An efficient benders decomposition for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"><mml:mi>p</mml:mi></mml:math>-median problem

The p-median problem is a classic discrete location with numerous applications. It aims to open p sites while minimizing the sum of distances each client its nearest site. We study Benders decomposition most efficient formulation in literature. show that cuts can be separated linear time. reformulation leads compact for problem. implement two-phase algorithm outperforms state-of-the-art methods on benchmark instances by an order magnitude and allows exactly solve first time several among which are large TSP BIRCH instances. also our implementation easily applies uncapacitated facility