An Inventory Service-Level Optimization Problem for a Multi-Warehouse Supply Chain Network with Stochastic Demands

This research aims to develop a mathematical model and a solution approach for jointly optimizing a global inventory service level and order sizes for a single-commodity supply chain network with multiple warehouses or distribution centers. The latter face stochastic demands, such as most real-world supply chains do nowadays, yielding significant model complexity. The studied problem is of high relevance for inventory management, inventory location, and supply chain network design-related literature, as well as for logistics and supply chain managers. The proposed optimization model minimizes the total costs associated with cycle inventory, safety stock, and stock-out-related events, considering a global inventory service level and differentiated order sizes for a fixed and known set of warehouses. Subsequently, the model is solved by employing the Newton–Raphson algorithm, which is developed and implemented assuming stochastic demands with a normal approximation. The algorithm reached optimality conditions and the convergence criterion in a few iterations, within less than a second, for a variety of real-world sized instances involving up to 200 warehouses. The model solutions are contrasted with those obtained with a previous widely employed approximation, where safety stock costs were further approximated and order sizes were optimized without considering stock-out-related costs. This comparison denotes valuable benefits without significant additional computational efforts. Thus, the proposed approach is suitable for managers of real-world supply chains, since they would be able to attain system performance improvements by simultaneously optimizing the global inventory service level and order sizes, thereby providing a better system cost equilibrium.