Solving the Pickup and Delivery Problem with 3D Loading Constraints and Reloading Ban

Abstract

In this paper, we extend the classical Pickup and Delivery Problem (PDP) to an integrated routing and three-dimensional loading problem, called PDP with 3D loading constraints (3L-PDP). A set of routes of minimum total length has to be determined such that each request is transported from a loading site to the corresponding unloading site. In the 3L-PDP, each request is given as a set of 3D rectangular items (boxes) and the vehicle capacity is replaced by a 3D loading space. This paper is the second one in a series of articles on 3L-PDP. In both articles we investigate which constraints will ensure that no reloading effort will occur, i.e. that no box is moved after loading and before unloading. In this paper, the focus is laid on the so-called reloading ban, a packing constraint that ensures identical placements of same boxes in different packing plans. We propose a hybrid algorithm for solving the 3L-PDP with reloading ban consisting of a routing and a packing procedure. The routing procedure modifies a well-known large neighborhood search for the 1D-PDP. A tree search heuristic is responsible for packing boxes. Computational experiments were carried out using 54 3L-PDP benchmark instances.