Logical reduction tests for the p‐problem

Abstract

Preprocessing plays a crucial role in solving combinatorial optimization problems. Itcan be realized through reduction tests which allow one to determine in advance the valuesthat 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 reducedcosts and those based on logical implications. The first rely on reduced costs of the LinearProgramming problem associated to continuous relaxation. The second are based on thespecial features of the problem and on combinatorial techniques. In this paper, some effectivereduction tests for the p‐median problem are proposed, showing their impact on the size ofthe instances and on model formulation. Finally, some work perspectives to embed reductiontests into solution algorithms for the p‐median problem are pointed out.