Inventory Positioning in Multi-Stage and Multi-Product Supply Chains

Yao Zhao, PhD

Professor in

Supply Chain Management

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The control of material flows in multi-product, multi-level supply chains with random demand and stochastic lead-times are practically important and technically challenging problems. These supply chains support the production and distribution of multiple end-products with complex multi-level bills of materials and multiple common components/subassemblies. One important issue is on setting the inventory policy for each item at each stage so as to minimize the system-wide inventory costs, subject to prescribed customer service requirements.

My research in this area focuses on exact analysis and evaluation of inventory replenishment policies, and design of efficient approximations and optimization algorithms.


Simchi-Levi, D., Y. Zhao (2005). Safety Stock Positioning in Supply Chains with Stochastic Lead-times.Manufacturing & Service Operations Management 7: 295-318.

Abstract: This paper considers a class of tree-structure supply chains under base-stock policies, and provides an exact treatment which is uniformly applicable to various network topologies such as serial, assembly and distribution systems. The paper develops exact recursive equations to characterize the intricate dependence among lead-times in multi-level assembly systems. It also derives new system properties and insights on safety-stock positions. Finally, it proposes an optimization algorithm based on dynamic programming to optimize the base-stock policies at all stages.

Zhao, Y. (2008). Evaluation and Optimization of Installation Base-Stock Policies in Supply Chains with Compound Poisson DemandOperations Research 56: 437-452.

Abstract: Batch demand processes complicate the analysis of general-structure supply chains considerably. This is true because different units of demand face statistically different stock-out delays at each stage, and the complex interactions among components in assembly networks are driven not only by the common demand inter-arrival times, but also by the common demand size processes.

This paper considers compound Poisson demand and a more general network topology (than tree topology), where there is at most one directed path between each pair of nodes. The paper presents an exact analysis for two-level general networks, and develops a unified approach to characterize the stock-out delay for each unit of demand at each stage of the supply chain. Based on the exact analysis, approximations are developed to facilitate efficient evaluation and optimization of the system performance.

Shi, J., Y. Zhao. (2010). Technical Note: Some Structural Results on Acyclic Supply Chains. Naval Research Logistics 57: 605613.

Abstract: Acyclic supply chains can often be found in practice, especially in multi-level assembly systems. This paper reveals several simple and unique properties for acyclic supply chains that allow complexity reduction. Specifically, we show that under certain conditions, an acyclic supply chain can be decomposed to a tree network which performs at least as well as the original system. We discuss the conditions on demand processes, inventory policies and lead-times under which the decomposition can be achieved.



Simchi-Levi, D., Y. Zhao (2012). Three Generic Methods for Evaluating Stochastic Multi-Echelon Inventory SystemsAdvances in Operations Research, Volume 2012: 1-34.

Abstract: One of the most important advances of supply chain management in recent years is the development of models and methodologies for controlling inventory in general supply networks under uncertainty. These developments are based on three generic methods: the queueing-inventory method, the lead-time demand method and the flow-unit method.

This paper compares and contrasts these methods along the following dimensions: network topology, inventory policy and demand process. In particular, it shows how to apply these methods systematically to characterize and evaluate various network topologies with either i.i.d. or sequential transit times, either unit or batch ordering policy and either unit or batch demand process. The network topology includes serial, distribution, assembly and two-level general networks, tree and more general networks. The paper surveys the literature of multi-echelon inventory systems together with recent developments by building connections among different methods and developing unified methodologies. The paper also sheds some lights on the strengths and limitations of each method.