Date of Graduation


Document Type


Degree Name

Master of Science in Industrial Engineering (MSIE)

Degree Level



Industrial Engineering


Sarah E. Root

Committee Member

Chase Rainwater

Second Committee Member

Ashlea Bennett Milburn


Social sciences, Applied sciences, Container loading, Logistics, Packing problems, Trucking


The under utilization in trucking leads to nearly 5 billion gallons of wasted fuel annually. One way to recapture part of this waste is to use collaborative logistics. This research focuses on one specific aspect of collaborative logistics: load mixing. Load mixing is the idea of mixing two or more items of different weights in the same container to reduce the number of trucks needed.

Load mixing is similar to other packing problems such as the knapsack and container loading problems. However, traditional packing problems typically only assume a single type of capacity (e.g., weight), whereas load mixing must simultaneously the weight and spatial capacities to effectively utilize containers. We propose a mathematical model with constraints for the space and weight limits that can be used to minimize the number of trailers used. Though there are some tractability issues associated with this formulation, a more fundamental issue is the existence of multiple optima for this type of problem. While solutions that all use the same number of containers to transport to the commodities are all viewed equally by the model, these solutions vary in terms of how easily they can be implemented. For these reasons, I propose a heuristic to solve the load mixing problem. The performance of the heuristic is tested against our exact formulation to compare solutions.

First a heuristic to load two commodities with different weight and demand - one heavy and one light - on a set of containers was created. The theoretical minimum number of containers needed is calculated based on the total demand and total weight of the commodities. Once this heuristic was examined it was generalized to handle more than two commodities. Both heuristics were implemented in C++. Testing for both heuristics shows both achieve the theoretical minimum in a large amount of cases. The testing of these heuristics also led to many insights about when to use or to not use load mixing. For example, when more of the demand is composed of lighter commodities the savings are greater than when the demand is mostly composed of heavy commodities.