Abstract: Systems, methods, and other embodiments associated with determining a promotion price schedule for each item in a group are described. In one embodiment, a method includes computing an item coefficient that corresponds to a change in a value of an objective function when the item is priced at the promotion price. The objective function is based on a multiple product demand model. An item coefficient is computed for each item, each time period in the price schedule, and each promotion price in a price ladder for the item. An approximate objective function is formulated that includes products of item coefficients and binary decision variables. The item coefficients, the approximate objective function, and constraints are provided to an optimizer that determines values of the decision variables that maximize the approximate objective function. A promotion price schedule is created for each item based on values of the decision variables.

Abstract: Techniques disclosed herein relate to generating a hierarchical classification model that includes a plurality of classification models. The hierarchical classification model is configured to classify an input into a class in a plurality of classes and includes a tree structure. The tree structure includes leaf nodes and non-leaf nodes. Each non-leaf node has two child nodes associated with two respective sets of classes in the plurality of classes, where a difference between numbers of classes in the two sets of classes is zero or one. Each leaf node is associated with at least two but fewer than a first threshold number of classes. Each of the leaf nodes and non-leaf nodes is associated with a classification model in the plurality of classification models of the hierarchical classification model. The classification model associated with each respective node in the tree structure can be trained independently.