Several approaches for the traveling salesman problem

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.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 servicequality 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

Un enfoque biobjetivo al problema del reparador

Objetivos y método de estudio: El objetivo principal de este trabajo consiste en el planteamiento y estudio de un problema biobjetivo con diversas aplicaciones potenciales. En este problema se tiene un conjunto de clientes que demanda algún producto o servicio. Se conoce el tiempo de servicio en cada cliente así como los tiempos de viaje entre cada par de clientes se busca encontrar la ruta que visite a todos los clientes partiendo de un depósito y volviendo a el, de forma tal que se minimice tanto la distancia recorrida por el vehículo en la ruta así como el tiempo de espera de los clientes. Para esto, se propone un modelo matemático biobjetivo en donde cada objetivo surge a partir de distintos puntos de vista. El punto de vista económico es el objetivo de distancia, en donde se desea minimizar la distancia total recorrida; desde el punto de vista social o de servicio al cliente, se tiene el objetivo de latencia en donde se desea minimizar el tiempo que el cliente espera para recibir el servicio. Se presenta una metodología de solución al problema, el cual es un algoritmo genético elitista que es muy utilizado en los problemas multiobjetivo gracias a los buenos resultados que ofrece. Contribuciones y conclusiones: La contribución de este trabajo se centra en el estudio realizado sobre un problema biobjetivo novedoso, dado que la revisión de la literatura mostró que no existen trabajos donde los objetivos que se buscó optimizar hayan sido tratados conjuntamente. Es por esto, que tanto el modelo biobjetivo presentado as´ı como el algoritmo propuesto se consideran contribuciones directas de este trabajo