Parametric Facility Location on a Tree Network with an L_p-Norm Cost Function

This paper examines the optimal location of a single facility on a tree network with the objective being to minimize the sum of weighted distances from each node measured by an L_p-norm-based cost function. Our goal is to trace the trajectory of the optimal location when the L_p-norm parameter p varies from one to infinity. Convexity of the objective function, when p is fixed, allows us to perform the parametric analysis. We characterize possible trajectory paths, and show that some surprising trajectory results can occur.