An efficient column-generation-based algorithm for solving a pickup-and-delivery problem

We introduce a new variation of the pickup-and-delivery problem. Current methods for solving this problem rely on column-generation subroutines embedded in a branch-and-bound tree. Yet, when applied to our problem, these techniques suffer from significant combinatorial explosion in the number of routes generated by the column-generation subroutine and the number of nodes explored in the branch-and-bound tree. In this paper, by exploiting the problem structure, we develop a specialized column-generation subroutine that reduces the combinatorial explosion significantly leading to a more efficient procedure to solve the problem.