Minisum multipurpose trip location problem on trees

We consider the problem of locating facilities of two types at nodesof a tree network. Customers may need just one type of service, or bothtypes; in the latter case, to minimize transportation costs, the customers visit facilities of both types in a single trip. Each facility incurs a fixed cost that depends on the type of the facility and the node where it is located. It is required to minimize the sum of the total transportation and fixed costs. For the problem with a single facility of each type, we present an O( n) exact algorithm, which improves on the algorithm presented in [2]. For the problem with multiple facilities of each type, we present an algorithm. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 154–159 2014