A MILP approach for the multi-drop container loading problem resolution in logistics 4.0

This paper addresses the multi-drop container loading problem (CLP), i.e., the problem of packing multiple bins -associated to multiple deliveries to one or more customers- into a finite number of transport units (TUs). Differently from the traditional CLP, the multi-drop CLP has been rarely handled in the literature, while effective algorithms to automatically solve this problem are needed to improve the efficiency and sustainability of internal logistics. To this aim, we propose a novel algorithm that solves a delivery-based mixed integer linear programming formulation of the problem. The algorithm efficiently determines the optimal composition of TUs by minimizing the unused space, while fulfilling a set of geometric and safety constraints, and complying with the delivery allocation. In particular, the proposed algorithm includes two steps: the first aims at clustering bins into groups to be compatibly loaded in various TUs; the latter aims at determining the optimal configuration of each group in the related TU. Finally, the proposed algorithm is applied to several realistic case studies with the aim of testing and analysing its effectiveness in producing stable and compact TU loading configurations in a short computation time, despite the high computational complexity of the multi-drop CLP.