In prior work [4], Anderson et al. introduced a new problem, the rankability problem, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. Ranking is a fundamental data science task with numerous applications that include web search, data mining, cybersecurity, machine learning, and statistical learning theory. Yet little attention has been paid to the question of whether a dataset is suitable for ranking. As a result, when a ranking method is applied to a dataset with low rankability, the resulting ranking may not be reliable.Rankability paper [4] and its methods studied unweighted data for which the dominance relations are binary, i.e., an item either dominates or is dominated by another item. In this paper, we extend rankability methods to weighted data for which an item may dominate another by any finite amount. We present combinatorial approaches to a weighted rankability measure and apply our new measure to several weighted datasets.

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How do we keep hot drinks hot and cold drinks cold? Companies such as Tervis, YETI, and Thermos spend their time researching and designing products around that very question. In this lesson, students will discover, through mathematical modeling, which materials provide the best insulation and be tasked with designing their own insulator. This lesson has been designed at two different levels for students from grade three through high school with an optional extension activity for more advanced students. Students will use technology to explore the rate of change of the temperature of hot water over two minutes using different insulation materials. After this exploration, students will use the data they have collected to determine the best materials for designing their own insulator. This insulator will then be judged based on the ability to keep a hot drink hot and on the aesthetic value.

We present an improved library for the ranking problem called RPLIB. RPLIB includes the following data and features. (1) Real and artificial datasets of both pairwise data (i.e., information about the ranking of pairs of items) and feature data (i.e., a vector of features about each item to be ranked). These datasets range in size (e.g., from small n = 10 item datasets to large datasets with hundred of items), application (e.g., from sports to economic data), and source (e.g. real versus artificially generated to have particular structures). ( 2) RPLIB contains code for the most common ranking algorithms such as the linear ordering optimization method and the Massey method. (3) RPLIB also has the ability for users to contribute their own data, code, and algorithms. Each RPLIB dataset has an associated .JSON model card of additional information such as the number and set of optimal rankings, the optimal objective value, and corresponding figures. Keywords ranking problem library • linear ordering problem • integer programming • linear programming • rankability • artificial data • Massey rankings • Colley rankings