Multi-Echelon Production/Inventory Systems: Optimal Policies, Heuristics, and Algorithms

The theory on multi-echelon production/inventory systems is a core theory within supply chain management. It provides useful insights for design of supply chains and may be used for tactical and operational planning decisions. The multi-echelon theory started with the seminal paper of Clark and Scarf in 1960. In this tutorial, we describe for which systems optimal policies are known, which key features are needed for these optimal policy structures, and we discuss heuristics for systems of which the optimal policy structure is not known. We describe the complete analysis for the most basic multi-echelon production/inventory system: the serial, two-echelon production/inventory system with linear inventory holding and backordering costs. We show that basestock policies are optimal, we derive a decomposition result for the determination of optimal basestock levels, we present Newsboy equations for the optimal basestock levels, and we discuss computational procedures. Next, we describe a variety of systems for which generalized classes of basestock policies have been derived to be optimal. This includes assembly systems and systems with fixed batch sizes, fixed replenishment intervals, generalized demand processes, and a service level constraint instead of backordering costs. Finally, we discuss approaches that have been taken for distribution systems and systems with a general structure.