Branch-and-price-and-cut algorithm for the capacitated single allocation hub location routeing problem

Abstract

The paper focuses on a variant of hub location routeing problem arising in the design of intra-city express service networks, named as capacitated single allocation hub location routeing problem, in which each non-hub node should be served by exactly one hub, and both hub capacity and vehicle capacity are considered. A new mixed-integer programming formulation for the problem is provided, and a solution algorithm is developed on the basis of the column generation scheme to exactly solve the problem for the first time. The pricing subproblem is solved by a bidirectional labelling algorithm, and the master problem is strengthened by valid inequalities. Numerical experiments are conducted on the instances generated from the Australian Post dataset to test the performance of the model and the developed algorithm. Computational results prove that the algorithm outperforms the CPLEX and is able to provide optimal solutions for instances with up to 35 non-hub nodes and high-quality solutions for instances with 40 non-hub nodes within reasonable computational time, which indicates the feasibility and efficiency of the model and algorithm proposed.