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

Background: Inventory planning in retail supply chains requires balancing cost efficiency and service reliability under demand uncertainty and financial limitations. The literature has seldom addressed the joint integration of stochastic demand, deterministic lead times, and supplier-specific constraints in multi-product and multi-warehouse settings, particularly in the context of small- and medium-sized enterprises. Methods: This study develops a Stochastic Pure Integer Linear Programming (SPILP) model that incorporates stochastic demand, deterministic lead times, budget ceilings, and trade credit conditions across multiple suppliers and warehouses. A two-step solution procedure is proposed, combining a chance-constrained approach to manage uncertainty with warm-start heuristics and relaxation-based preprocessing to improve computational efficiency. Results: Model validation using data from a Colombian retail distributor showed cost reductions of up to 17% (average 15%) while maintaining or improving service levels. Computational experiments confirmed scalability, solving instances with more than 574,000 variables in less than 8800 s. Sensitivity analyses revealed nonlinear trade-offs between service levels and planning horizons, showing that very high service levels or short planning periods substantially increase costs. Conclusions: The findings demonstrate that the proposed model provides an effective decision support system for inventory planning under uncertainty, offering robust, scalable, and practical solutions that integrate operational and financial constraints for medium-sized retailers.