Assemble-to-Order Systems, Allocation Rules and Component Commonality

Yao Zhao, PhD

Professor in

Supply Chain Management

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Assemble-to-Order (ATO) system is an important operational strategy for manufacturing firms to achieve both fast response to demand and low finished good inventory. This strategy applies not only to manufacturers who provide customized products (e.g., Dell, IBM), but also applies to mail-order and online retailers (e.g.,

My research in this area focuses on efficient inventory replenishment policy, common component allocation rules and design of material flow topologies (e.g., component commonality).


Zhao, Y., D. Simchi-Levi (2006). Performance Analysis and Evaluation of Assemble-to-Order Systems with Stochastic Sequential Lead-timesOperations Research 54: 706-724.

Abstract: Assemble-to-Order Systems represent important supply chain strategies that allow manufacturers to better match supply and demand. In such a system, manufacturers keep inventory of components and assemble finished goods only after demand is realized. A long standing challenge in the inventory control literature is the exact analysis of even simple assembly systems with random demand and stochastic sequential lead-times. Real world Assemble-to-Order systems, such as the one used by Dell Computers, pose even more substantial challenges both analytically and computationally because they involve both assembly and distribution systems. In this paper, we developed a unified modeling approach, namely, the backward flow-unit method, that facilitates exact analysis and efficient evaluation of various Assemble-to-Order systems with stochastic sequential lead-times, with multiple products and when component inventories are controlled by either base-stock or batch ordering policies.

Song, J.S., Y. Zhao (2008). The Value of Component Commonality in A Dynamic Inventory System with Lead TimeManufacturing & Service Operations Management 11: 493-508.

Abstract: Component commonality has been widely recognized as a key factor in achieving product variety at low cost. Yet, the theory on the value of component commonality is rather limited in the inventory literature. The existing results were built primarily on single-period models or periodic-review models with zero lead times. In this paper, we consider a continuous-review system with positive lead times. We find that while component commonality is in general beneficial, its value depends strongly on component costs, lead times and dynamic allocation rules. Under certain conditions, several previous findings based on static models do not hold here. In particular, component commonality does not always generate inventory benefits under certain commonly used allocation rules. We provide insight on when component commonality generates inventory benefits and when it may not. We further establish some asymptotic properties that connect component lead times and costs to the impact of component commonality. Through numerical studies, we demonstrate the value of commonality and its sensitivity to various system parameters in between the asymptotic limits. In addition, we show how to evaluate the system under a new allocation rule, a modified version of the standard FIFO rule.

Lu, Y., J.S. Song, Y. Zhao (2009). Non-holdback Allocation Rules in Assemble-to-Order SystemsOperations Research 58: 691-705.

Abstract: This paper analyzes a class of common-component allocation rules, termed no-holdback (NHB) rules, in continuous-review assemble-to-order (ATO) systems. We assume that component inventories are replenished following base-stock policies, subject to positive lead times. Different from the usually assumed FCFS component allocation rule, a NHB rule will not allocate a component to a product demand unless doing so will lead to immediate fulfillment of that demand. We identify metrics as well as cost and product structures under which NHB rules outperform all other component allocation rules. For systems with certain product structures, we obtain closed-form key performance expressions for NHB rules and compare them with those under FCFS. For general product structures, we present performance bounds and approximations. Finally, we discuss the applicability of these results to more general ATO systems.



Zhao, Y. (2009). Performance Analysis of Assemble-to-Order Systems with Compound Poisson Demand and Batch Ordering PoliciesEuropean Journal of Operational Research 198: 800-809.

Abstract: This paper extends Zhao and Simchi-Levi (2006) to a class of multi-product and multi-component Assemble-to-Order (ATO) system with compound Poisson demand and continuous-time batch ordering policies. The replenishment lead-times of components are stochastic, sequential and exogenous. We derive exact expressions for key performance metrics under either the assumption that each demand must be satisfied in full (non-split orders), or the assumption that each unit of demand can be satisfied separately (split orders). We also develop an efficient sampling method to estimate these metrics, e.g., the expected delivery lead-times and the order-based fill rates. Based on the analysis and a numerical study of an example motivated by a real-world application, we characterize the impact of the component interaction on system performance, demonstrate the efficiency of the numerical method and quantify the impact of order splitting.