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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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 ...
5
votes
0answers
53 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 ...
5
votes
0answers
164 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.
3
votes
0answers
61 views

Multi-commodity flow (or path selection) 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 ...
3
votes
0answers
55 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 ...
2
votes
0answers
88 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) $$ \...
1
vote
0answers
99 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} ...