Common inventory modeling assumptions that fall short: Arborescent networks, Poisson demand, and single-echelon approximations

Traditional multi-echelon inventory theory focuses on arborescent supply chains that use a central warehouse which replenishes remote warehouses. The remote warehouses serve customers in their respective regions. Common assumptions in the academic literature include use of the Poisson demand process and instantaneous unit-by-unit replenishment. In the practitioner literature, single-echelon approximations are advised for setting safety stock to deal with lead time, demand, and supply variations in these settings. Using data from a U.S. supplier of home improvement products, we find that neither the assumptions from the academic literature nor the approximations from the practitioner literature necessarily work well in practice. ariation of the strictly arborescent supply chain, the central warehouse at our real company not only replenishes other warehouses but also meets demand from customers in the region near the central warehouse. In this paper, we study this dual-role central warehouse structure, which we believe is common in practice. Using high and low volume product demand data from this company, we use Monte Carlo simulations to study the impact of (1) the use of a dual-role centralized warehouse, (2) common demand assumptions made in multi-echelon research, and (3) single-echelon approximations for managing a multi-echelon supply chain. We explore each of these under both centralized and decentralized control logic. We find that the common assumptions of theoretical models impede their usefulness and that heuristics that ignore the actual supply chain structure fail to account for additional opportunities to utilize safety stock more effectively. Researchers should be aware of the gap between standard assumptions in traditional literature and actual practice, and critically evaluate their assumptions to find a reasonable balance between tractability and relevance.