Integrated Planning of Supply and Inventory Under Seasonal Demand Uncertainty

This study investigates several classes of integrated supply and inventory (SI) planning problems, addressing supplier selection with limited or unlimited capacities, distribution, and centralized or decentralized inventory planning for various products with uncertain demand. Our focus is on retailers specializing in fashion products characterized by seasonal demand, extended lead times, and the inability to restock during midselling seasons, requiring salvage of unsold items at diminished returns. We formulate the capacitated problems as convex mixed-integer programs and show they are strongly NP-hard. To address these complex problems, we propose employing Lagrangian relaxation methods for analytically deriving lower bounds, establishing optimal multiplier ranges, and deriving worst-case error bounds. Additionally, we introduce heuristics to generate feasible solutions. Computational studies demonstrate that our relaxation-based heuristics produce solutions closely approaching optimality. Furthermore, we demonstrate that uncapacitated SI problems can be solved analytically, providing closed-form optimal solutions. This research contributes significant managerial insights for practitioners involved in supplier selection, distribution strategies, and inventory management within centralized and decentralized supply chains. Particularly noteworthy are our analytical findings on the benefits of centralization, especially under correlated Gaussian and heavy-tailed stable demand distributions. Our computational experiments further explore the influence of critical factors such as economies of scale, demand correlation, demand distribution characteristics, and upstream and downstream costs. Specifically, we assess how these factors impact the efficacy of centralization versus decentralized inventory management in minimizing expected inventory and overall system costs. Supplemental Material: The online supplement is available at https://doi.org/10.1287/trsc.2025.0026 .