In this paper we investigate how to choose an optimal position of a specific facility that is constrained to a network tree connecting some given demand points in a given area. A bilevel formulation is provided and existence results are given together with some properties when a density describes the construction cost of the networks in the area. This includes the presence of an obstacle or of free regions. To prove existence of a solution of the bilevel problem, that is framed in Euclidean spaces, a lower semicontinuity property is required. This is obtained proving an extension of Golab's theorem in the general setting of metric spaces, which allows for considering a density function.

Locating network trees by a bilevel scheme / Greco, L.; Guarino Lo Bianco, S.; Mallozzi, L.. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - (2024), pp. 1-14. [10.1007/s10479-024-05833-9]

### Locating network trees by a bilevel scheme

#### Abstract

In this paper we investigate how to choose an optimal position of a specific facility that is constrained to a network tree connecting some given demand points in a given area. A bilevel formulation is provided and existence results are given together with some properties when a density describes the construction cost of the networks in the area. This includes the presence of an obstacle or of free regions. To prove existence of a solution of the bilevel problem, that is framed in Euclidean spaces, a lower semicontinuity property is required. This is obtained proving an extension of Golab's theorem in the general setting of metric spaces, which allows for considering a density function.
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2024
1
14
Locating network trees by a bilevel scheme / Greco, L.; Guarino Lo Bianco, S.; Mallozzi, L.. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - (2024), pp. 1-14. [10.1007/s10479-024-05833-9]
Greco, L.; Guarino Lo Bianco, S.; Mallozzi, L.
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