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...

In this paper we develop a network location model that combines the characteristics of ordered median and gradual cover models resulting in the Ordered Gradual Covering Location Problem (OGCLP). The Gradual Cover Location Problem (GCLP) was specifically designed to extend the basic cover objective to capture sensitivity with respect to absolute travel distance. Ordered Median Location problems ...

A new heuristic algorithm for solution of bi-objective discrete competitive facility location problems is developed and experimentally investigated by solving different instances of a facility location problem for firm expansion. The proposed algorithm is based on ranking of candidate locations for the new facilities, where rank values are dynamically adjusted with respect to behaviour of the a...

We present two heuristic methods for solving the Discrete Ordered Median Problem (DOMP), for which no such approaches have been developed so far. The DOMP generalizes classical discrete facility location problems, such as the p-median, p-center and Uncapacitated Facility Location problems. The first procedure proposed in this paper is based on a genetic algorithm developed by Moreno Vega [MV96]...

Discrete location theory is one of the most dynamic areas of operations research. We present the basic mathematical models used in this field, as well as their properties and relationship with pseudo-Boolean functions. We also investigate the theory of PLS-complete problems, average and worst case computational complexity of the local search algorithms, and approximate local search. Finally, we...

Discrete location theory is one of the dynamic areas in operations research. We present some mathematical models in this field concerning the hierarchical optimization. Main properties of the models and computational methods are reviewed.