Open Travelling Salesman ProblemGenetic algorithm for travelling salesman problem with multiple salesmentravelling salesmantravelling salesman understanding constraintsTravelling Salesman on Subset of PointsTravelling salesman problem as an integer linear programTravelling Salesman VariationIs there a vehicle routing problem without time and cost constraints, whose objective is to maximize revenue?Constraints in Vehicle Routing Problem Programming FormulationCriteria in Capacitated Vehicle Routing ProblemDelivery Assignment Optimization
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Open Travelling Salesman Problem
Genetic algorithm for travelling salesman problem with multiple salesmentravelling salesmantravelling salesman understanding constraintsTravelling Salesman on Subset of PointsTravelling salesman problem as an integer linear programTravelling Salesman VariationIs there a vehicle routing problem without time and cost constraints, whose objective is to maximize revenue?Constraints in Vehicle Routing Problem Programming FormulationCriteria in Capacitated Vehicle Routing ProblemDelivery Assignment Optimization
$begingroup$
I am trying to find a linear program for the open Travelling Salesman Problem, where the salesman does not need to return to the starting point. More precisely, I have to do this with multiple possible depots and multiple salesmen (trucks).
The formulation for the non open version of the problem is the following (forget about the green box):
LP for closed multi depot vehicle routing problem:
N is the number of customers, M is the number of depots, K is the number of trucks. My idea was to delete constraint (3) and (4), because still every place needs to be visited, but not from all places a truck needs to leave. But when I put this in the solver, he gives me tours with subtours.
Why is that the case and/or are there other ways to solve this?
linear-programming mathematical-modeling discrete-optimization operations-research
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
asked 17 hours ago
PeterPeter
133
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$begingroup$
I am trying to find a linear program for the open Travelling Salesman Problem, where the salesman does not need to return to the starting point. More precisely, I have to do this with multiple possible depots and multiple salesmen (trucks).
The formulation for the non open version of the problem is the following (forget about the green box):
LP for closed multi depot vehicle routing problem:
N is the number of customers, M is the number of depots, K is the number of trucks. My idea was to delete constraint (3) and (4), because still every place needs to be visited, but not from all places a truck needs to leave. But when I put this in the solver, he gives me tours with subtours.
Why is that the case and/or are there other ways to solve this?
linear-programming mathematical-modeling discrete-optimization operations-research
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
asked 17 hours ago
PeterPeter
133
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am trying to find a linear program for the open Travelling Salesman Problem, where the salesman does not need to return to the starting point. More precisely, I have to do this with multiple possible depots and multiple salesmen (trucks).
The formulation for the non open version of the problem is the following (forget about the green box):
LP for closed multi depot vehicle routing problem:
N is the number of customers, M is the number of depots, K is the number of trucks. My idea was to delete constraint (3) and (4), because still every place needs to be visited, but not from all places a truck needs to leave. But when I put this in the solver, he gives me tours with subtours.
Why is that the case and/or are there other ways to solve this?
linear-programming mathematical-modeling discrete-optimization operations-research
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
asked 17 hours ago
PeterPeter
133
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am trying to find a linear program for the open Travelling Salesman Problem, where the salesman does not need to return to the starting point. More precisely, I have to do this with multiple possible depots and multiple salesmen (trucks).
The formulation for the non open version of the problem is the following (forget about the green box):
LP for closed multi depot vehicle routing problem:
N is the number of customers, M is the number of depots, K is the number of trucks. My idea was to delete constraint (3) and (4), because still every place needs to be visited, but not from all places a truck needs to leave. But when I put this in the solver, he gives me tours with subtours.
Why is that the case and/or are there other ways to solve this?
linear-programming mathematical-modeling discrete-optimization operations-research
linear-programming mathematical-modeling discrete-optimization operations-research
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
asked 17 hours ago
PeterPeter
133
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
asked 17 hours ago
PeterPeter
133
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
edited 17 hours ago
Rodrigo de Azevedo
13.1k41960
13.1k41960
asked 17 hours ago
PeterPeter
133
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 17 hours ago
PeterPeter
133
asked 17 hours ago
PeterPeter
133
133
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Peter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
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The easiest way to handle the Open TSP is to consider a regular TSP, and to change the cost function such that every arc to the depot has cost $0$. Keep all the constraints, and just change $c_i,depot=0$ for all nodes $i$.
answered 17 hours ago
KuifjeKuifje
7,2652726
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1 Answer
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1 Answer
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active
oldest
votes
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oldest
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$begingroup$
The easiest way to handle the Open TSP is to consider a regular TSP, and to change the cost function such that every arc to the depot has cost $0$. Keep all the constraints, and just change $c_i,depot=0$ for all nodes $i$.
answered 17 hours ago
KuifjeKuifje
7,2652726
$endgroup$
add a comment |
$begingroup$
The easiest way to handle the Open TSP is to consider a regular TSP, and to change the cost function such that every arc to the depot has cost $0$. Keep all the constraints, and just change $c_i,depot=0$ for all nodes $i$.
answered 17 hours ago
KuifjeKuifje
7,2652726
$endgroup$
add a comment |
$begingroup$
The easiest way to handle the Open TSP is to consider a regular TSP, and to change the cost function such that every arc to the depot has cost $0$. Keep all the constraints, and just change $c_i,depot=0$ for all nodes $i$.
answered 17 hours ago
KuifjeKuifje
7,2652726
$endgroup$
The easiest way to handle the Open TSP is to consider a regular TSP, and to change the cost function such that every arc to the depot has cost $0$. Keep all the constraints, and just change $c_i,depot=0$ for all nodes $i$.
answered 17 hours ago
KuifjeKuifje
7,2652726
answered 17 hours ago
KuifjeKuifje
7,2652726
answered 17 hours ago
KuifjeKuifje
7,2652726
answered 17 hours ago
KuifjeKuifje
7,2652726
7,2652726
add a comment |
add a comment |
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