

Since max flow formulation can be easily solved using LP, I wanted to ask the following: I am trying to solve a simple max flow problem where the graph is bipartite but with one added constraint. The ...
15
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1answer
216 views

Was there something specific that caused graph cuts to lose popularity in the last 5 years?

Almost every graph-cut paper I look at seems to have exactly the same pattern of monotonic growth in citations and then monotonic decline starting around 5 years ago: For privacy I've cut the all ...
6
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1answer
272 views

Network flow model - How can I turn this diagram into a matrix that when converted to RREF solves for max flow?

I have the following network flow model diagram and I have already calculated maximum flow using the R package igraph to be 28. However, what I would like to know ...
7
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1answer
103 views

References for “metric” network flow problems

Network flow problems are very well studied in the literature (e.g., see the Network Flows book), and the first DIMACS challenge was dedicated to these problems. Very efficient implementation of ...
5
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1answer
130 views

What is the impact of making flow fractional rather than integer?

When creating a network flow formulation you can set up sinks with integer flow requirement $\ge 1$. This yields solutions with the total amount of flow along an edge. I have also seen this as a ...