Enhancing pallet load stability: a MILP model for the Manufacturer’s Pallet Loading Problem with interlocking constraints

Abstract

The Manufacturer’s Pallet Loading Problem involves optimising the packing of a maximal number of identical rectangular boxes onto a single rectangular pallet. This problem arises in various logistic operations that involve the storage and transportation of boxed products, where efficient packing can result in substantial cost reductions and improved operational efficiency. Logistics managers anticipate that some boxes can be damaged during handling and transport, so the stability of the pallet load is essential to avoid such damage. The interlocking method is commonly used in practice to improve stability when loading pallets, minimising product damage and reducing the risk of injury to personnel handling the pallet. This study introduces a Mixed Integer Linear Programming model that addresses the Manufacturer’s Pallet Loading Problem, promoting static stability through interlocking. Stability is evaluated with respect to the relationship between successive layers of the loading plan, with three types of interlocking incorporated into the mathematical model. Computational experiments with real-world instances were conducted to assess the model’s performance using different objective functions and post-optimisation heuristics that target real-world requirements. Three stability metrics were used to evaluate the load plans generated by the mathematical model. The results show the interlocking method’s benefits on the pallet loads’ stability while maximising the pallet volume usage.