Logical reduction tests for the p-problem

Preprocessing plays a crucial role in solving combinatorial optimization problems. It can be realized through reduction tests which allow one to determine in advance the values that a set of variables will take in the optimal solution, thus reducing the size of an instance. Reduction tests can be summarily classified in two main families: those based on reduced costs and those based on logical implications. The first rely on reduced costs of the Linear Programming problem associated to continuous relaxation. The second are based on the special features of the problem and on combinatorial techniques. In this paper, some effective reduction tests for the p-median problem are proposed, showing their impact on the size of the instances and on model formulation. Finally, some work perspectives to embed reduction tests into solution algorithms for the p-median problem are pointed out.