# Complexity of vehicle routing and scheduling problems

@article{Lenstra1981ComplexityOV, title={Complexity of vehicle routing and scheduling problems}, author={Jan Karel Lenstra and Alexander H. G. Rinnooy Kan}, journal={Networks}, year={1981}, volume={11}, pages={221-227} }

The complexity of a class of vehicle routing and scheduling problems is investigated. We review known NP-hardness results and compile the results on the worst-case performance of approximation algorithms. Some directions for future research are suggested. The presentation is based on two discussion sessions during the Workshop to Investigate Future Directions in Routing and Scheduling of Vehicles and Crews, held at the University of Maryland at College Park, June 4–6, 1979.

## 1,059 Citations

On the worst-case performance of some heuristics for the vehicle routing and scheduling problem with time window constraints

- Computer ScienceNetworks
- 1986

Analysis of approximation methods for the vehicle routing and scheduling problem with time window constraints shows that their worst-case behavior on n customer problems is at least order of n for minimizing the number of vehicles used, the total distance traveled, and the total schedule time.

THE VEHICLE SCHEDULING PROBLEM: A SURVEY

- Engineering
- 1981

SUMMARY The vehicle scheduling problem is concerned, with routing a fleet of vehicles each with a capacity constraint and which are based at a central depot, to visit a set of delivery points. The…

Modeling and Solving Location Routing and Scheduling Problems

- 2008

This paper studies location routing and scheduling problems, a class of problems in which the decisions of facility location, vehicle routing, and route assignment are optimized simultaneously. For a…

Vehicle Routing Problem

- Computer ScienceEncyclopedia of GIS
- 2017

This paper discusses, discusses and extends both exact and approximate methods for solving VRP's, and gives some results on the properties offeasible solutions which help to reduce the computational effort in solving such problems.

On some matching problems arising in vehicle scheduling models

- Computer Science, MathematicsNetworks
- 1987

Two bipartite matching problems arising in Vehicle Scheduling are considered and a heuristic algorithm based on Lagrangean relaxation for the capacitated version of the multicommodity matching is presented together with experimental results.

A unified tabu search heuristic for vehicle routing problems with time windows

- Computer ScienceJ. Oper. Res. Soc.
- 2001

A unified tabu search heuristic for the vehicle routing problem with time windows and for two important generalizations: the periodic and the multi-depot vehicle routing problems with timewindows is presented.

Sequential Simulated Annealing for the Vehicle Routing Problem with Time Windows

- Computer Science
- 2009

A new simulated annealing algorithm is presented that provides very high quality solutions to the vehicle routing problem with time windows and can be successfully applied to bi-criterion optimization problems.

New assignment algorithms for the multi-depot vehicle routing problem

- Computer ScienceJ. Oper. Res. Soc.
- 2002

This paper considers the design and analysis of algorithms for the multi-depot vehicle routing problem with time windows (MDVRPTW), finding that the heuristics with the best results are those with the largest computational efforts.

Vehicle Routing and Scheduling Problems with time window constraints - Optimization Based Models

- Engineering
- 2013

Vehicle Routing Problems have been extensively analyzed to reduce transportation costs. More particularly, the Vehicle Routing Problem with Time Windows (VRPTW) imposes the period of time of customer…

Solution Improvement Heuristics for the Vehicle Routing and Scheduling Problem with Time Window Constraints

- Computer Science
- 1986

Two test data sets for the vehicle routing and scheduling problem with time window constraints are studied and initial solutions are obtained using a variety of heuristics, then improved using branch exchange procedures modified to incorporate the timewindow constraints.

## References

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The intent in this paper is to define a capacitated arc routing problem, to provide mathematical programming formulations, to perform a computational complexity analysis, and to present an approximate solution strategy for this class of problems.

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Several polynomial time approximation algorithms for some NP-complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined.…

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Abstract : An O(n sup 3) heuristic algorithm is described for solving n-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as…