We present a deterministic kinetic data structure for the facility location problem that maintains a subset of the moving points as facilities such that, at any point of time, the accumulated cost for the whole point set is at most a constant factor larger than the current optimal cost. At any point of time, the cost that arise for a point depends on the status and the position of the point. In...

The location of facilities anywhere in an area in which several competing facilities already exist and serving the demand points has been brought to light in this work. Because of the great importance of health care systems in the health of the people, these systems have been studied in the present paper. Creation and maintenance of competitive advantage in health care systems requires optimizi...

The Connected Facility Location (ConFL) problem combines facility location and Steiner trees: given a set of customers, a set of potential facility locations and some inter-connection nodes, ConFL searches for the minimum-cost way of assigning each customer to exactly one open facility, and connecting the open facilities via a Steiner tree. The costs needed for building the Steiner tree, facili...

The objective of the present paper is to review my personal contributions in the field of uncapacitated facility location problems. These contributions took place throughout my academic career, from the time I was a Ph.D. student at Imperial College to the present day. They cover approximately 30 years, from 1973 to 2003; they address: algorithms developed for the p-median problem and for a gen...

We give a new LP-rounding 1.724-approximation algorithm for the metric Fault-Tolerant Uncapacitated Facility Location problem. This improves on the previously best known 2.076-approximation algorithm of Shmoys & Swamy. Our work applies a dependent-rounding technique in the domain of facility location. The analysis of our algorithm benefits from, and extends, methods developed for Uncapacitated ...

Consider a network facility location problem where congestion arises at facilities, and is represented by delay functions that approximate the queueing process. We strive to minimize the sum of customers' transportation and waiting times, and facilities' xed and variable costs. The problem is solved using a column generation technique within a Branch-and-Bound scheme. Numerical results are repo...

An integrated model considers all parameters and elements of different deficiencies in one problem. This paper presents a new integrated model of a supply chain that simultaneously considers facility location, vehicle routing and inventory control problems as well as their interactions in one problem, called location-routing-inventory (LRI) problem. This model also considers stochastic demands ...