Optimal Inventory Planning at the Retail Level, in a Multi-Product Environment, Enabled with Stochastic Demand and Deterministic Lead Time

This study focuses on developing a decision support system to facilitate inventory decision-making in the retail sector. The proposed model incorporates both stochastic and deterministic parameters, integrating elements that have rarely been jointly addressed in the literature. The research formulates a stochastic mixed-integer programming model and a two-step solution procedure for inventory planning in a multi-product, multi-warehouse, and multi-period context with resource constraints. The first step applies a chance-constrained planning approach to handle uncertainty. The second step incorporates warm-start heuristics and relaxation-based preprocessing to improve computational efficiency. The model is validated through instance analysis and sensitivity testing, demonstrating favourable CPU performance with significant time reductions in medium-scale cases.