We develop a variant of Benders decomposition for mixed-integer programming that solves each master problem by explicit enumeration. By storing the master problem's current objective-function value for each potential solution, computational effort remains essentially constant across iterations. Using both serial and parallel processing, tests against competing methods show computational speedups that exceed two orders of magnitude.

The concept of big data has caught the attention of business leaders. However, there is still widespread confusion in industry as to how to treat such data. We describe one such encounter with big data from an industrial parts supplier who was concerned with unexpected variability in its prices. Unable to discern trends in the data, a point of contact for the supplier worked with us to explore this concern. Analysis showed that customers at different branches of the company were experiencing significantly different levels of price variation, and that some customers within a specific branch were being offered products at widely varying prices, which were apparently uncorrelated with the quantity of products purchased. Such behaviors are unacceptable to end customers, and rectification of these behaviors has led to increased customer satisfaction for this company. Furthermore, we were able to demonstrate general methodologies to help the company with future analyses.