Iterative Demand Optimization Using the Discrete Functional Particle Method

Modern companies face immense pressure to accelerate and refine decisions related to product assortment due to rapid changes and growing competition in the retail landscape. The volume, velocity, and volatility of business data make intuitive or situational approaches insufficient. Advances in optimization theory and forecasting models enable the design of robust, flexible decision-support systems that bridge the gap between business intuition and data-driven strategy. In retail, risk manifests primarily through operational inefficiencies, such as capital immobilized in unsold inventory and delayed responsiveness to demand changes. This demands a rethinking of risk modeling tailored specifically to the retail domain. At the same time, simplistic forecasting tools often prioritize short-term fluctuations at the expense of strategic seasonal trends, thereby undermining long-term planning. As a result, there is a critical need for integrated models that combine predictive accuracy with optimization under uncertainty. Such models must not only capture patterns in consumer demand but also align with operational constraints to ensure that solutions are implementable in practice. This work proposes a novel, multi-layered framework for assortment optimization that incorporates two key components: SARIMAX-based demand forecasting and the Discrete Functional Particle Method (DFPM) for iterative optimization. Additionally, we introduce a new operational risk measure Inventory Efficiency Ratio (IER) designed to quantify inefficiencies in the retail pipeline. By embedding these techniques into a unified system, we offer a practical solution for improving capital productivity, reducing inventory holding costs, and enhancing responsiveness in assortment planning. The methodology is validated through realworld data and demonstrates substantial performance improvements over standard planning strategies.