On cent-dians of general networks

Most classical location studies focus on the minimisation of the average distance or the minimisation of the maximum distance to service facilities. In this paper, we analyse solution concepts related to the bicriteria model, providing some compromise between these two criteria. We show that the classical approaches based on the λ-cent-dian and the generalised centre solution concepts have some flaws, when applied to a general network. In order to avoid these flaws, we propose a new solution concept of the Chebyschev λ-cent-dian. This parametric solution concept allows us to identify all Pareto-optimal compromise locations on any network. We also show how the algorithm for finding λ-cent-dian can be modified to generate Chebyschev λ-cent-dians.