A new criterion of classification for the network plant location

Network plant location problems with min-sum criterion consist of determining a subset of plants minimizing the sum of fixed cost of opening and delivery costs to a set of clients. These problems can be classified according to several conditions. In this work a new condition is introduced, based on the structure of delivery costs. This structure can be such that a client j exists for which the delivery cost from plant j located in the same node is not less than the delivery cost from the remaining plants iℝj. Moreover there is the possibility that the structure of delivery costs is such that for each client j the delivery cost from plant j located in the same node is less than the delivery cost from the other plants iℝj. This new criterion makes it possible to develop some considerations about Simple Plant Location and p-Median models, to formulate a new p-Median model and to define a new problem, named Median Plant Location. These new formulations open new algorithmic perspectives, based on the polyhedral analysis of the Plant Location Problems.