Abstract
This work proposes a bi-objective mathematical optimization model and a two-stage heuristic for a real-world application of the heterogeneous Dynamic Dial-a-Ride Problem with no rejects, i.e., a patient transportation system. The problem consists of calculating route plans to meet a set of transportation requests by using a given heterogeneous vehicle fleet. These transportation requests can be either static or dynamic, and all of them must be attended to. In the first stage of the proposed heuristic, the problem’s static part is solved by applying a General Variable neighborhood Search based algorithm. In the second stage, the dynamic requests are dealt with by implementing a simple insertion heuristic. We create different instances based on the real data provided by a Brazilian city’s public health care system and test the proposed approach on them. The analysis of the results shows that the higher the level of dynamism, i.e., the number of urgent requests on each instance, the smaller the objective function value will be in the static part. The results also demonstrate that a higher level of dynamism increases the chance of a time window violation happening. Besides, we use the weighted sum method of the two conflicting objectives to analyze the trade-off between them and create an approximation for the Pareto frontier.
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Acknowledgements
This work was partly done when the first author was a visiting researcher at the University of Bremen thanks to the Bremen IDEA scholarship. The authors would like to thank the National Council for Scientific and Technological Development (CNPq) for a Doctoral Degree scholarship granted to the second author and also for the support to the third and last authors (Grants 438473/2018-3 and 303266/2019-8, respectively). We also thank the Minas Gerais State Foundation for Research Support (FAPEMIG, grant CEX-PPM-00676-17), the Federal University of Ouro Preto (UFOP), and the Coordination for the Improvement of Higher Education Personnel (CAPES)—Finance Code 001—for supporting the development of the present study. We want to express special thanks to the transportation sector of the Ouro Preto’ health care system for providing information for modeling the problem addressed.
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Souza, A.L.S., Bernardo, M., Penna, P.H.V. et al. Bi-objective optimization model for the heterogeneous dynamic dial-a-ride problem with no rejects. Optim Lett 16, 355–374 (2022). https://doi.org/10.1007/s11590-020-01698-6
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DOI: https://doi.org/10.1007/s11590-020-01698-6