The Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries and Two-Dimensional Loading Constraints

We introduce and solve the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries and Two-Dimensional 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 bi-directional 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 loading constraints are very hard to tackle in reasonable computational times. To this end, we propose an optimization framework which employs memorization techniques designed for the 2L-SPD model, to accelerate the solution methodology. To assess the performance of our routing and packing algorithmic components, we have solved the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries (VRPSPD) and the Vehicle Routing Problem with Two-Dimensional Constraints (2L-CVRP). Computational results are also reported on newly constructed 2L-SPD benchmark problems. Apart from the basic 2L-SPD version, we introduce the 2L-SPD with LIFO constraints which prohibit item rearrangements along the routes. Computational experiments are conducted to understand the impact of the LIFO constraints on the routing plans obtained.