A branch-and-price approach to the vehicle routing problem with simultaneous distribution and collection

The vehicle routing problem with simultaneous distribution and collection is the variation of the capacitated vehicle routing problem that arises when the distribution of goods from a depot to a set of customers and the collection of waste from the customers to the depot must be performed by the same vehicles of limited capacity and the customers can be visited in any order. We study how the branch-and-price technique can be applied to the solution of this problem and in particular we compare two different ways of solving the pricing subproblem: exact dynamic programming and state space relaxation. By applying a bidirectional search we experimentally prove its effectiveness in solving the subproblem. We also devise suitable branching strategies for both the exact and the relaxed approach and we report on an extensive set of computational experiments on benchmark instances with both simple and composite demands.