Mathematical Models to support territorial re-organization decisions in the public sector

Facility location decisions represent a critical element in strategic planning in both private and public sectors, as they can have a strong and lasting impact on operational and logistic performance. In the OR literature, the two classes of problems traditionally used to address decisions related to the territorial organization of services are: Facility Location and Districting Problems. Most of the proposed models in this field are aimed at positioning new facilities; however, some occurring circumstances could require strategies oriented to reduce costs by reorganizing existing systems, composed of facilities already located in the study region. To this aim, different strategies could be adopted, such as the closure of some active facilities, their repositioning in different points of the location space, the downsizing of the capacities of the available services and so on. Any reorganization action perturbs the interaction between the facilities and the demand, and could produce some effects on the users that should be carefully evaluated. Moreover, in this context, decisions may depend on various factors such as the nature of the service and the characteristics of the market (competitive or non-competitive), the objectives to be achieved and the constraints to be satisfied. In this work we analyze the problem of the spatial re-organization of an existing service and formulate some new mathematical models in order to support such decisions in the context of public services. Computational tests have been performed in order to evaluate the capability of the proposed models to be optimally solved within limited running times. Furthermore, two applications to real-world problems have been analyzed and solved. The obtained results show that the use of mathematical models can actually represent a suitable and reliable support for these kinds of problems.