General modelling and exact solution techniques for restricted facility location problems

Abstract

The aim of this thesis is to devise new optimisation techniques for restricted continuous facility location problems. In this work, forbidden regions and barriers are considered as the main restriction types for locations.

In the first search paper, a general modelling framework for restricted facility location problems is introduced with arbitrarily shaped forbidden regions or barriers. Phi-objects are canonically closed sets of points and efficient tools in mathematical modelling of 2D and 3D geometric optimisation problems. Point sets that contain isolated points, points that are removed from an object (deleted points) and objects with self-intersection of their frontiers are not classified as phi-objects. In the first research paper, the phi-objects are used to model real objects mathematically. It is shown that the proposed modelling framework can be applied to both median and center facility location problems, either with barriers or forbidden regions. The instances from the existing literature for this class of problems are solved to optimality using the new framework. Further, a realistic multi-facility problem instance derived from an archipelago vulnerable to earthquakes is also solved to optimality. This problem instance is significantly more complex than any other instance described in the literature.

In the second research paper, a new formulation based on multi-commodity flows with unknown destination is described and adapted to the problem type at hand. The proposed model is defined on a discretised space and this discretisation technique can also be applied to deterministic and stochastic continuous restricted location problems using any distance metric. As a solution method for the presented formulation, a solution algorithm, based on Benders Decomposition, is developed to take advantage of the discrete network structure. Extensive computational experiments, which are derived from a well-known and complex instance from the literature are carried out, on both deterministic and stochastic multi-facility restricted location problems. Results are analysed to evaluate the performance of the proposed solution technique.

In the third research paper, capacitated versions of the restricted facility location problems are studied. To the best of our knowledge, these have not been studied before. Similar to the second research paper, the continuous space is discretised and a model developed on a discrete space. Various acceleration techniques for Benders Decomposition are tested to improve the efficiency of solving the problem instances. A large number of deterministic instances is generated from three core instances. Two of these are well-known instances in the literature. The other instance is newly proposed in this paper. Numerical results are presented to determine the most efficient solution approach for the approximated continuous problem.

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Identifiers

ORCID for Tolga Bektas: orcid.org/0000-0003-0634-144X

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