Branch-and-price algorithm for the location-routing problem with time windows

• This study models the branch-and-price algorithm to solve the LRPTW to optimality.
• The acceleration strategies have been developed to improve computational processes.
• New test instances of the LRPTW, modified from literature are presented and expected to be the new benchmarks.
• The effects and characteristics of time windows in location-routing are highlighted.
• The newly developed exact algorithm can be used to solve small scale instances of the LRPTW directly.

This study proposes a branch-and-price algorithm to solve the Location-Routing Problem with Time Windows (LRPTW) which has never been attempted with the exact solutions before. The problem is solved by the simplex algorithm in the master problem and elementary shortest path problems with resource constraint corresponding to column generation in the subproblem until only the non-negative reduced cost columns remain. The proposed algorithm can solve many testing instances effectively. The computational results and the effect of time windows are also compared and discussed.