Using the Callback to eliminate sub-routing in a vehicle routing problem with simultaneous pick-up and delivery of multiple products

Roza Maria Zoellner Lopes, Ruany Batista Leite Doehnert, Gustavo Valentim Loch, José Eduardo Pécora Junior, Cassius Tadeu Scarpin


The Vehicle Routing Problem with simultaneous pick-up and delivery of multiple products (VRPSPD) is addressed in practice when just collecting the product is not sufficient to meet the client’s requirements. This article aims to apply Callback available in Gurobi software to the elimination of sub-routes in a VRPSPD using lazy constraints. In order to test the efficiency of the proposed method, we first solved the relaxed problem of Mixed Integer Programming (MIP), and then the same problem was solved using the Callback. The performed tests show that the use of Callback is efficient leading to time reductions in runtime to prove the optimality.


Vehicle Routing Problem; Simultaneous Delivery and Pick-Up; Multiple products; Callback; Lazy Constraints

Texto completo:

PDF (English)


ALSHAMRANI, A.; MATHUR, K.; BALLOU, R. H. Reverse logistics: simultaneous design of delivery routes and returns strategies. Computers and Operations Research, v. 34, n. 2, p. 595–619, 2007.

BOUANANE, K.; BENADADA, Y.; BENCHEIKH, G. Application of a hybrid genetic algorithm to solve the multi-depots vehicle routing problem with simultaneous delivery and pickup and inventory restrictions. Proceedings - GOL 2018: 4th IEEE International Conference on Logistics Operations Management, n. April, p. 1–9, 2018.

GUIMARÃES, T. A. et al. The two-echelon multi-depot inventory-routing problem. Computers and Operations Research, v. 101, p. 220–233, 2019.

HEMMATI GOLSEFIDI, A.; AKBARI JOKAR, M. R. A robust optimization approach for the production-inventory-routing problem with simultaneous pickup and delivery. Computers and Industrial Engineering, v. 143, p. 106388, 2020.

HOF, J.; SCHNEIDER, M. An adaptive large neighborhood search with path relinking for a class of vehicle-routing problems with simultaneous pickup and delivery. Networks, v. 74, n. 3, p. 207–250, 2019.

HORNSTRA, R. P. et al. The vehicle routing problem with simultaneous pickup and delivery and handling costs. Computers and Operations Research, v. 115, p. 104858, 2020.

LI, H. et al. The generalized rollon-rolloff vehicle routing problem and savings-based algorithm. Transportation Research Part B: Methodological, v. 113, p. 1–23, 2018.

LUNDELL, A.; KRONQVIST, J. Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints. AIP Conference Proceedings, v. 2070, n. February, 2019.

WANG, F. et al. Backpropagation with continuation callbacks: Foundations for efficient and expressive differentiable programming. Advances in Neural Information Processing Systems, v. 2018-Decem, n. Nips, p. 10180–10191, 2018.

WANG, Z. Delivering meals for multiple suppliers: Exclusive or sharing logistics service. Transportation Research Part E: Logistics and Transportation Review, v. 118, n. August, p. 496–512, 2018.

YOUSEFIKHOSHBAKHT, M.; DIDEHVAR, F.; RAHMATI, F. A Mixed Integer Programming Formulation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem. Journal of Optimization in Industrial Engineering, v. 18, p. 37–46, 2015.

ZHANG, Z. et al. Multi-commodity demand fulfillment via simultaneous pickup and delivery for a fast fashion retailer. Computers and Operations Research, v. 103, p. 81–96, 2019.



  • Não há apontamentos.

Licença Creative Commons

Está licenciado com uma Licença Creative Commons - Atribuição-NãoComercial 4.0 Internacional

e-ISSN: 1984-2430
GEPROS. Gest. prod. oper. sist., Bauru, São Paulo-SP (Brasil).

Departamento de Engenharia de Produção da Faculdade de Engenharia da UNESP - Bauru

Av. Eng. Edmundo Carrijo Coube, n° 14-01 Fone: 55-14-3103-6122