A new optimization algorithm for the vehicle routing problem with time windows
Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows
New ideas in optimization
Multidimensional divide-and-conquer
Communications of the ACM
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
2-Path Cuts for the Vehicle Routing Problem with Time Windows
Transportation Science
A Column Generation Approach for Large-Scale Aircrew Rostering Problems
Operations Research
A computational study of vehicle routing applications
A computational study of vehicle routing applications
Solving capacitated arc routing problems using a transformation to the CVRP
Computers and Operations Research
Location-Routing Problems with Distance Constraints
Transportation Science
Selected Topics in Column Generation
Operations Research
Formulations and exact algorithms for the vehicle routing problem with time windows
Computers and Operations Research
Column Generation Algorithms for the Capacitated m-Ring-Star Problem
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Computers and Operations Research
Exploiting sparsity in pricing routines for the capacitated arc routing problem
Computers and Operations Research
Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows
Transportation Science
A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows
Computers and Operations Research
Solving capacitated arc routing problems using a transformation to the CVRP
Computers and Operations Research
Path-Reduced Costs for Eliminating Arcs in Routing and Scheduling
INFORMS Journal on Computing
Multi-objective and multi-constrained non-additive shortest path problems
Computers and Operations Research
A multi-agent approach to load consolidation in transportation
Advances in Engineering Software
A branch-cut-and-price algorithm for the capacitated arc routing problem
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem
Operations Research
The time dependent traveling salesman problem: polyhedra and branch-cut-and-price algorithm
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Ant colony system for optimizing vehicle routing problem with time windows (VRPTW)
ICIC'06 Proceedings of the 2006 international conference on Computational Intelligence and Bioinformatics - Volume Part III
A branch-and-cut-and-price approach for the capacitated m-ring-star problem
Discrete Applied Mathematics
A column generation approach for a school bus routing problem with resource constraints
Computers and Operations Research
The Fixed-Charge Shortest-Path Problem
INFORMS Journal on Computing
Cut-First Branch-and-Price-Second for the Capacitated Arc-Routing Problem
Operations Research
Lifted and Local Reachability Cuts for the Vehicle Routing Problem with Time Windows
Computers and Operations Research
Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows
Transportation Science
Combined location and routing problems for drug distribution
Discrete Applied Mathematics
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The elementary shortest-path problem with resource constraints (ESPPRC) is a widely used modeling tool in formulating vehicle-routing and crew-scheduling applications. The ESPPRC often occurs as a subproblem of an enclosing problem, where it is used to generate implicitly the set of all feasible routes or schedules, as in the column-generation formulation of the vehicle-routing problem with time windows (VRPTW). As the ESPPRC problem is NP-hard in the strong sense, classical solution approaches are based on the corresponding nonelementary shortest-path problem with resource constraints (SPPRC), which can be solved using a pseudo-polynomial labeling algorithm. While solving the enclosing problem by branch and price, this subproblem relaxation leads to weak lower bounds and sometimes impractically large branch-and-bound trees. A compromise between solving ESPPRC and SPPRC is to forbid cycles of small length. In the SPPRC with k-cycle elimination (SPPRC-k-cyc), paths with cycles are allowed only if cycles have length at least k + 1. The case k = 2 forbids sequences of the form i - j - i and has been successfully used to reduce integrality gaps. We propose a new definition of the dominance rule among labels for dealing with arbitrary values of k ≥ 2. The numerical experiments on the linear relaxation of some hard VRPTW instances from Solomon's benchmark show that k-cycle elimination with k ≥ 3 can substantially improve the lower bounds of vehicle-routing problems with side constraints. The new algorithm has proven to be a key ingredient for getting exact integer solutions for well-known hard problems from the literature.