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Exact and heuristic dynamic programming algorithms for the traveling salesman problem with flexible time windows

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Abstract

This article proposes extensions of exact and heuristic dynamic programming algorithms for the traveling salesman problem with flexible time windows, which are a limited enlargement of the generally referred to as hard time windows. The service of a customer can be started before or after the hard time window at a penalty cost. The addressed problem thus requires the determination of a sequence of customers and their respective service start times in order to minimize the sum of traveling cost with earliness and lateness cost. Computational tests are conducted on a variety of symmetric and asymmetric instances proposed in the literature, and the advantages of flexible windows are stressed.

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Acknowledgements

This research was funded by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq-Brazil, Grants 141064/2015-3 and 305577/2014-0) and the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP-Brazil, Grants 2016/01860-1 and 2016/06566-4). We are grateful for the valuable suggestions made by the editor and referees.

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  1. Faculdade de Engenharia Elétrica e de Computação, Universidade Estadual de Campinas, Campinas, SP, 13083-852, Brazil

    Ramon Faganello Fachini & Vinícius Amaral Armentano

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  1. Ramon Faganello Fachini
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  2. Vinícius Amaral Armentano
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Correspondence to Ramon Faganello Fachini.

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Fachini, R.F., Armentano, V.A. Exact and heuristic dynamic programming algorithms for the traveling salesman problem with flexible time windows. Optim Lett 14, 579–609 (2020). https://doi.org/10.1007/s11590-018-1342-y

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