We consider the distributor’s pallet loading problem, whose aim is to pack on the lowest number of pallets a set of different boxes, satisfying a given set of constraints. We focus on a real-world scenario where a stability restriction and a compression limit must be respected. Each pallet is loaded with a set of layers of boxes that must not overhang beyond the maximum dimensions of the pallet. The problem has been addressed in [12] with a two phases method that starts by defining a huge set of possible layers made of boxes, and uses an integer linear program (ILP) to select the layers which pack all boxes while minimizing the number of pallet used and satisfy all constraints. Unfortunately, the computing time needed to solve the ILP can be extremely long. In this paper we present a proposal for solving the problem which, first, builds layers heuristically, secondly, through machine learning algorithms, classifies by “importance” and then, uses the classification to resolve a ILP. With “importance” we are meaning how much high is the “probability” that each layer will be used to resolve the instance. We validate our proposed method, comparing results obtained with and without the machine learning approach.

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A Machine Learning Approach to Speed up the Solution of the Distributor’s Pallet Loading Problem

  • Matteo Magnani,
  • Giorgia Franchini,
  • Mauro Dell’Amico,
  • Luca Zanni

摘要

We consider the distributor’s pallet loading problem, whose aim is to pack on the lowest number of pallets a set of different boxes, satisfying a given set of constraints. We focus on a real-world scenario where a stability restriction and a compression limit must be respected. Each pallet is loaded with a set of layers of boxes that must not overhang beyond the maximum dimensions of the pallet. The problem has been addressed in [12] with a two phases method that starts by defining a huge set of possible layers made of boxes, and uses an integer linear program (ILP) to select the layers which pack all boxes while minimizing the number of pallet used and satisfy all constraints. Unfortunately, the computing time needed to solve the ILP can be extremely long. In this paper we present a proposal for solving the problem which, first, builds layers heuristically, secondly, through machine learning algorithms, classifies by “importance” and then, uses the classification to resolve a ILP. With “importance” we are meaning how much high is the “probability” that each layer will be used to resolve the instance. We validate our proposed method, comparing results obtained with and without the machine learning approach.