Is circular vs. linear the right framework?

Let’s start with an observation from the 2021 State of Supply Chain Sustainability.1 According to the 2,400 people who responded to the survey — the vast majority of which work in a supply chain role — end-of-life management and supply chain circularity were less of a focus than the prior year for both goals and investments (see Figure 1). One notable exception to this is the healthcare industry. (I would encourage you to explore the data for yourself and see where your industry stacks up.)

This observation raises several interesting questions. First, I would love to better understand why companies are less focused on supply chain circularity. I suspect that the pandemic and other events of 2020 put their focus on other areas of sustainability such as employee welfare and safety or supplier diversity, equity and inclusion (DEI). However, I don't have data I can point to for that analysis today.

The question I want to address builds on the definition of end-of-life management and supply chain circularity. It could be argued that these terms do not capture the essence of circular supply chains or the broader concept of a circular economy. 

Staying within the context of the survey for the moment, it does make sense to narrow the concept of circular supply chains to end-of-life management and supply chain circularity. One challenge when constructing a survey like this is using terms that allow measurement specificity with complex concepts that overlap. A broader definition of circular supply chains would overlap many if not most of the topics in that figure, thus reducing the specificity of the analysis. This balance has to be weighed with most of those measures. Using more granular terms would reduce overlap and increase the survey's length and complexity, which reduces response.

Now, let's take a step back and consider the broader concept of a circular supply chain. When does it make sense to talk about a circular supply chain rather than more narrow strategies like end-of-life management? This question is about ontology and methodology. (To be clear, I don't mean the methodology of the survey referenced above but the methodology of supply chain theory and strategy.) Unpacking this question lies at the heart of my approach to this project, and it's why I wanted to restart post-hiatus with this topic.

A circular economy — and the circular supply chains in it — is defined in contrast to the linear economy and linear supply chains. My first introduction to these concepts came from Cradle to Cradle by William McDonough and Michael Braungart almost two decades ago.2 The field has advanced tremendously since then, with the Ellen MacArthur Foundation3 helping lead the charge.

The basic concept of a circular economy is simple. The way material things are brought to market (supply chains) flows in two ways — at least definitionally. The supply chains in a linear economy flow is a straight line — hence "linear" — from raw material extraction to a landfill when a product reaches the end of its life. This is often called "take-make-waste" (see Figure 24).

In contrast, supply chains in a circular economy use what a linear economy considers "waste" as inputs to upstream processes. If we freeze the frame of reference, the return of materials and/or products to the supply chain creates loops and a reverse flow — the geometric terms go a long way in illustrating the difference between the linear and circular models. Many processes can close these loops, including reusing, repairing, remanufacturing, recycling, etc. Figure 35 illustrates these loops.

This framework — linear-vs-circular supply chains — is a simple ontology for complex supply chains. Additionally, the assumptions this framework makes can be evaluated based on their network topology.6 A simple linear supply chain is equivalent to serial systems where each echelon (node) has a single predecessor and single successor. Visualizing a serial system (a in Figure 4) looks identical to the linear supply chain above.

Serial systems (a) are important from a theoretical perspective because there are robust techniques to solve problems using stochastic-service and guaranteed-service models. The limitation with serial systems — and the linear supply chain concept more generally — is that it often doesn't resemble supply chains. For example, in a serial system for distribution there is only a single facility at each step. Products flow from a supplier to a single distribution center, then to a single retail location, and finally to a customer. If we want to model multiple suppliers, facilities, and/or customers, we have to aggregate the characteristics for each into a single node (e.g., average customer demand) or use more complex network topologies.

Assembly systems (b) describe a typical bill-of-material structure for product supply chains allowing multiple sources for materials and assembly upstream. These are then consolidated as they move downstream toward the final product. From a theoretical perspective, assembly systems are useful because they can be transformed into an equivalent serial system and take advantage of serial solution methods. Distribution (c), tree (d), and general (e) systems are more complex but they resemble many supply chains. And there are techniques such as integer and dynamic programming to solve some guaranteed-device models. Often, especially for complex general systems, there are no solutions.

This is also where we can start to explore the models for circular supply chains. Circular supply chains are based around loops where products and materials flow back upstream to serve as inputs. There are no reverse flows or loops for assembly, distribution, and tree systems (hybrids of assembly and distribution). In graph theory, we call these cycles. Cycles can be directed — meaning the arrows in the graph flow one way — or undirected — where we remove arrows, and flows can go both ways. General systems allow cycles, so we use this form of network topology to model circular supply chains. One crucial assumption we make here is that products and/or materials flow back within the boundaries of the supply chain. For example, we recycle aluminum cans which feedback into the production of new aluminum cans.

It's also possible for those flows to occur outside of the boundaries that we define for our supply chain. For example, recycled aluminum can be used in the production of other aluminum products. In this case, we can use a more tractable tree system because the aluminum flows outside of the system. So if we want to include the loop in our system, we have to expand the boundaries — and complexity — of our system.

This is where our linear-vs-circular framework starts to break down. Both serial and general (with cycles) systems are powerful analytical tools. However, with general systems there are many cases where we will not be able to evaluate solutions and have to simplify the system to something resembling a linear supply chain. That may or may not be ok. It depends on what you're trying to do, and it doesn't address the question I am trying to answer: When does it make sense to talk about a circular supply chain?

The answer to this question sneaks in when we consider the boundaries of our supply chain. As discussed above, the loops that are introduced for a circular supply chain can be within the boundary — and we'll have our work cut out for us if we want to solve optimization problems — or not. If the loop is not within the boundary, then it's not really a loop. Instead, we treat that node or flow as a boundary. For example, we may be using recycled aluminum as the input for our aluminum can production, but if that recycling loop is outside of the boundary of our system, that material input is no different topologically than virgin material.

This result may seem obvious, and this whole discussion of network topologies unnecessary. However, what is not as obvious is when we define those boundaries. That is when our linear-vs-circular framework breaks down. And it has significant implications for our ability to develop solutions to circular supply chain problems. Those solutions will be inherently linear. We may be using better materials, but we're not actually talking about a circular supply chain — it's linear.

The alternative is to expand the scope of our model to include the loop. If we do so, developing solutions will be much harder, but at least we're capturing the circular flow and the network connections needed to create new loops. This is why many practitioners in the space advocate for thinking about small loops. It reduces topological complexity, and the problems are more tractable. 

So if we consider the original question — when does it make sense to talk about a circular supply chain — we approach an answer when we define the boundaries of the supply chain. If we are building a new supply chain, we have the opportunity to define those boundaries with the loops and stay grounded in supply chain theory. This will allow us to compare potential circular solutions to linear ones. And the network structure provides measures (centrality, flow betweenness, reciprocity, and others) to assess the viability of the supply chain we are building.

With an existing supply chain, there is an existing network to consider. If we want to explore circular solutions, we can either close loops within the system or redefine the boundaries. Again, this allows us to compare networks with loops to those without — circular vs. linear.

The consistent theme across all of this is that the linear-vs-circular characteristics of a supply chain are its network structure — whether it has loops or not. This allows us to generalize our original question. Rather than just asking when the linear-vs-circular framework makes sense, we can ask if it makes sense to talk about circular supply chains.

Both linear and circular supply chains are networks — "supply chain" is a misnomer in many cases. From an ontological perspective, however, there is a critical difference between linear and circular supply chains. Supply chain networks are genuinely linear, but circular supply chains are not exactly circular. Even if we take the circular strategy to the extreme — closing every loop imaginable in the network — the second law of thermodynamics ensures there will always be some linearity. This means there are not really linear or circular supply chains. There are just supply chains — or perhaps more precisely supply chain networks — with different degrees of circularity. 

This also means we are not transitioning from linear to circular supply chains — or maybe even from a linear to a circular economy. We are transitioning to more sustainable supply chains — and thus a more sustainable economy — by identifying opportunities to add circularity in our supply chains. 

If our goal is to be more sustainable — or perhaps regenerative if we're ambitious — then the right framework might not be linear versus circular. Maybe we should finally embrace the networked nature of supply chains and start measuring circularity. There's even a convenient formula7 for that:

Have thoughts or feedback? Did I miss anything? Email me at You also can reach me on LinkedIn and Twitter.

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Lawrence V. Snyder, Zuo-Jun Max Shen (2011). Fundamentals of Supply Chain Theory. Hoboken, NJ: Wiley.