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. 
On the worst-case performance of some heuristics for the vehicle routing and scheduling problem with time window constraints
TLDR
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
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
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
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
TLDR
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.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 35 REFERENCES
Capacitated arc routing problems
TLDR
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.
Approximation algorithms for some routing problems
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.
Evaluating a Sequential Vehicle Routing Algorithm
TLDR
This paper focuses on evaluating the accuracy of the Clarke-Wright procedure in its sequential form and presents examples of pathological behavior and suggests algorithm modifications to help overcome these problems.
A fundamental problem in vehicle routing
TLDR
The classical Traveling Salesman Problem and the Chinese Postman Problem are shown to be special limiting cases of the General Routing Problem, and the algorithm provides a unified approach to both node and arc oriented routing problems.
On general routing problems
TLDR
It is shown that a proposed conversion of required nodes to required arcs is not allowed and that the problem remains polynomial complete if Q = θ, and the proposed transformations from M vehicle to single vehicle problems are shown to be incorrect.
P-Complete Approximation Problems
For P-complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is
On the Complexity of Local Search for the Traveling Salesman Problem
It is shown that, unless $P = NP$, local search algorithms for the traveling salesman problem having polynomial time complexity per iteration will generate solutions arbitrarily far from the optimal.
Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane
  • R. Karp
  • Mathematics, Computer Science
    Math. Oper. Res.
  • 1977
TLDR
This work considers partitioning algorithms for the approximate solution of large instances of the traveling-salesman problem in the plane, in which partitioning is used in conjunction with existing heuristic algorithms.
Approximation Algorithms for Some Postman Problems
TLDR
Approxtmatton algorithms for several NP-complete edge-covermg routing problems are presented and analyzed and a worst-case bound of 2 is proved for the mixed postman algortthm of Edmonds and Johnson.
Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem
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
...
1
2
3
4
...