Integrated sales planning for in-store retail: A multi-stage stochastic optimization approach

Effective sales planning is critical in the retail industry but is challenging to outline and implement. In fact, the future demand of new or existing products is complex to predict due to its intricate relationship with pricing strategies and consumer behaviors, whereas optimizing product assortment requires capturing inter-product effects and the impact on inventory management and costs. Tackling these interconnected challenges effectively remains a key issue in retail planning. In this paper, we focus on low-margin, high-volume brick-and-mortar retail businesses, in which the baseline product price is fixed by the supplier, but markdowns and promotions can be leveraged to steer sales. We develop a multi-stage stochastic linear program that accounts for demand uncertainty and jointly optimizes product assortment, inventory, and promotion decisions, while embedding a novel demand elasticity formulation. To define the input demand scenarios to the stochastic program, we consider historical sales data by an Italian electronics retailer aggregated by product category, calibrate a stochastic process to this data, and construct a scenario tree that captures the process dynamics. Extensive numerical experiments show that the model can be solved efficiently with a commercial optimization solver for instances at varying number of products, categories, and scenarios. Furthermore, we show that the expected profit from our stochastic program increases compared to a forecast-based reoptimization policy by 15%, an expert-based heuristic inspired by current practice by 22%, and a benchmark that neglects demand elasticity by 5%. Our approach can thus support in-store retail planners to enhance their competitiveness.