Let A be a nonempty nite subset of the plane representing the geographical coordinates of a set of demand points (towns,. . .), to be served by a facility, whose location within a given region S is sought. Assuming that the unit cost for a 2 A if the facility is located at x 2 S is proportional to dist(x; a) | the distance from x to a | and that demand of point a is given by ! a , minimizing th...

Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers. Motivated by these platforms, we formulate a set of facility location problems that we term Two-sided Facility location. In our model, agents arrive at nodes in an ...

Dr. Christoph Witzgall, the honoree of this Symposium, can count among his many contributions to applied mathematics and mathematical operations research a body of widely-recognized work on the optimal location of facilities. The present paper offers to non-specialists a sketch of that field and its evolution, with emphasis on areas most closely related to Witzgall's research at NBS/NIST.

Given a terrain defined as a piecewise-linear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the surface of) a polyhedron. To compute the o...

a facility location is said to be competitive when other facilities are present in the market and new facilities have to compete with these existing facilities for a market share. in other words, in a competitive facility location problem we do not see monopoly that exists in classic location models. in such a situation, existing facilities react to locate new facilities by adjusting their attr...