Packing isn’t just about fitting everything into a certain space – it’s also about being able to retrieve important items quickly and correctly. In a pair of new studies, researchers from North Carolina State University developed packing models that optimize spatial usage while including item priority, location and weight distribution. The new models could improve efficiencies in areas ranging from combat loading in military logistics to warehouse storage and multi-drop delivery services.
“For the vast majority of packing models, the primary goal is to waste as little space as possible,” says William Kirschenman, first and corresponding author of both studies. Kirschenman led the research while a Ph.D. student at NC State and is now an assistant professor at the Naval Postgraduate School.
“But in many real-world settings, you also want the right things in the right places, like keeping the items a customer ordered together or placing the most urgent shipment closest to the exit. So, we designed the model to include those real-world priorities.”
“My experience as a company commander was a major motivation for this research,” Kirschenman says. “I always wanted my unit organized in the order that best supported the mission. Wargaming amphibious landings showed me how difficult that becomes in a chaotic or contested environment.”
The researchers designed a model that considered item priority, accessibility, groupings, and space. However, adding these additional pieces to the model meant the potential combinations quickly outstripped available computing power. So they added a “sliding window” matheuristic that essentially broke the larger problem down into bite-sized pieces, allowing the computer to quickly obtain a good solution.
They tested their sliding-window approach against a commercially available optimization solver and found that the sliding window performed better in terms of both speed and solution quality.
But let’s say that you aren’t just packing a truck or a warehouse, but a large ship. Now you must add stability to the mix – because too much weight in the wrong place could cause the ship to list, or tilt too far to one side.
“Adding the extra constraint of stability means that you’re working around a fixed center of gravity, and you won’t know whether you’ve done it correctly until the entire area is packed, so you will probably need to make adjustments,” says Brandon McConnell, research associate professor in the Edward P. Fitts Department of Industrial and Systems Engineering and the military and veteran liaison for NC State’s College of Engineering. McConnell is a co-author on both studies.
The team tested different approaches and found that the most efficient path was to run the existing model with the sliding window, then adjust selected lower priority items at the end as needed to achieve stability.
The researchers believe that their model provides fast, high-quality solutions to both military and real-world packing challenges.
“This model could help ensure that mission-critical gear is offloaded first, save a warehouse worker’s time and energy, and lead to faster goods retrieval with fewer mistakes for any delivery business,” McConnell says.
The first study, “The 2-D Orthogonal Packing Problem with Multiple Levels of Prioritization: A Spatial Optimization Perspective,” appears in Naval Research Logistics. The second study, “Enhancing Military Load Planning: A Prioritized 2-D Orthogonal Packing Approach,” appears in Omega. Kirschenman is currently an assistant professor at the Naval Postgraduate School and a two-time selectee for the General Omar Bradley Research Fellowship in Mathematics, which helped support the research. Other NC State contributors are: Sebastian Heese, Owens Distinguished Professor of Supply Chain Management; Michael Kay, associate professor of industrial and systems engineering; and Russell King, the Dopaco Distinguished Professor of Industrial and Systems Engineering.
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