Important Service Part Multi Echelon Inventory Optimization Books


It is very interesting to find out about the origins of service parts inventory optimization. It’s rarely discussed, though I thought I would write and article on this topic.

Guest Co-Author

For this post we have a guest co-author. Wayne Fu, a Senior Product Manager at Servigistics provides a perspective on what he considers some of the pioneering works in multi-echelon inventory optimization.


Mult-Echelon Inventory Optimization is interesting but relatively more challenging arena than other popular optimization practice like production scheduling. This is due the fact that the performance measurements in inventory management (fill rate, back order, availability etc…) are largely non-linear. Thus some common methods like linear programming are not easily applied to the problem. And because it is a solution that requires a holistic “hovering-view,” the problem cannot be segregated in smaller scope very easily. This fact places challenges on performance and scalability. These issues are even more severe in the service part environment due to larger volume.

One of the major publish in Service Part Inventory Optimization is the “Optimal Inventory Modeling of System” by Craig C. Sherbrooke. Sherbrooke laid out both the METRIC and Vari-METRIC algorithms in this book. They are generally recognized as the foundation of many heuristic based optimization algorithms today. (for more on “heuristic based algorithms” see this post below.)

METRIC is specifically designed to address the multi-echelon issue while Vari-METRIC is an enhanced version of METRIC to resolve multi-indenture problem.

METRIC and Marginal Analysis

In simplified terms, METRIC is an algorithm based on marginal analysis. This approach still recognized as the most accurate and effective approach, but is very computationally intensive. Several issues merged in practice of METRIC also. Sherbrooke generally assumed the inventory policy to be (S,s-1) and operated under relatively low demand environment. And it is dominated by fill rate (no stock out) measurement. Thus, the application of METRIC is limited to specific industries that fit this model, most notably aerospace and defense. Vari-METRIC, on the other hand, placed more emphasis on availability. Fill rate applies to any supply planning environment, whereas, availability is primarily used in service operations. A service level agreement (SLA) will guarantee an availability of unit such as a plane or piece of industrial equipment. Availability is then used to model this the uptime of this equipment, which is dependent upon the fill rates of a variety of service parts that support that unit, all of which have different failure rates, part costs, etc.. (to read about SLAs, see this post)

METRIC measures the fill rate and other measures at the intermediate location, which ended up being a highly debated aspect of METRIC.











At What Locations to Measure Service Level?

In fact, where to measure service level is an extremely important topic in and differentiation between inventory optimization products. Currently, the vast majority of supply planning organizations measure service level at their internal locations in addition to measuring it at the customer location.











As we will see in the following section, another researcher who followed Sherbrook’s work changed this location service level measurement assumption.

Measuring at the Intermediate Location

The second most influential publication in service parts inventory optimization“Analysis and Algorithms for Service Parts Supply Chain” by John A. Muckstadt. Dr. Muckstadt’s model could be said as an updated version of Sherbrooke’s. It is an availability based algorithm and avoids the need of approximations required in METRIC due to convexity problem. Muckstadt also proposed some novel approaches to reduce the performance and scalability issues during implementation. Perhaps most importantly, Muckstadt moved always from measuring the satisfaction at intermediate level location, measuring the customer facing demand only. However, Muckstadt is still based on the (S,s-1) order policy and assumed in low demand environment. This means that Muckstadt’s model faces some of the similar challenges as do Sherbrooke’s in broader application. (for a description of the (S,s-1) order policy, see the link below:


The previous paragraphs were an overview of two of the most important publications in service part inventory optimization and distinct from finished goods inventory optimization. Sherbrooke’s and Muckstadt’s algorithms are used in service parts planning products to this day, with alterations here and there.

Author Thanks

I wanted to thank Wayne Fu for his contribution. I was not aware of many of the details which are described above, and I think this should be of interest to anyone who practices in this field.

Author Profile




Wayne Fu is a Senior Product Management in Servigistics.With operation management background, Wayne has worked in service part planning domain for more than a decade. In Servigistics, he led the research and development of various areas like install-base (provisioning) forecasting, inventory optimization and distribution planning. Currently, he is focusing on the effectiveness of forecast techniques in Last Time Buy.







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