Using the TSP Solution for Optimal Route Scheduling in Construction Management

This paper presents the optimal route scheduling in construction management by using the solution of the traveling salesman problem (TSP). The TSP is a well-known combinatorial optimization problem which holds a considerable potential for applications in construction management. The aim of this paper is to bring forward the solution of the TSP to the wider expert community. For this purpose, the TSP model formulation, the applicability of the TSP optimization model and the commercially available software for modelling and solving the TSP are presented. An example of the optimal route scheduling by using the solution of the TSP is demonstrated at the end of the paper to show the applicability of the TSP model

Diseño de un modelo para un problema de distribución de tuberías, con entregas divididas y flota heterogénea.

OBJETIVO Y MÉTODO DE ESTUDIO En esta tesis se describe el problema de ruteo de vehículos de una empresa regiomontana de tubería ligera. La empresa debe distribuir desde cualesquiera de sus 5 plantas sus productos a un grupo determinado de clientes que se encuentran dispersos en toda la República Mexicana, actividad que se realiza en base a la experiencia del encargado de ruteo y no en un sistema de optimización el cual evitaría el uso ineficiente de recursos y generaría grandes ahorros en el costo de transportación y por lo tanto en el costo logístico de la empresa. El Problema de Ruteo de Vehículos (VRP) se refiere al grupo de problemas que abordan la distribución a un conjunto de clientes dispersos geográficamente utilizando una flota de vehículos. Su finalidad es encontrar un camino, o ruta, que recorra todos los clientes minimizando los costos relacionados con el recorrido satisfaciendo cierto número de restricciones. El VRP es un problema de optimización que se puede encontrar en diversas situaciones de la vida real, ya sea en la industria, en los servicios o en el mismo vivir de las personas. Uno de los propósitos de esta tesis es presentar un modelo de optimización basado en las características particulares de la empresa y de su sistema de transporte como lo son: uso de flota heterogénea, múltiples productos, entregas divididas. Otro de los objetivos es probar con la ayuda del software de optimización los ahorros que se generarían al integrar dicho modelo como parte de sus operaciones en el ruteo de vehículos

A cutting plane algorithm for minimum perfect 2-matchings

A cutting plane algorithm for minimum perfect 2-matchings / by M. Grötschel, O. Holland. - In: Computing. 39. 1987. S. 327-34

Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization

Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes