Abstract: A price optimization system determines the pricing of a plurality of items. The system receives an initial price vector for the items and an objective function, and assigns the initial price vector as a current price vector. The system determines a first new price vector by randomly choosing a first set of allowed prices for the items, and assigning the first set of allowed prices as the current price vector when the objective function is improved. The system then determines a second new price vector by randomly choosing a second set of allowed prices for the items and assigning the second set of allowed prices as the current price vector when the objective function does not decrease by more than a predetermined value. The system sequentially repeats this functionality until a terminating criteria is reached and then it determines the pricing.

Abstract: A system for determining product pricing for a product category receives a non-linear problem for the product category, in which the non-linear problem includes a demand model. For a plurality of pair of products in the product category, the system determines coefficients for a change in demand of a first product when a price of a second product is changed. The system then generates an approximate Mixed Integer Linear Programming (“MILP”) problem that includes a change of demand based on a sum of the determined coefficients. The system then solves the MILP problem to obtain a MILP solution, which provides the product pricing.

Abstract: A system determines a revised price on a pricing ladder for a product over a pricing markdown period. For a first time interval of the markdown period, the system computes an optimal price for the product based on an inventory level of the product, where the inventory level is based on a ratio of a current on-hand inventory and a maximal on-hand inventory. The system then determines if the optimal price is approximately less than a current price of the product. When the optimal price is approximately less than a current price of the product, the system assigns to the product a lower price on the price ladder as the current price of the product.

Abstract: A system for determining an optimized pre-pack solution receives demand data and constraints and initializes a current pre-pack configuration comprising a current pre-pack design that comprises a plurality of pre-pack types, each pre-pack type comprising one or more different products. The system optimizes a pre-pack allocation based on the current pre-pack configuration and determines an objective function value improvement comprising, for each product in each pre-pack type, changing a level of the product by one unit and determining if the objective function value has improved. If the objective function value has improved, the system generates a new pre-pack design based on the changed level of the product and assigns the new pre-pack design as the current pre-pack design and re-optimizes the allocation. The system repeats until the objective function value stops improving. The system then outputs an optimized pre-pack configuration and optimized pre-pack allocation.

Abstract: A system determines an optimized pre-pack configuration with an optimized pre-pack allocation and an optimized pre-pack design. The system receives demand data and constraints and initializes a current pre-pack allocation and a current pre-pack design. For the current pre-pack allocation, the system determines a new pre-pack design by solving a multi-choice integer knapsack problem, and then determines if the new pre-pack design is different than the current pre-pack design. When the new pre-pack design is different than the current pre-pack design, the system determines a new pre-pack allocation and assigns the new pre-pack allocation as the current pre-pack allocation and the new pre-pack design as the current pre-pack design and repeats the determining the new pre-pack design and the determining if the new pre-pack design is different than the current pre-pack design until the new pre-pack design is the same as the current pre-pack design.