A scaleable projection‐based branch‐and‐cut algorithm for the p‐center problem

The $p$-center problem (pCP) is a fundamental in location science, where we are given customer demand points and possible facility locations, want to choose $p$ of these locations open such that the maximum distance any point its closest minimized. State-of-the-art solution approaches pCP use connection set cover solve an iterative fashion by repeatedly solving problems. classical textbook integer programming (IP) formulation usually dismissed due size bad linear (LP)-relaxation bounds. We present novel approach works on new IP can be obtained projection from formulation. solved means branch-and-cut, cuts for iteratively generated. Moreover, strengthened with combinatorial information obtain much tighter LP-relaxation. In particular, way lower bound stronger cuts. show LP-relaxation our has same strength as best known literature, which based semi-relaxation. Finally, also computational study instances literature up more than 700000 customers locations. Our algorithm competitive highly sophisticated set-cover-based algorithms, depend various components parameters.