Abstract: Embodiments generate an optimized demand model for a retail item. Embodiments train a tree ensemble machine learning model comprising a plurality of trees, the training comprising storing upper bounds for each of the trees, the trees comprising levels and branches that correspond to the demand features that influence demand for the item. Embodiments generate an objective function for the demand model. At a top split of each tree, embodiments determine optimal child nodes using the stored upper bounds and calculate a new feasible region for each tree. Using bounds on the new feasible region, embodiments move down each tree to a next level of splits and generate the optimized demand model when a leaf node of every tree has been reached.

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: Systems, methods, and other embodiments associated with predicting customer behavior are described. The method can include identifying a group comprising customers who satisfy a defined criterion, and receiving input that identifies a factor that influences a decision by the customers to purchase a product. A likelihood that the factor will induce the customers in the group to purchase the product is generated. A customer influence on the generated likelihood is estimated independently of data expressly identifying relationships between the customers in the group. The likelihood is modified by combining the likelihood and the customer influence according to a predictive model, and one or more of the customers eligible for a promotional offer related to the product is identified based, at least in part, on the modified likelihood. Transmission of the promotional offer is controlled to transmit the promotional offer to the identified customers in the group.

Abstract: An aspect of the disclosure includes a method, a system and a computer program product for determining a personalized bundle offer for a consumer. The method includes determining an interest in an initial product by a consumer. A demand group is identified based on the initial product. A purchase probability is determined for the consumer to purchase the product. An inventory expected profit-to-go is determined for the product. At least one additional product from the demand group is determined based at least in part on the purchase probability and the inventory expected profit-to-go, the expected profit to go being based on a current inventory state of the product and the at least one additional product. A signal is transmitted to the consumer, the signal including at least one additional product and a price for a bundle containing both the product of interest and the at least one additional product.

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: A system that determines promotional pricing for a product and for an objective function receives a non-linear time-dependent optimization problem for the product, where the non-linear problem includes a demand model and a plurality of constraints, and the constraints include a price ladder that includes a plurality of time periods and a non-promotional price for the product at each time period. For each of the time periods, the system determines a change in the objective function when the price at that time period includes a promotional price and all other prices on the price ladder are set to the non-promotional price to generate coefficients. The system determines a maximum value of the coefficients at each time period, and generates an approximate Mixed Integer Programming (“MIP”) problem based on the coefficients. The system determines a Linear Programming (“LP”) relaxation of the MIP problem, and solves the LP relaxation.