Barbati, Maria (2013) Models and Algorithms for Facility Location Problems with Equity Considerations. [Tesi di dottorato]

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A Facility Location Problem (FLP) deal with strategic and long term decisions involving huge investment costs. When a facility is positioned, it produces effects, positive or negative, on the users (actual or potential), whose intensity can be considered depending on the mutual distance. In many practical applications, described as FLPs, it is important to consider how the effects are distributed among the users. In particular it should be proper that the effects are distributed in "equitable or equal" manner. However, although equity and/or equality represent critical issues, they are not straightforward concepts to be defined and then to be measured. As a consequence general equality measures proposed to formulate FLPs have been adapted from other contexts (political, economic, social) and concern calculations related to the distribution of distances between users and patronized facilities. In this thesis we mainly focus on the following objectives. The first objective have been the definition of new properties able to support the choice of decision makers of the more appropriate measures to be adopted to effectively represent a FLP in a given context. To this aim some empirical analyses have been performed investigating on properties of available measures for FLPs in order to highlight differences and similarities. Second we defined and formulated a transportation problem with multiple sources and single destination in terms of FLP. In particular to reduce risks of congestion in the dynamic of flow arrivals at the common destination, an appropriate equality measure is introduced. In order to solve the formulated problem, some exact and heuristic methodologies have been developed and computational results are showed.

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