A Branch-and-Price Algorithm for Facility Location with General Facility Cost Functions

Most existing facility location models assume that the cost is either a fixed setup or made up of and problem-specific concave submodular term. This structural property plays critical role in developing fast branch-and-price, Lagrangian relaxation, constant ratio approximation, conic integer programming reformulation approaches for these NP-hard problems. Many practical considerations complicating factors, however, can make no longer submodular. By removing this restrictive assumption, we study new model considers general nonlinear costs to operate facilities framework. The does not even admit any approximation algorithms unless P = NP because it takes unsplittable hard-capacitated metric problem as special case. We first reformulate set-partitioning then propose branch-and-price approach. Although corresponding pricing NP-hard, effectively analyze its properties design an algorithm solve efficiently. numerical results obtained from two implementation examples demonstrate effectiveness solution approach, reveal managerial implications, validate importance