On-line three-dimensional packing problems: A review of off-line and on-line solution approaches

Three-Dimensional Packing Problems (3D-PPs) can be applied to effectively reduce logistics costs in various areas, such as airline cargo management and warehouse management. In general, 3D-PP studies can be divided into two different streams: those tackling the off-line problem, where full knowledge about items is available beforehand; and those tackling the on-line (real-time) problem, where items arrive one by one and should be packed immediately without having full prior knowledge about them. During the past decades, off-line and on-line 3D-PPs have been studied in the literature with various constraints and solution approaches. However, and despite the numerous practical applications of on-line problems in real-world situations, most of the literature to date has focused on off-line problems and is quite sparse when it comes to on-line solution methods. In this regard, and despite the different nature of on-line and off-line problems, some approaches can be applied in both environments. Hence, we conducted an in-depth and updated literature review to identify and structure various constraints and solution methods employed by researchers in off-line and on-line 3D-PPs. Building on this, by bringing together the two separate streams of the literature, we identified several off-line approaches that can be adopted in on-line environments. Additionally, we addressed relevant research gaps and ways to bridge them in the future, which can help to develop this research field.