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 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.

Abstract: A system for determining time-dependent 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 at each of a plurality of time periods 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.