The rectilinear distance minisum problem with minimum distance constraints

This paper describes a mathematical model for locating a single facility on a continuous plane, which considers transportation (or service) costs between the facility and a set of demand points as well as social costs arising from the undesirable characteristics of the facility. The transportation costs are given by a standard minisum objective function, while the social costs appear implicitly in the form of lower bound constraints on the distances between the facility and the demand points. The model is analyzed under the assumption that distances are measured by the rectilinear norm, and an efficient branch-and-bound algorithm is derived to solve this case.