A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen

We address a variant of the vehicle routing problem with time windows that includes the decision of how many deliverymen should be assigned to each vehicle. In this variant, the service time at each customer depends on the size of the respective demand and on the number of deliverymen assigned to vi...

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Bibliographic Details
Published in:TOP 2018-10, Vol.26 (3), p.437-464
Main Authors: Munari, Pedro, Morabito, Reinaldo
Format: Article
Language:English
Subjects:
Business and Management
Columns (process)
Customer services
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Formulations
Heuristic methods
Industrial and Production Engineering
Insurance
Integer programming
Management
Operations Research/Decision Theory
Optimization
Original Paper
Route planning
Routing
Solvers
Statistics for Business
Upper bounds
Vehicle routing
Windows (intervals)
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Summary:We address a variant of the vehicle routing problem with time windows that includes the decision of how many deliverymen should be assigned to each vehicle. In this variant, the service time at each customer depends on the size of the respective demand and on the number of deliverymen assigned to visit this customer. In addition, the objective function consists of minimizing a weighted sum of the total number of routes, number of deliverymen and traveled distance. These characteristics make this variant very challenging for exact methods. To date, only heuristic approaches have been proposed for this problem, and even the most efficient optimization solvers cannot find optimal solutions in a reasonable amount of time for instances of moderate size when using the available mathematical formulations. We propose a branch-price-and-cut method based on a new set partitioning formulation of the problem. To accelerate the convergence of the method, we rely on an interior-point column and cut generation process, a strong branching strategy and a mixed-integer programming-based primal heuristic. Additionally, a hierarchical branching strategy is used to take into account the different components of the objective function. The computational results indicate the benefits of using the proposed exact solution approach. We closed several instances of the problem and obtained upper bounds that were previously unknown in the literature.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-018-0481-8