A Branch and Price Algorithm for the Multi-Period Single-Sourcing Problem

In this paper we propose a Branch and Price algorithm for solving multi-period single-sourcing problems. In particular, we generalize a Branch and Price algorithm that was developed for the Generalized Assignment Problem (GAP) to a class of convex assignment problems. We then identify an important subclass of problems, containing many variants of the multi-period single-sourcing problem (MPSSP), as well as variants of the GAP, for which we derive an efficient solution procedure for the pricing problem, a critical factor in the efficiency of the Branch and Price algorithm. We execute an extensive numerical comparison between the performances of the Branch and Price algorithm and the MIP solver of CPLEX for a particular variant of the MPSSP.