A branch-and-bound method for multicommodity location with balancing requirements

The authors present a branch-and-bound algorithm for the multicommodity location-allocation problem with balancing requirements. Although the formulation displays a number of characteristics common to classical location models, it also unveils, due to the presence of the balancing requirements, a network flow structure that is most favorable to efficient algorithmic developments. In particular, tight bounds may be efficiently computed by using a reformulation of the weak relaxation of the problem as a minimum cost multicommodity flow problem. The authors also develop and analyse various branching criteria, and show that the branching rules which form the most efficient branch-and-bound procedure for the present problem are quite different from those used to solve classical location problems. The experimentation has been conducted both on several randomly generated problems and on a large scale application.