Promotion Optimization for Multiple Items in Supermarkets
研究了超市如何为多种商品同时制定价格促销，提出一种整数规划近似方法，考虑商品间的替代与互补效应及促销后销量回落，并通过线性规划和舍入方案求解，对零售商有实际应用价值。
Promotions are a critical decision for supermarket managers, who must decide the price promotions for a large number of items. Retailers often use promotions to boost the sales of the different items by leveraging the cross-item effects. We formulate the promotion optimization problem for multiple items as a nonlinear integer program. Our formulation includes several business rules as constraints. Our demand models can be estimated from data and capture the postpromotion dip effect and cross-item effects (substitution and complementarity). Because demand functions are typically nonlinear, the exact formulation is intractable. To address this issue, we propose a general class of integer programming approximations. For demand models with additive cross-item effects, we prove that it is sufficient to account for unilateral and pairwise contributions and derive parametric bounds on the performance of the approximation. We also show that the unconstrained problem can be solved efficiently via a linear program when items are substitutable and the price set has two values. For more general cases, we develop efficient rounding schemes to obtain an integer solution. We conclude by testing our method on realistic instances and convey the potential practical impact for retailers. This paper was accepted by Yinyu Ye, optimization.