**Author, as appears in the article.: **Gimenez-Gomez, Jose-Manuel; Peris, Josep E.; Subiza, Begona;

**Department: **Economia

**URV's Author/s: **Giménez Gómez, José Manuel

**Keywords: ** Minimum cost spanning tree problem Cost sharing rules Core selection Claims problem

**Abstract: **We propose to allocate the cost of a minimum cost spanning tree by defining a claims problem and using claims rules, then providing easy and intuitive ways to distribute this cost. Depending on the starting point that we consider, we define two models. On the one hand, the benefit-sharing model considers individuals' costs to the source as the starting point, and then the benefit of building the efficient tree is shared by the agents. On the other hand, the costs-sharing model starts from the individuals' minimum connection costs (the cheapest connection they can use), and the additional cost, if any, is then allocated. As we prove, both approaches provide the same family of allocations for every minimum cost spanning tree problem. These models can be understood as a central planner who decides the best way to connect the agents (the efficient tree) and also establishes the amount each agent has to pay. In so doing, the central planner takes into account the maximum and minimum amount they should pay and some equity criteria given by a particular (claims) rule. We analyze some properties of this family of cost allocations, specially focusing in coalitional stability (core selection), a central concern in the literature on cost allocation.

**Thematic Areas: ** Strategy and management Statistics, probability and uncertainty Operations research & management science Numerical analysis Modeling and simulation Management science and operations research Management of technology and innovation Interdisciplinar Economia Computational theory and mathematics Ciencias sociales

**Author's mail: **josemanuel.gimenez@urv.cat

**Author identifier: **0000-0003-0202-4623

**Record's date: **2023-02-19

**Papper version: **info:eu-repo/semantics/acceptedVersion

**Link to the original source: **https://link.springer.com/article/10.1007/s12351-021-00632-7

**Licence document URL: **http://repositori.urv.cat/ca/proteccio-de-dades/

**Papper original source: **Operational Research. 22 (3): 2785-2801

**APA: **Gimenez-Gomez, Jose-Manuel; Peris, Josep E.; Subiza, Begona; (2022). A claims problem approach to the cost allocation of a minimum cost spanning tree. Operational Research, 22(3), 2785-2801. DOI: 10.1007/s12351-021-00632-7

**Article's DOI: **10.1007/s12351-021-00632-7

**Entity: **Universitat Rovira i Virgili

**Journal publication year: **2022

**Publication Type: **Journal Publications