Desenvolvimento de sequenciador para um Problema de Roteamento de Veículos

Este projecto tem como objectivo a optimização das rotas dos técnicos de serviço após venda da Schmitt+Sohn Elevadores, associadas à realização das manutenções preventivas a cada elemento contratado à empresa (elevadores, escadas rolantes, etc). Como tal, é necessário fazer uma distribuição dos equipamentos que se encontram em carteira, por um dos técnicos que assegura a manutenção, pelos vários dias úteis de cada mês, e pelas horas de trabalho de cada dia. Apesar do técnico ter disponíveis, por dia, 8h de trabalho, apenas 6h podem ser preenchidas com manutenções preventivas. As 2h restantes são essencialmente para possíveis manutenções correctivas para as quais o técnico seja solicitado. Caso o técnico não seja contactado para resolver nenhuma avaria, essas horas podem ser utilizadas pelo mesmo para adiantar trabalho do dia seguinte, isto é, visitar já alguns dos próximos pontos de manutenção preventiva do dia seguinte, ou para compensar trabalho que esteja atrasado. De salientar que, para cada dia, as deslocações do técnico de qualquer local ao primeiro ponto de uma rota ou de regresso do último ponto de uma rota não são contabilizadas. O trabalho desenvolvido nesta dissertação pretende dar resposta ao problema apresentado pela Schmitt+Sohn Elevadores. Para isso foi desenvolvida uma heurística para a optimização das rotas dos técnicos. Esta é baseada no conceito de “vizinho mais próximo” que procura sempre o ponto que se apresenta mais perto do último ponto que foi adicionado à rota. Com base nesta metodologia, nos processos de escolha dos pontos que formam clusters, e na selecção dos pontos iniciais de cada uma das rotas diárias, a ferramenta de optimização resultante define as rotas diárias para que o percurso efectuado por cada técnico num mês seja o menor possível. São feitas alterações às rotas definidas inicialmente quando encontrados pontos de uma mesma entrada a serem visitados em dias diferentes. Isto obrigaria o técnico a fazer duas viagens ao mesmo local. Por fim, o resultado é apresentado num documento Word a ser utilizado pelo técnico como guia diário das suas deslocações aos equipamentos que necessitam de verificações periódicas. Os resultados obtidos foram comparados com as rotas que estavam a ser usadas pela empresa, tendo apresentado resultados de melhor qualidade, constatando-se a eficiência da solução criada pelo algoritmo proposto neste trabalho.The objective of this project is to optimize the routes of the service technicians after sales of Schmitt+Sohn Elevators, related to the execution of the preventive maintenance to each element contracted to the company (elevators, escalators, etc). Thus, it is necessary to make a distribution of the equipments that are on the wallet, by one of the technicians that ensure the maintenance, by all the available days of the week of each month and by the hours of work of each day. Although the technician has 8 hours of work available by day, only 6 of them can be associated with planned preventive maintenances. The other 2 hours are essencially to possible corrective maintenances that the technician could be called to solve. If the technician isn’t called to solve a breakdown those other hours could be used by him to advance work of the next day, like visiting already some of the following points of preventive maintenance of the next day, or compensate work that is late. Noteworthy that, for each day, the traveling time of the technician from any location to the first point of a route or from the last point of a route at the end of the day aren’t count in the solution. The work developed in this thesis provides an answer to the problem presented by Schmitt+Sohn Elevators. For that was developed an heuristic to the optimization of the technician routes. This heuristic is based on the “nearest neighbor” concept which searches always for the point that is closer to the last one that was added to the route. Based on this methodology, on the choice processes of the points that form clusters, and on the selection of the initial points of each route for each day, the optimization tool defines the daily routes for the course done by each technician on a month to be the shortest possible. Changes are made to the routes defined initially when points from the same entry are founded being visited in different days. This would force the technician to do two trips to the same place. In the end, the result is presented in a Word document to be used by the technician as a daily guide to his travels to the equipments that need periodic verifications. The obtained results were compared with the routes that were being used by the company, with the first ones presenting results of better quality, confirming the efficiency of the algorithm proposed in this work

Advanced analysis of branch and bound algorithms

Als de code van een cijferslot zoek is, kan het alleen geopend worden door alle cijfercom­binaties langs te gaan. In het slechtste geval is de laatste combinatie de juiste. Echter, als de code uit tien cijfers bestaat, moeten tien miljard mogelijkheden bekeken worden. De zogenaamde 'NP-lastige' problemen in het proefschrift van Marcel Turkensteen zijn vergelijkbaar met het 'cijferslotprobleem'. Ook bij deze problemen is het aantal mogelijkheden buitensporig groot. De kunst is derhalve om de zoekruimte op een slimme manier af te tasten. Bij de Branch and Bound (BnB) methode wordt dit gedaan door de zoekruimte op te splitsen in kleinere deelgebieden. Turkensteen past de BnB methode onder andere toe bij het handelsreizigersprobleem, waarbij een kortste route door een verzameling plaatsen bepaald moet worden. Dit probleem is in algemene vorm nog steeds niet opgelost. De economische gevolgen kunnen groot zijn: zo staat nog steeds niet vast of bijvoorbeeld een routeplanner vrachtwagens optimaal laat rondrijden. De huidige BnB-methoden worden in dit proefschrift met name verbeterd door niet naar de kosten van een verbinding te kijken, maar naar de kostentoename als een verbinding niet gebruikt wordt: de boventolerantie.

Distance-constrained vehicle routing problem: exact and approximate solution (mathematical programming)

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The asymmetric distance-constrained vehicle routing problem (ADVRP) looks at finding vehicle tours to connect all customers with a depot, such that the total distance is minimised; each customer is visited once by one vehicle; every tour starts and ends at a depot; and the travelled distance by each vehicle is less than or equal to the given maximum value. We present three basic results in this thesis. In the first one, we present a general flow-based formulation to ADVRP. It is suitable for symmetric and asymmetric instances. It has been compared with the adapted Bus School Routing formulation and appears to solve the ADVRP faster. Comparisons are performed on random test instances with up to 200 customers. We reach a conclusion that our general formulation outperforms the adapted one. Moreover, it finds the optimal solution for small test instances quickly. For large instances, there is a high probability that an optimal solution can be found or at least improve upon the value of the best feasible solution found so far, compared to the other formulation which stops because of the time condition. This formulation is more general than Kara formulation since it does not require the distance matrix to satisfy the triangle inequality. The second result improves and modifies an old branch-and-bound method suggested by Laporte et al. in 1987. It is based on reformulating a distance-constrained vehicle routing problem into a travelling salesman problem and uses the assignment problem as a lower bounding procedure. In addition, its algorithm uses the best-first strategy and new branching rules. Since this method was fast but memory consuming, it would stop before optimality is proven. Therefore, we introduce randomness in choosing the node of the search tree in case we have more than one choice (usually we choose the smallest objective function). If an optimal solution is not found, then restart is required due to memory issues, so we restart our procedure. In that way, we get a multistart branch and bound method. Computational experiments show that we are able to exactly solve large test instances with up to 1000 customers. As far as we know, those instances are much larger than instances considered for other VRP models and exact solution approaches from recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in literature. Moreover, this approach is general and may be used in solving other types of vehicle routing problems. In the third result, we use VNS as a heuristic to find the best feasible solution for groups of instances. We wanted to determine how far the difference is between the best feasible solution obtained by VNS and the value of optimal solution in order to use the output of VNS as an initial feasible solution (upper bound procedure) to improve our multistart method. Unfortunately, based on the search strategy (best first search), using a heuristic to find an initial feasible solution is not useful. The reason for this is because the branch and bound is able to find the first feasible solution quickly. In other words, in our method using a good initial feasible solution as an upper bound will not increase the speed of the search. However, this would be different for the depth first search. However, we found a big gap between VNS feasible solution and an optimal solution, so VNS can not be used alone unless for large test instances when other exact methods are not able to find any feasible solution because of memory or stopping conditions

Lower tolerance-based Branch and Bound algorithms for the ATSP

In this paper, we develop a new tolerance-based Branch and Bound algorithm for solving NP-hard problems. In particular, we consider the asymmetric traveling salesman problem (ATSP), an NP-hard problem with large practical relevance. The main algorithmic contribution is our lower bounding strategy that uses the expected costs of including arcs in the solution to the assignment problem relaxation of the ATSP, the so-called lower tolerance values. The computation of the lower bound requires the calculation of a large set of lower tolerances. We apply and adapt a finding from [23] that makes it possible to compute all lower tolerance values efficiently. Computational results show that our Branch and Bound algorithm exhibits very good performance in comparison with state-of-the-art algorithms, in particular for difficult clustered ATSP instance