Solving the Facility Location Problem using Graph Theory and Shortest Path Algorithms

• Main Authors: Zarabi, Patrick, Denes, August
• Format: Bachelor Thesis
• Language: English
• Published: KTH, Optimeringslära och systemteori 2018
• Subjects: Computational Mathematics; Beräkningsmatematik; Kiruna
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-229979

This thesis in systems engineering and optimization theory aims to solve a facility location problem within the context of a confined space with path and proximity constraints. The thesis was commissioned by LKAB Kiruna, to help in their decision of where to construct a new facility on their industrial premises. The facility location problem was divided into a main problem of finding the best position of the facility, and a sub-problem of how to model distances and feasible areas within this particular context. The distance and feasibility modeling was solved by utilizing graph theory to construct a graph representation of a geographic area and then obtain the necessary distances using Dijkstra’s shortest path algorithm. The main problem was then solved using a mixed integer linear programming formulation which utilizes the distances obtained through the Dijkstra algorithm. The model is also extended to not only decide the placement of one facility but to accommodate the placement of two facilities. The extended model was solved in three ways, a heuristic algorithm, a mixed integer non linear formulation and a mixed integer linear formulation. The results concluded that the implementation of the single facility model was able to obtain optimal solutions consistently. Regarding the extension, the mixed integer linear formulation was deemed to be the best model as it was computationally fast and consistently produced optimal solutions. Finally, several model improvements are identified to increase the applicability to different cases. These improvements could also allow the model to provide more strategical and managerial insights to the facility location decision process. Some future research into metaheuristics and machine learning are also suggested to further improve the usability of the models. Detta examensarbete inom systemteknik och optimeringslära syftar till att lösa ett lagerplaceringsproblem. Lagret ska ställas inom en liten yta med hänsyn till ruttbegränsningar och närhet till andra byggnader. Denna ...