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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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Multi-Commodity Flow with "group edges"

I'm currently working on a special variation of the Multi-Commodity flow problem. My goal is to solve this variation via column generation, because the graph can become very large. Description Given......
jatsqi's user avatar
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0 votes
1 answer
65 views

Inconsistencies in modeling a binary variable that indicates a switch

this is a follow-up question to this post here and to @RobPratt's answer. I have implemented the whole thing, and now it happened that on day 1 the machine did not run and was only used for the first ...
marvelfab12'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
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
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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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
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
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
4 votes
1 answer
243 views

Can we add a certain binary row to a matrix which preserves total unimodularity?

Suppose I have a matrix $A\in \{-1, 0, 1\}^{m\times n}$ which is Totally Unimodular (TU), and a vector $b^T \in \{-1, 0, 1\}^{1\times n}$ which has exactly one entry which is $1$ and exactly one entry ...
graphtheory123's user avatar
1 vote
1 answer
178 views

Lagrangian Relaxation Lower Bound exceeds the Upper bound and the Optimal solution

I'm trying to minimize an MIP model employing a Lagrangian relaxation approach. However, I've encountered an issue where, in certain instances, the lower bound (resulting from the Lagrangian sub-...
NCyeah's user avatar
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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
2 answers
123 views

Capacited Vehicle Routing Problem with flow formulations

I'm trying to solve the CVRP based on flow-formulation. In such a model, we have a decision variable with two-index, $x_{ij}$, where I'm using the MTZ formula to eliminate sub-tours. We have then a ...
MAYA's user avatar
  • 129
1 vote
1 answer
144 views

Column generation for solving minimum cost multicommodity flow problem with additional edge disjoint constraints

I'm working on an integer programming problem that's fundamentally a minimum cost multicommodity flow (MCMF) problem with additional constraints. I'm exploring the use of column generation to solve it,...
Sina_Alef's user avatar
-1 votes
1 answer
108 views

Grocery Store Problem

I have an issue with my Excel function for a grocery store problem and I am not sure where I messed up the constraints. I have the value of the solution it should be (cost = 8,283). I need to make a ...
zoomonkey101'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
2 votes
1 answer
55 views

Shortest path problem with time as a random variable with correlation

I'm trying to solve the $\alpha$-reliable shortest path problem with correlated time variables (travel time per arc), i.e. the shortest path subject to the constraint that the probability of arriving ...
Mathematician....'s user avatar
0 votes
1 answer
111 views

Interpret the formulation of a pricing model in crowdshipping

I am trying to run the pricing model from the paper "Designing pricing and compensation schemes by integrating matching and routing models for crowd-shipping systems" on python with Gurobi, ...
Last_Mile's user avatar
2 votes
2 answers
137 views

Transportation Problem

I want to create a transportation model. I have identified importing and exporting countries with their estimated demand and supply. The cost of transportation per one uni is already calculated for ...
user avatar
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
1 vote
2 answers
274 views

Graph models - Maximum flow problem and minimum cost flow problem

I'm trying to solve this problem: An investment agency holds the rights to six investment projects: I1, I2, ..., I6. Projects I1, I2 and I3 are research and technological development projects and the ...
Carmen González's user avatar
4 votes
0 answers
1k views

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
2 votes
2 answers
328 views

Improve Network Flow computation with additional Pyomo constraints based on previous computation

I am performing several max-flow computations on extremely similar networks and I seek to improve their execution time based on information from previous computations (As there is a lot of repetitive ...
Pia MiA's user avatar
  • 390
3 votes
2 answers
151 views

Partial Lagrangian in the Max-Flow problem

In the question: "Partial" Lagrangian Dual in LP It is argued that considering a partial Lagrangian $L_{partial}$, where we Dualize only some of the constraints, results in a tighter ...
Cris's user avatar
  • 143
3 votes
2 answers
131 views

Transportation problem with consolidation within path

There's a supply network design problem that I'm trying to solve, which is as follows: A certain amount of goods need to be transported from point A to B, and can have stoppages in between with a ...
J. Alan's user avatar
  • 31
2 votes
1 answer
100 views

Modify the network model to accommodate multiple vehicles

Given a directed network (or graph) $G = (V,E)$ with each edge $e_{ij}$ having a non-negative cost as the travel time from $i$ to $j$. Each node has an associated demand $d_i$. If the demand is ...
endeavor's user avatar
  • 145
2 votes
1 answer
61 views

Find the shortest path connecting some (s,t) - a greedy (?) criterion to a multi-commodity flow problem

At page 7 from these slides there is a Greedy algorithm I want to implement. It says let $P_i$ be the shortest path (if one exists) that [...] connects some ($s_j$, $t_j$) pair that is not yet ...
Daniele Cuomo's user avatar
5 votes
1 answer
210 views

Flow problem with side constraints: how to eliminate subtours?

I am working on a flow problem with side constraints. More specifically, I have a usual flow problem, with constraints that require some arcs to have exactly one unit of flow on them. This makes the ...
Kuifje's user avatar
  • 13.5k
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
3 votes
1 answer
125 views

Modeling a special case of conservation of flow

At a particular mode, there are 2 inflow arcs, a and b, and two or more outflow arcs, which is kept to 3 for this example, i.e., c, d and e The first requirement is that only one of the two inflow ...
Mike's user avatar
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3 votes
1 answer
442 views

Minimum cost flow problem with multiple arcs between nodes in Python / Google OR

Is it possible to work with multiple arcs between 2 nodes within Google OR? Or are there better modeling techniques? I want to optimize flow from supply to demand areas, where supply and demand are ...
Fabian's user avatar
  • 31
3 votes
1 answer
90 views

Reformulating undirected to directed edges for MCF

As stated in this paper, there is a technique to reformulate a multi-commodity flow problem (MCF) with undirected edges to its equivalent version with directed edges. By quoting them: The ...
Daniele Cuomo's user avatar
6 votes
1 answer
390 views

How to Model Path Being Only Through Adjacent Cells

I am trying to develop a MILP for a path planning problem. I am operating on a grid of cells that represents a map. The arrangement of cells in the grid represents the placement of the cells in real ...
Raghav Thakar's user avatar
-1 votes
1 answer
104 views

Assignment Problem with continuous decision variable

I have to solve a problem from industry where there are a number of machines which should be assigned to a number of tasks. The difference from the general assignment problem is tough, that the ...
Harun Gül's user avatar
1 vote
1 answer
157 views

Help with dual of a problem

Could anyone confirm me if I write the correct dual for my problem? The different sets confuse me a lot. $s$ is the source node and $t$ the sink node. I'm uncertain if the last dual constraint in ...
orpanter's user avatar
  • 517
2 votes
1 answer
580 views

Model the TSP as a shortest path

We have a directed graph $G=(N,A)$ where $N$ are the verticies $N=0,1,2,3,4,5,..,n$ the starting location is node 0. For each arc $a=i-j$ in A we have a distance $d_a>0$ So we want to start and ...
Fernando Martinez's user avatar
0 votes
1 answer
112 views

How to model a simple routing problem using nodes and arcs

I have the following problem. I have a route which begins at node $0$. I want to begin and end in $0$ which is a depot. Now in this route even customer will be visited in order for example customer 2 ...
Fernando Martinez'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
3 votes
4 answers
550 views

How to see constraint violation for network flow problem

I am testing to see if my network is balanced as part of a larger protection-interdiction-restoration problem. To do this, I'm solving the problem as a minimum cost network flow problem to see if the ...
Emma Kuttler's user avatar
4 votes
2 answers
181 views

How to fix unbalanced multi-commodity network flow with equal supply and demand?

I have a fairly large network with eleven commodities and arc capacities that are commodity-dependent (i.e. an arc may have a higher capacity for one commodity than another). I'm solving a protection-...
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
3 votes
2 answers
658 views

Designing a multi-commodity network flow optimizer

I'm trying to solve multi commodity multi source network flow optimization problem using Python-PuLP. Here is how my problem looks like: The numbers on the arcs represent the order of priority a ...
themlchic's user avatar
2 votes
2 answers
217 views

Min cut network for patients

I'm trying to formulate a min cut algorithm There are two classes of patients: 1, 2, and the maximum number of patients that can be assigned to each bed per day is shown below as well. $$ \begin{array}...
Devita J's user avatar
6 votes
2 answers
325 views

Multi-commodity Network Flow: Convert a node-arc solution to an arc-path solution

For a logistics optimization problem I am working on, the most natural expression of the problem is using a node-arc formulation of the MCNF. It is solved using an LP/MIP solver like CPLEX/Gurobi. ...
anerjee's user avatar
  • 119
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
  • 105
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
2 votes
1 answer
385 views

How to solve a minimum cost flow problem with time constraints

In the following picture, the decision-maker has to make deliveries to node $V=\{1,2,3,4,5,6\}$. He has two options: use cars or bikes. In both cases, he has to make a stop at a relay point where the ...
Bree's user avatar
  • 115
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
3 votes
1 answer
101 views

Does multi-commodity flow problem (MCF) block cycling flows?

I am working with multi-commodity flow at integral flow with unit demand for each operation. Since I use the MCF formulation to model path finding, in my scenario cycles are just a waste of resources. ...
Daniele Cuomo's user avatar
5 votes
1 answer
174 views

(Integral) multi-commodity flow on undirected graph

Usually in (integral) multi-commodity flow problems the graph is assumed to be directed. Instead, I am working with an undirected graph. Is it possible to transform it in a digraph? Does such a ...
Daniele Cuomo's user avatar