Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees
We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph with n + 1 nodes, a K-tree is defined to be a set of n + K edges that span the graph. We show that the vehicle routing problem can be modeled...
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| Published in | Operations research Vol. 42; no. 4; pp. 626 - 642 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Baltimore, Md
INFORMS
01.07.1994
Operations Research Society of America Institute for Operations Research and the Management Sciences |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0030-364X 1526-5463 |
| DOI | 10.1287/opre.42.4.626 |
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| Abstract | We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph with n + 1 nodes, a K-tree is defined to be a set of n + K edges that span the graph. We show that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with two K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once. The side constraints are dualized to obtain a Lagrangian problem that provides lower bounds in a branch-and-bound algorithm. This algorithm has produced proven optimal solutions for a number of difficult problems, including a well-known problem with 100 customers and several real problems with 25–71 customers. |
|---|---|
| AbstractList | We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph with n + 1 nodes, a K-tree is defined to be a set of n + K edges that span the graph. We show that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with two K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once. The side constraints are dualized to obtain a Lagrangian problem that provides lower bounds in a branch-and-bound algorithm. This algorithm has produced proven optimal solutions for a number of difficult problems, including a well-known problem with 100 customers and several real problems with 25-71 customers. The problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints is considered. Given a graph with n + 1 nodes, a K-tree is defined to be a set of n + K edges that span the graph. It is shown that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with 2 K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once. The side constraints are dualized to obtain a Lagrangian problem that provides lower bounds in a branch-and-bound algorithm. This algorithm has produced proven optimal solutions for a number of difficult problems, including a well-known problem with 100 customers and several real problems with 25-71 customers. We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph with n + 1 nodes, a K-tree is defined to be a set of n + K edges that span the graph. We show that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with two K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once. The side constraints are dualized to obtain a Lagrangian problem that provides lower bounds in a branch-and-bound algorithm. This algorithm has produced proven optimal solutions for a number of difficult problems, including a well-known problem with 100 customers and several real problems with 25–71 customers. |
| Author | Fisher, Marshall L |
| Author_xml | – sequence: 1 fullname: Fisher, Marshall L |
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| Snippet | We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph... We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph... The problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints is considered. Given a... |
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| SubjectTerms | Algorithms Cost efficiency Heuristics integer Lagrangian function Linear programming Marketing strategies Operations research Optimal solutions optimization algorithm programming relaxation/subgradient: k-tree based Routing Scheduling Studies Time windows transportation Travel expenses Vehicle capacity vehicle routing Vehicles |
| Title | Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees |
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