Static stability versus packing efficiency in online three-dimensional packing problems: A new approach and a computational study

In online three-dimensional packing problems where items are received one by one and require immediate packing decisions without prior knowledge of upcoming items, considering the static stability constraint is crucial for safely packing each arriving item in real time. Unstable loading patterns can result in risks of potential damage to items, containers, and operators during loading/unloading operations. Nevertheless, static stability constraints have often been neglected or oversimplified in existing online heuristic methods in the literature, undermining the practical implementation of these methods in real-world scenarios. In this study, we analyze how different static stability constraints affect solutions’ efficiency and cargo stability, aiming to provide valuable insights and develop heuristic algorithms for real-world online problems, thus increasing the applicability of this research field. To this end, we embedded four distinct static stability constraints in online heuristics, including full-base support, partial-base support, center-of-gravity polygon support, and novel partial-base polygon support. Evaluating the impact of these constraints on the efficiency of a wide range of heuristic methods on real instances showed that regarding the number of used bins, heuristics with polygon-based stabilities have superior performance against those under full-base and partial-base support stabilities. The “static mechanical equilibrium” approach offers a necessary and sufficient condition for the cargo static stability, and we employed it as a benchmark in our study to assess the quality of the four studied stability constraints. Knowing the number of stable items under each of these constraints provides valuable managerial insight for decision-making in real-world online packing scenarios.