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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| Veröffentlicht in: | European journal of operational research |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier B.V
01.10.2025
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| ISSN: | 0377-2217 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Tamke, Felix Linß, Florian Buscher, Udo Kuttner, Leopold |
| Author_xml | – sequence: 1 givenname: Felix orcidid: 0000-0003-1650-8936 surname: Tamke fullname: Tamke, Felix email: felix.tamke@tu-dresden.de organization: Faculty of Business and Economics, TU Dresden, Dresden, 01062, Germany – sequence: 2 givenname: Florian orcidid: 0000-0002-5869-0425 surname: Linß fullname: Linß, Florian email: florian.linss@tu-dresden.de organization: Faculty of Business and Economics, TU Dresden, Dresden, 01062, Germany – sequence: 3 givenname: Leopold orcidid: 0000-0002-9359-8835 surname: Kuttner fullname: Kuttner, Leopold email: leopold.kuttner@tu-dresden.de organization: Faculty of Business and Economics, TU Dresden, Dresden, 01062, Germany – sequence: 4 givenname: Udo orcidid: 0000-0003-4711-2184 surname: Buscher fullname: Buscher, Udo email: udo.buscher@tu-dresden.de organization: Faculty of Business and Economics, TU Dresden, Dresden, 01062, Germany |
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| Keywords | Routing Branch-and-cut Container loading Constraint programming |
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