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Proposal of a Dynamic Algorithm for the Maintenance and Vehicle Routing Problem with Time Windows

Context:  In the context of business organizations, every process in which the product is immersed has a cost and time associated with it. The area of maintenance planning and scheduling is no exception; however, it is an aspect in which few companies specialize, tending to be outsourced. In this sense, the application of combinatorial models is a tool with a high potential to improve the overall performance of the organization through the understanding of the integral maintenance process.
Method: A two-phase (maintenance and routing) dynamic algorithm is proposed which considers a set of clients distributed in a maintenance network (distance), where each of the technicians start from the same central node (depot), which, in turn, is the endpoint of each assigned route. The objective is to minimize the total cost associated with the development of preventive and corrective maintenance of all machines to be evaluated. With this purpose, the formulation of the mathematical problem for each of the phases and its interrelation method is proposed. Then, performance measures are expressed to evaluate the achieved objectives.
Results: The results satisfy a consistent alternative for the resolution of problems of the NP-Hard type, which generates a high level of complexity to the model. That is, it proposes a tool for solving problems of these characteristics in low computational response times and with appealing results.
Conclusions: The combined maintenance and routing model using a dynamic algorithm addresses the maintenance and routing problem satisfactorily. The model shows good results with respect to the comparison optimization model in percentage gaps of performance measures lower than 5%. As for the computational time required, a reduction of up to 98% was achieved, which makes it an ideal alternative for highly complex scenarios. Finally, achieving a higher level of characterization, employing multi-objective decision criteria and a greater number of constraints to the problem, is proposed in future research.
Acknowledgements: To the High-Performance Computing Center (CECAD - Centro de computación de Alto Desempeño) of Universidad Distrital Francisco José de Caldas for their support, as well as for providing us with a virtual machine to run the proposed mathematical model, which was an essential element in the results obtained.