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 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.

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.