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.