In the Universal Facility Location problem we are given a set of demand points and a set of facilities. The goal is to assign the demands to facilities in such a way that the sum of service and facility costs is minimized. The service cost is proportional to the distance each unit of demand has to travel to its assigned facility, whereas the facility cost of each facility i depends on the amoun...

In out last lecture, we discussed the LP Rounding technique for producing approximation algorithms. The idea behind LP Rounding is to write the problem as an integer linear program, relax its integrality restraints to efficiently solve the general linear program, and then move the LP solution to a nearby integral point in the feasible solution space. The difficulty of this process lies in the r...

The paper proposes methodologies to convert discrete spatial data into continuous functions in a metric space so that the continuous approximation (CA) optimization framework can be applied to a general class of discrete facility location problems. We integrated a range of computational geometry methods to estimate the optimal system costs and the optimal number of facilities, and then develope...

proposing a robust designed facility location is one of the most effective ways to hedge against unexpected disruptions and failures in a transportation network system. this paper considers the combined facility location/network design problem with regard to transportation link disruptions and develops a mixed integer linear programming formulation to model it. with respect to the probability o...

The facility location problem has occupied a central place in operations research since the early 1960's, as it models design decisions on the placement of factories, warehouses, schools, or hospitals to serve a set of customers efficiently. For an overview of previous work see the survey chapter by Cornue-jols, Nemhauser & Wolsey in [21]. Recently, it has received renewed research interest bec...

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...