Some results on the reliability of multiple path-shaped facility location on networks Justo Puerto 1,2 Department of Statistic and OR Institute of Mathematics University of Seville (IMUS) Universidad de Sevilla Sevilla, Spain Federica Ricca 1,3 Sapienza, Universit`a di Roma, (Italy) Andrea Scozzari 1,4 Universit`a degli Studi “Niccol`o Cusano”, Roma, (Italy) Abstract In this paper we study a location problem on networks that combines three impor- tant issues: 1) it considers that facilities are extensive, 2) it handles simultaneously the location of more than one facility, and 3) it incorporates reliability aspects related to the fact that facilities may fail. The problem consists of locating two path-shaped facilities minimizing the expected service cost in the long run, assum- ing that paths may become unavailable and their failure probabilities are known in advance. We discuss several aspects of the computational complexity of problems of locating two or more reliable paths on graphs, showing that multifacility path loca- tion - with and without reliability issues - is a difficult problem even for 2 facilities and on very special classes of graphs. In view of this, we focus on trees and provide