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Several approaches for the traveling salesman problem

  • Autores: Nancy Aracely Arellano Arriaga
  • Directores de la Tesis: Julián Molina Luque (dir. tes.)
  • Lectura: En la Universidad de Málaga ( España ) en 2019
  • Idioma: inglés
  • Tribunal Calificador de la Tesis: Iris Abril Martínez Salazar (presid.), Ada M. Álvarez Socarrás (secret.), Elisa Schaeffer (voc.), Irma Delia García Calvillo (voc.), Julián Molina Luque (voc.)
  • Programa de doctorado: Programa de Doctorado en Economía y Empresa por la Universidad de Málaga
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  • Resumen
    • This doctoral dissertation studies and characterizes of a combination of objectives with several logistic applications. This combination aims to pursue not only a company benefit but a benefit to the clients waiting to obtain a service or a product. In classic routing theory, an economic approach is widely studied: the minimization of traveled distance and cost spent to perform the visiting is an economic objective. This dissertation aims to the inclusion of the client in the decision-making process to bring out a certain level of satisfaction in the client set when performing an action.

      We part from having a set of clients demanding a service to a certain company. Several assumptions are made: when visiting a client, an agent must leave from a known depot and come back to it at the end of the tour assigned to it. All travel times among the clients and the depot are known, as well as all service times on each client. This is to say, the agent knows how long it will take to reach a client and to perform the requested service in the client location. The company is interested in improving two characteristics: an economic objective as well as a service-quality objective by minimizing the total travel distance of the agent while also minimizing the total waiting time of the clients.

      We study two main approaches: the first one is to fulfill the visits assuming there is a single uncapacitated vehicle, this is to say that such vehicle has infinite capacity to attend all clients. The second one is to fulfill the visits with a fleet of k-uncapacitated vehicles, all of them restricted to an strict constraint of being active and having at least one client to visit. We denominate the single-vehicle approach the minimum latency-distance problem (mldp), and the k-sized fleet the k-minimum latency-distance problem (k-mldp).

      As previously stated, this company has two options: to fulfil the visits with a single-vehicle or with a fixed-size fleet of k agents to perform the visits. We characterize both approaches, mldp and k-mldp, with several methodologies; both a linear and a non-linear mathematical formulation are proposed. Additionally, the design and implementation of an exact methodology to solve both linear formulations is implemented and with it we obtained exact results. Due to the large computation time these formulations take to be solved with the exact methodology proposed, we analyse the complexity each of these approaches and show that both problems are NP-hard.

      As both problems are NP-hard, we propose three metaheuristic methods to obtain solutions in shorter computation time. Our solution methods are population based metaheuristics which exploit the structure of both problems and give good quality solutions by introducing novel local search procedures which are able to explore more efficiently their search space and to obtain good quality solutions in shorter computation time.

      Our main contribution is the study and characterization of a bi-objective problematic involving the minimization of two objectives: an economic one which aims to minimize the total travel distance, and a service-quality objective which aims to minimize of the waiting time of the clients to be visited. With this combination of objectives, we aim to characterize the inclusion of the client in the decision-making process to introduce service-quality decisions alongside a classic routing objective.


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