Formulations and solution algorithms for dynamic assembly routing problem

We study a dynamic version of the assembly routing problem. The assembly lot sizing section deals with decisions concerning the production phase, whereas the routing section organises the collection of raw materials necessary for the production. Traditionally, these two problems are treated separately, and more specifically, in a hierarchical way. We propose three linear programming models: a non-vehicle index model, a two-commodity flow formulation and a logic-based benders decomposition. We develop aggregated rounded capacity constraints for non-vehicle index model and separated them dynamically during the Branch & Cut procedure. Logic-based benders decomposition algorithm solves the Dynamic Assembly Routing Problem iteratively and obtains a feasible solution at each iteration. The numerical tests show that, the two first models are particularly effective at finding the optimal solutions in a reasonable amount of time on instances with up to 50 components and 3 periods.