Mechanisms for feasibility and improvement for inventory-routing problems

Abstract

Inventory-routing problems (IRPs) define a class of combinatorial optimization problems, encompassing inventory management and vehicle routing decisions into the same framework. In this article, we propose a new modular mechanism capable of recovering feasibility and improving even partial solutions by reorganizing delivery routes and optimizing inventory flows. It can be embedded into different optimization algorithms, either heuristic or exact ones. We exploit the use of this mechanism to improve a traditional branch-and-cut scheme and evaluate it by solving the multi-vehicle IRP (MIRP) and the multi-depot IRP (MDIRP). The results show that our method is very effective; outperforming other approaches on well-known benchmark instances from the literature. Regarding the MIRP, our algorithm obtains 417 optimal solutions for 638 small instances, the best result among all exact algorithms, with nine new ones. On a large data set, our method finds all optimal solutions for instances with up to 50 customers for the single-vehicle, besides providing 90% of new best-known solutions (BKS) for 100 customers. On the MDIRP, our approach finds 27 new optimal solutions and 73% of new BKS, improving previous BKS by more than 7% on average.

Keywords:

• Inventory
• vehicle routing
• integer programming

Acknowledgements

Thanks are due to Masoud Chitsaz and Claudia Archetti for making their results available. We also thank the C3SL (Centro de Computação Científica e Software Livre) from Federal University of Paraná for providing parallel computing facilities. We thank the editor, an associate editor, and two referees for their valuable contributions on an earlier version of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This article was partly funded by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—grant 1554767, and by the Canadian Natural Science and Engineering Research Council (NSERC) under grant 2019-00094.