We introduce and solve the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries and TwoDimensional Loading Constraints (2L-SPD). The 2L-SPD model covers cases where customers raise delivery and pick-up requests for transporting non-stackable rectangular items. 2L-SPD belongs to the class of composite routing-packing optimization problems. However, it is the first such problem to consider bidirectional material flows dictated in practice by reverse logistics policies. The aspect of simultaneously satisfying deliveries and pick-ups has a major impact on the underlying loading constraints: feasible loading patterns must be identified for every arc traveled in the routing plan. This implies that 2L-SPD generalizes previous routing problem variants with two-dimensional loading constraints which call for one feasible loading per route. From a managerial perspective, the simultaneous service of deliveries and pick-ups may bring substantial cost-savings, but the generalized loadi...
Emmanouil E. Zachariadis, Christos D. Tarantilis,