Research shows why slight increase in flexibility of manufacturing plants optimizes efficiency and cost

December 2012


Ensuring that goods are always on hand requires that corporations build flexibility into their manufacturing operations so they can respond to changes in supply and demand as they arise. Full flexibility is achieved when every manufacturing facility of a company has the capacity to produce every product. But costs can quickly skyrocket with the full flexibility model because a company needs to invest in tools and processes to ensure that every plant is capable of producing all products.

In a seminal paper published in Management Science in 1995, William Jordan of General Motors and Stephen Graves of the MIT Sloan School introduced the concept of chaining, defined as a group of products and plants connected directly or indirectly by product assignment. They show empirically that a small investment in flexibility designed appropriately can achieve almost all the benefits of full flexibility. More specifically, their numerical experiments show that a chaining strategy called the “long chain” — in which plants are endowed with the capacity to produce exactly two different products and every product is produced by exactly two plants — is nearly as efficient as full flexibility, but costs far less. Since then, numerous research papers have demonstrated through numerical experiments that the long chain design can be applied to other systems, including the cross-training of workers on an assembly line, supply chains, queuing networks, and people and tasks in a call center. But until now, nobody has explained or proven why the long chain works better than other flexibility models.


The long chain is so named because on paper, it connects a list of manufacturing facilities with a list of products by arcs to create a chain. Facility A can produce Product 1 as well as Product 2. Facility B can produce Product 2 and Product 3, and so on with the final facility in the chain able to produce both the last and first products [see figure]. The addition of this final arc from the last facility to first product is called closing the chain. Interestingly, researchers observed that closing the chain is critical to the effectiveness of this design. In order to characterize mathematically that effectiveness, MIT Professor David Simchi-Levi and doctoral student Yehua Wei applied a combination of optimization and stochastic methodologies. This approach allowed them to explain the power of the long chain for any system, determine precisely the numerical difference between the performance of the long chain and that of the full flexibility design, and provide new insights and guidelines that companies can use when designing flexible strategies.


First, using optimization, Simchi-Levi and Wei found that the flexible arcs in the long chain are supermodular — the incremental benefits increase as more arcs are added, but adding the last arc from the final plant to the first product provides the greatest impact. This explains why closing the chain is essential to maximizing performance. Then, to gain more insight into exactly how the long chain’s performance compares with that of full flexibility, they developed a method to compute the performance of long chains by combining optimization with stochastic methodologies. They showed that the performance of the long chain can be characterized as the difference between the performance of two open chains, and it turns out that it is easier to analyze open chains than closed chains. This led to three important results: the long chain is optimal among all sparse flexibility designs; a precise characterization of the gap between the performance of the long chain and that of full flexibility; and new design guidelines.


Now that the mathematical basis for the long chain design has been defined, Simchi-Levi and Wei can help companies compare flexibility options and better respond to disruptions in the supply chain, be they in supply, demand, energy prices, currency exchanges or other influences. At present, they are applying their findings to an auto manufacturer’s operations.


A paper by David Simchi-Levi and Yehua Wei appears in the September/October issue of Operations Research. The concept is also discussed in Simchi-Levi’s Operations Rules: Delivering Customer Value Through Flexible Operations (MIT Press, 2010).

This figure illustrates the pairing of products and plants using long chain and full-flexibility designs.

This figure illustrates the pairing of products and plants using long chain and full-flexibility designs. Figure / David Simchi-Levi

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