Approximation of solutions for location problems
Journal of Optimization Theory and Applications
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A note on center problems with forbidden polyhedra
Operations Research Letters
Subclasses of solvable problems from classes of combinatorial optimization problems
Cybernetics and Systems Analysis
Simultaneous scheduling and location (ScheLoc): the planar ScheLoc makespan problem
Journal of Scheduling
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It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by finding a finite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location.In this paper it is first established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems.Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal objective value. For the approximation problem two different approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed ε - to polynomial approximation algorithms with accuracy ε for solving the general model considered in this paper.