A branch-and-cut algorithm for vehicle routing problems with three-dimensional loading constraints

This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously infeasible route can become feasible by adding a new customer if...

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Bibliographic Details
Published in:European journal of operational research
Main Authors: Tamke, Felix, Linß, Florian, Kuttner, Leopold, Buscher, Udo
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2025
Subjects:
Branch-and-cut
Constraint programming
Container loading
Routing
Routing
Branch-and-cut
Container loading
Constraint programming
ISSN:0377-2217
Online Access:Get full text
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Summary:This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously infeasible route can become feasible by adding a new customer if support constraints are enabled in the loading subproblem and call this the incremental feasibility property. Consequently, different infeasible path definitions apply to different 3L-CVRP variants and we introduce several variant-depending lifting steps to strengthen infeasible path inequalities. The loading subproblem is solved exactly using a flexible constraint programming model to determine the feasibility or infeasibility of a route. An extreme point-based packing heuristic is implemented to reduce time-consuming calls to the exact loading algorithm. Furthermore, we integrate a start solution procedure and periodically combine memoized feasible routes in a set-partitioning-based heuristic to generate new upper bounds. A comprehensive computational study, employing well-known benchmark instances, showcases the significant performance improvements achieved through the algorithmic enhancements. Consequently, we not only prove the optimality of many best-known heuristic solutions for the first time but also introduce new optimal and best solutions for a large number of instances. [Display omitted] •Infeasible three-dimensional loadings can be converted to feasible ones by adding items.•Container loading problem is solved by constraint programming and a packing heuristic.•The comprehensive branch-and-cut algorithm can deal with multiple loading variants.•Many instances are solved to proven optimality for the first time.•We publish an open-source repository.
ISSN:0377-2217
DOI:10.1016/j.ejor.2025.10.010