A two‐stage packing problem procedure

Abstract

This paper deals with a two-stage packing problem that has to be solved in the daily distribution process of a Portuguese trading company. In the first stage, boxes including goods are to be packed on pallets, while in the second stage these pallets are loaded into one or more trucks. The boxes have to be transported to different customers, and the main goal is to guarantee a sufficient utilization of the truck loading space. A two-stage packing procedure is proposed to cover both problem stages. First, boxes are loaded onto pallets by means of a well-known container loading algorithm. Then, trucks are filled with loaded pallets by a tree search algorithm. The performance of the two-stage approach was evaluated using a set of instances that are based on actual company data.

The static stability of support factor‐based rectangular packings: an assessment by regression analysis

“…As previously mentioned, only considering a support factor of 100% it is possible to ensure that the conditions for static stability are met. This approximation to deal with real situations has motivated several authors to consider this value for the support factor (e.g., Bischoff and Ratcliff, 1995; Davies and Bischoff, 1999; Bortfeldt and Gehring, 2001; Eley, 2002; Gehring and Bortfeldt, 2002; Moura and Oliveira, 2005; Araújo and Armentano, 2007; Moura and Oliveira, 2009; Fanslau and Bortfeldt, 2010; Gonçalves and Resende, 2012; Junqueira et al., 2012; Zhu and Lim, 2012; Bortfeldt and Homberger, 2013; Araya and Riff, 2014; Moura and Bortfeldt, 2017; Reil et al., 2018).…”

An Entropy-Guided Monte Carlo Tree Search Approach for Generating Optimal Container Loading Layouts

“…Although Iori [ 26 ] considered loading based on a “last in, first out” principle, the emphasis was on the decisions associated with the choice of vehicles and the travelling salesman route issue, rather than the container layout. More recently, Moura and Bortfeldt [ 27 ] discussed how the process could be optimised for distribution to multiple customers with trucks packed in two layers, optimising numbers of trucks used, while Alonso et al [ 28 ] took a mathematical approach to optimise loading and unloading effort by minimising the number of trucks to be used.…”

“…Moura and Oliveira [ 31 ] have used MCTS in their work on combining the travelling salesman problem with container loading, but they provided their own Greedy Randomised Adaptive Search Procedure (GRASP) for the CLP aspects of the problem, using the MCTS to direct the combination of load selection and route. Moura and Bortfeldt also used a tree search algorithm for filling trucks in the work mentioned earlier [ 27 ] but in this case, the tree search was not Monte Carlo—it was a recursive process to ensure the pallets were stacked in an order suitable for delivery. Edelkamp, Gath and Rohde in [ 32 ] also used a sub-variant of MCTS called Nested Rollout Policy Adaptation (NRPA) which is a variant of Nested Monte Carlo Search (NMCS) for both two- and three-dimensional variants of the container loading problem and reported some success.…”

“…Firstly, issues relating to stackability and the loading process make a fully three-dimensional approach unfeasible. Secondly, the strongly heterogeneous version of the problem is usually associated with a scenario in which the goods need to be unloaded in different locations, meaning that the container loading problem has to be combined with a travelling salesman problem as in [ 25 , 26 , 27 , 28 ].…”

Algorithms for Pallet Building and Truck Loading in an Interdepot Transportation Problem

“…To deal with axle weight constraints, stacks are sequenced by alternating the heaviest and lightest stacks. Moura and Bortfeldt [5] deal with the same problem in two steps. In the first step, boxes are packed onto pallets, while in the second step these pallets are loaded into trucks.…”