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
My research in this area
focuses on exact analysis and evaluation of inventory replenishment
policies, and design of efficient approximations and optimization
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 Demand. Operations
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: 605–613.
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 Systems. Advances 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.
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.