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ArticlePublished in partnership with RMIT University

https://doi.org/10.1038/s42949-024-00153-0

Spatial optimization of circulartimber hubs
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Tanya Tsui1

, Titus Venverloo

2, Tom Benson

2& Fábio Duarte

2

In the European Union, construction is responsible for 36% of CO2 emissions and 40% energy
consumption. The reuse of construction materials has been receiving increasing attention, including
regulations established by the European Union, and cities establishing goals to reuse construction
materials. This is the case for Amsterdam, which established the goal of reusing 50% of construction
materials in new construction by 2030. Part of the challenge of reuse of construction materials in urban
areas is to optimize the waste-to-resource loops: ﬁnding the optimal scale and location for circularconstruction hubs—facilities that collect, store, and redistribute construction waste as secondary
construction materials. In this paper, we use the supply and demand of timber construction materials
in Amsterdam as a case study to ﬁnd the optimal scale and location for construction hubs. We used thespatial simulated annealing algorithm as an optimization method for balancing the trade-off between
small and large-scale hubs, using cost-effectiveness to compare potential locations and identify the
optimal solution. We found that the optimal number of hubs for our study area is 29, with an average
service radius of 3 km. This study has implications for policymakers, urban planners, and companies
seeking to implement circular economy principles.

Cities consume 60–80% of natural resources globally, produce around 50%of global waste and 75% of greenhouse gas emissions1. The situation mightworsen, with the urban population expected to reach 6.5 billion by 2050, theequivalent of two-thirds of the future global population2. Reducing emissions and increasing resource efﬁciency is a major challenge for cities, andtransitioning to a circular economy (CE) has been proposed by policymakers as a potential solution3. While there is no common deﬁnition for CE,
it is generally understood as a closed-loop system that employs circular
processes such as reuse, refurbishing, remanufacturing, and recycling toconvert waste into secondary resources, to keep materials and products attheir highest level of use for as long as possible4.
Since 2016, The Netherlands has aimed to achieve a fully circular
economy by 20505. In response to this goal, a number of Dutch municipalities and provinces have produced “circular city”6–9 and “circularregion”10,11 strategic documents detailing how CE could be implemented at the city or regional level. However, these documents often
focus on an urban governance perspective, discussing policy analysis
and stakeholder management; rather than an urban planning perspective, understanding the spatial requirements and restrictions for a
CE. In fact, when discussing the circular transition, the Dutch National
Strategy on Spatial Planning and the Environment (Nationale

Omgevingsvisie - NOVI) states that, “the consequences of this (circular
economy) transition on transport ﬂows, use of space, the environmentand security remain uncertain”12.
Dutch construction and demolition companies have responded to CE
policy goals by starting circular construction hubs: facilities that collect,
store, process, and redistribute construction waste to be reused as secondary
construction materials13,14. A previous study on circular construction hubs
in the Netherlands found that hubs vary in terms of their spatial scale ofoperations (regional versus local), and tend to deal with speciﬁc material
types, such as wood, bulk materials, or building components13. However,locations and scales of hubs are arbitrarily chosen by individual companies,
without a broader overview of the spatial impact of hubs on their surrounding region as a whole.
In recent years, researchers in industrial ecology, economic geography,
and urban planning have highlighted the signiﬁcance of spatial factors, suchas proximity to industrial clusters and accessibility to secondary resources,
as a key element in the study of circular cities, as these elements play animportant role in the success of a CE15–18. Within this literature, a recurringquestion is the spatial scale of waste-to-resource ﬂows, and whether resource
loops should be closed at the local or global scale. This issue has been mostly
explored by the ﬁelds of industrial symbiosis and waste management, where1

Department of Architectural Engineering and Technology, Delft University of Technology, Delft, the Netherlands. 2Department of Urban Studies and Planning,e-mail: tanya.tsui@ams-institute.org
Massachusetts Institute of Technology, Cambridge, MA, USA.

npj Urban Sustainability | (2024)4:13

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https://doi.org/10.1038/s42949-024-00153-0

researchers have debated the beneﬁts and trade-offs of organizing resource
ﬂows at the local, regional, national, or global scale.
Some studies have shown that material loops can be closed at the local
scale, with resource exchange distances of around 2–5 km. Cases can befound in industrial symbiosis literature, where companies located in thesame industrial park19,20 or even the same facility21 exchange resources suchas electricity, heat, and organic waste. These ﬁndings are prominent inearlier industrial ecology literature, strengthened by the empirical ﬁndingson the Kalundborg Eco-industrial Park in Denmark - a seminal case study ofindustrial symbiosis19.
Other studies have shown the validity of closing material loops at theregional scale, with resource exchange distances of 30–50 km. An analysis oflocation data for industrial symbiosis partnerships in the United Kingdom
found that the average distance between industrial symbiosis partners was
32.6 km22,23. Additionally, a study in Germany’s Rhine-Neckar region
concluded that the regional scale is large enough to provide a diverse enoughgroup of industries and enough waste volumes that could allow for resilientand stable industrial symbiosis24. A spatial optimization study of concrete
recycling plants in the Netherlands also resulted in facilities operating at theregional scale25.
Finally, studies have also argued for closing material loops at the global
scale. The spatial scale of ﬂows in the waste industry was largely determinedby economic concerns - imbalances in supply and demand, transportation
cost - which often lead to the decision to close loops globally26. In a study onAustralia’s metal industry27, researchers found that it was impossible to havea CE for metals in one country alone, as no country has the capacity toprovide the full cycle of processes, including extraction, production, use,
disposal, and recovery. A spatial optimization of the German food industry
found that growing the majority of food in Brazil and transporting it back toGermany led to lower emissions than growing locally28, disputing thecommon assumption that the local scale leads to both environmental
beneﬁts.
As seen within existing literature, quantitative factors for determining the spatial scale of closing material loops include the value andweight of the material; and ﬁnancial concerns of the operation, such astransportation costs or proﬁt margins. Qualitative factors may include
market maturity for CE, existing regulations, and well as knowledge andskills of the construction industry. From waste management literature,spatial scales seem to be determined by ﬁnancial or logistical reasons.
For example, the threshold for a recycling ﬁrm is the minimum volume
of waste generated in an area at which a ﬁrm can proﬁtably aggregate,
process, and ship to a customer29. This means the location should be in
an area with a high enough density of waste producers (municipal,
commercial, industrial) to generate enough waste within an area thatcan be covered by their transportation costs.
From industrial symbiosis literature, more emphasis is placed on thefeasibility of material reuse as a factor affecting the scale of closing material
loops19,23,24. Materials that are difﬁcult to reuse as a resource tend to travel
longer distances, as it is more difﬁcult to ﬁnd a match between supply anddemand close by. With increasing costs of land-ﬁlling, companies are also
more willing to invest in long-distance travel for industrial symbiosis to
avoid disposal costs.
We use the reuse of timber construction materials in the Amsterdam
Metropolitan Area (MRA, Metropoolregio Amsterdam in Dutch) as a casestudy in ﬁnding the optimal scale of closing resource loops. The MRA has anarea of more than 2500 square kilometers, consists of 30 municipalities, witha population of 2.5 million inhabitants. We chose the MRA as our casebecause of the region’s combined policy goals in circular and timber construction. In 2021, the municipalities within the region signed a green deal
on timber construction, aiming for 20% of new construction in the city to bemade of timber by 2025, which corresponds to approximately 3000 timber
constructed homes per year30. As of 2021, 7400 timber-framed homes were
either being built or had won a tender. Additionally, the municipality of
Amsterdam has set ambitious goals for transitioning to a CE since 201631,
aiming to use 50% less raw materials by 20306. As of 2021, the extent of raw
npj Urban Sustainability | (2024)4:13

Articlematerial use in the Netherlands has hardly changed since 2010, althoughmaterial efﬁciency has increased32.
The goal to increase timber construction in the MRA is driven byenvironmental beneﬁts associated with building with timber. Timber is arenewable resource if forests are harvested responsibly. CO2 is sequesteredin trees as they grow, and when timber is used in construction, the carbon
remains stored in the timber, effectively removing it from the atmosphere
during the life of the building, or longer if the timber is reused. Timber also iswell suited for reuse in circular construction, as it is light and easy tomanipulate, making it well suited for dry, detachable connections33.
There are currently a small number of construction hubs in the region
storing and exchanging timber. These hubs are currently operated by socialorganizations at a local scale, usually collecting materials from within
5–10 km13,14. As MRA’s policy goals increase the demand for circular timberin the future, hubs will need to scale up accordingly as well. However, it isunclear how these hubs will scale up - will there be a small number of largescale hubs operating at a regional scale, or a large number of small-scale hubs
collectively covering the region, each operating at a local scale? Existing
surveys of circular hubs have found that their spatial scale is determined bysimilar factors identiﬁed in waste management and industrial symbiosis
literature, such as transportation, storage, and processing costs13,14, but theseﬁndings have not yet been veriﬁed using statistical methods.
While there is ample literature discussing the spatial scales of closing
material loops, none have applied this knowledge to circular construction
hubs. Moreover, most studies on spatial scale have surveyed existing companies and made conclusions based on the existing status quo, rather thanimagining a future where CE is the norm. Consequently, very few studies
have used spatial optimization to determine the optimal scale of material
loops25,28. Finally, existing spatial optimization studies have neglected two
important factors: land prices, and supply and demand matching. High land
prices in central areas could increase storage costs, potentially pushing hubs
to the periphery. If future demand for construction waste greatly exceeds
supply, less space would be required to store materials before they are
redistributed.
Since circular hubs are a relatively new phenomenon, the current
understanding on suitable locations and scales is limited. Hub locations are
currently chosen arbitrarily by individual companies, without a holistic
understanding of their impact on the region as a whole. Without this topdown perspective, there is the risk of the region establishing the wrong
number of hubs, or setting up hubs at the wrong scale, resulting in inefﬁciencies in terms of transportation emissions, material exchanges oroperational costs.
The aim of this study is therefore to use spatial optimization methods toﬁnd the optimal scale and locations of circular timber hubs in the MRA. We
aim to ﬁnd a solution that balances the trade-offs between large and smallscale resource exchanges mentioned in existing literature - minimizing
transportation distances with small-scale exchanges on one hand, while
maximizing supply and demand matching with large-scale exchanges on
the other23,24. We aim to add to existing literature on circular construction
hubs by taking into account CO2 reduction of timber reuse, land price, as
well as supply and demand matching in the optimization model.
Spatial simulated annealing was used as an optimization algorithm todetermine the optimal number and locations of circular timber hubs in the
MRA for the study period of 2022–2026. Cost-effectiveness, measured ineuros per tCO2eq reduction, was used in our algorithm to select the optimal
solution. Costs (in euros) consisted of transportation and storage costs,
while total emissions reductions (in tCO2eq) took into account transportation emissions and emissions reductions from timber reuse. The candidate
hub locations were industrial sites in the study area with an environmental
zoning category34 of 2–3: industrial sites 30–100 km from quiet residential
areas, and 0–50 km from mixed areas35. The locations of future supply anddemand for secondary timber were taken from a scenario study of material
stocks and ﬂows of construction materials in the Netherlands36. The study
uses locations of future demolition and construction sites to predict where
and how much secondary construction materials will be supplied and2Articlehttps://doi.org/10.1038/s42949-024-00153-0

demanded from 2022 to 2050. A detailed description of the optimization
algorithm, cost-effectiveness calculations, and data is supplied in the
Methods section at the end of this paper.

Results
Using the spatial simulated annealing optimization, the cost per
tCO2eq reduction was calculated for a range of possible number of hubs
in the MRA, from 1 to 135—which is the total number of industrial sites
in the area. This resulted in a cost per tCO2eq reduction curve, where
the x-axis represents the number of hubs, and the y-axis represents thecost per tCO2eq reduction (Fig. 1). We found that placing 29 hubs inthe study area resulted in the lowest cumulative cost per tCO2eq
reduction, although the value remains consistently low for 20 to 40
hubs, at around 45–46 euros / tCO2eq reduction. When compared to
sub-optimal hub numbers, the optimal number of hubs (29) allows fora total cost reduction of 21.3 million euros and a total CO2eq reductionof 499 kilo tons, which is 94.6% of the maximum tCO2eq reduction
possible for the MRA.
The service radii of circular timber hubs ranged from around 1 km to
23 km, with an optimal average service radius of 3 km, at 29 hubs (Fig. 2).
Service areas for each hub vary – areas with higher material density (e.g. in
Amsterdam city center) tend to have hubs with smaller service areas. This
could be because areas of higher material density are often urban centers,

and tend to have higher rental prices, making it more cost-efﬁcient toconstruct smaller hubs as a strategy to reduce storage costs.
Our model resulted in optimal hub locations for 135 scenarios, with thenumber of hubs ranging from 1–135. We overlapped all 135 scenarios andcounted, for each industrial site, how many times it was chosen by the
optimization algorithm as an optimal location, and found that someindustrial sites were more frequently chosen than others (Fig. 3). These
locations can therefore be considered as potential key future locations forcircular timber hubs. Since construction hubs are currently built by individual companies or communities without any top-down coordination, it
may be difﬁcult for the Dutch government to control the exact number oftimber hubs built. If this were the case, focusing on these key future locations
may be even more important for policy decisions than the exact ‘optimal’
number and locations of hubs. There were also industrial sites that were
never selected for any of the hub numbers (gray dots in Fig. 3). These
locations are therefore less important for the creation of circular timberhubs, and could be prioritized for other functions.

Discussion
The cost per tCO2eq reduction curve shows that the cost rapidly decreases as
the number of hubs goes from 2–20, remains relatively constant from 20–40
hubs, then increases steadily from 40 hubs onwards (Fig. 1). When thenumber of hubs is lower (nHubs = 2–20), cost / tCO2eq reduction decreases

Fig. 1 | Summary of results. Line charts showing changes in A cost per tCO2 reduction, B total costs, and C total emissions reductions as number of hubs increases. For chart
C, the line for “total emissions reduction” (in blue) is hidden behind the line for “CO2 reduction” (in red), because the two values are very similar.

npj Urban Sustainability | (2024)4:13

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https://doi.org/10.1038/s42949-024-00153-0

ArticleFig. 2 | Optimal locations and service areas for 1, 29, and 135 hubs. Black crosses = hub locations, black dotted lines = service areas, blue dots = timber supply, pink dots =timber demand, gray lines = road network.

Fig. 3 | Popularity of candidate hub locations. Circle size represents the number of times the location has been chosen as an optimal location. Red dots are locations thatwere chosen at least once, gray dots are locations that were never chosen.

when more hubs are added. This is because, at these hub numbers, adding
more hubs decreases the transportation cost rapidly. When the number ofhubs is roughly between 20–40, cost/tCO2eq remains roughly constantbecause all the components (transportation cost and emissions, storage cost,and CO2eq reductions) remain roughly the same when more hubs areadded. When the number of hubs goes above ~40, cost/tCO2eq increases
steadily mainly due to storage costs. As more hubs are added to the city,some hubs start to become redundant—they are barely storing any materials(or not storing any materials at all), but still using up space, resulting in
unnecessary high rent and building costs (Fig. 4).
Each of the four components of the cost/tCO2eq calculation has adifferent effect on the ﬁnal cost curve. Transportation costs affect the curve
at nHubs = 2–20 — it accounts for the rapid decrease in price when morehubs are added. The transportation cost seems to decrease exponentially as
npj Urban Sustainability | (2024)4:13

the number of hubs increases. For lower hub numbers, adding an extra hub
decreases the transportation cost signiﬁcantly, whereas at higher hub
numbers, adding an extra hub only has a minor impact.
Storage costs affect the curve starting nHubs = 40. Here, redundanthubs start to appear when more hubs are added, which increase rent andbuilding costs unnecessarily. The increase in storage costs from adding
redundant hubs follows a linear trend.
CO2eq emission reductions do not have a large effect on the curve –adding more hubs does not make a signiﬁcant difference in reducing CO2eq
emissions. While there is a slight decrease in CO2eq reductions as thenumber of hubs increase, the change is not as large as the changes intransportation and storage costs. This is because the future demand oftimber far exceeds the future supply in the MRA – within the study period of2022 to 2027, the total future timber demand is around 710,000 tons, while4Articlehttps://doi.org/10.1038/s42949-024-00153-0

Fig. 4 | Redundant hubs for solutions with 30, 80, and 125 hubs. Black crosses = functioning hubs, red crosses = redundant hubs.

the future timber supply is only around 350,000 tons. This excess demand
guarantees that most of the secondary timber is reused regardless of hub size.
Finally, transportation emissions do not have an effect on the curve, because
the values are much lower than CO2eq reduction from timber reuse.
The results in this section indicate a number of recommendations forplanning circular timber hubs in the MRA. As mentioned in the introduction section, circular hubs currently processing timber are usuallyoperated by communities at the local scale. However, when demand forcircular timber increases in the future, timber hubs will need to scale up
accordingly as well. According to our results, the average service radius ofcircular timber hubs should be around 3 km, which is similar to the service
area of existing timber hubs. We, therefore, recommend the MRA toincrease the total number of hubs but keep each of the hubs operating at the
local scale. This would be an alternative to increasing the scale of the existing
hubs, resulting in a few large-scale hubs covering the entire region.
Policies encouraging the establishment of circular hubs should ensurethat there are no more than 40 timber hubs established in the MRA at one
time, as more hubs lead to redundancy. This is especially important given
the scarcity of land in the MRA - policy needs to balance spatial needs forcircularity with other priorities, such as housing, health, energy, or
biodiversity37.
The optimal number of hubs were constrained by transportation andstorage costs, rather than emissions associated with transportation andmaterial reuse. This suggests that, for the MRA, the argument for optimizing
circular timber hubs is not reducing emissions, but rather reducing costs.
The amount of emissions reductions in the region would have been similar
regardless of the number of hubs, but the optimal number of hubs we
identiﬁed (29) would be the cheapest solution.
The constraints of costs versus emissions would look different for other
cities, due to different density, morphology, and building types. For
example, other cities with less land scarcity would have lower land prices,
resulting in a smaller effect of storage costs on the optimization curve. The
constraints could also look different for other materials, as they have different cost and emissions calculations. For example, optimizing concrete
recycling plants would take into account emissions from recyclingmachinery25. Finally, expanding the study to a larger area (the whole country
for example) could also lead to a different optimal hub scale. In this case,hubs may beneﬁt from settling in the periphery of urban areas, where land ischeap but materials are still close by.
This study has a number of limitations and shows the difﬁculty ofmaking spatial planning decisions solely based on a mathematical model.
Like all urban areas, the MRA is a complex system, containing dynamics thatcannot be fully captured in one study. These dynamics may include futurechanges in infrastructure and land use, emerging waste processing technologies, and changing public opinions, stakeholder interests, or environmental laws. The results of this study should therefore not directly lead topolicy decisions but rather be seen as insights informing policymakers.
npj Urban Sustainability | (2024)4:13

While the data set on future supply and demand of timber has predictions from 2022 to 2050, we chose a shorter study period of the optimization algorithm – 2022–2026. With this choice, we assume that hubs will
not be permanent, but will rather change locations approximately every 5
years depending on future locations of construction and demolition sites.
Currently, circular hubs are often simple storage structures that can bedisassembled and reassembled with minimal environmental impact.
Therefore, we assume that the transportation emissions savings fromchanging hub locations every 5 years would outweigh emissions for dis- andre-assembling the facility.
Materials from demolition sites are highly homogenous. While thedataset categorized materials by type (such as concrete, glass, and timber), it
does not make ﬁner distinctions within each material type. This means there
is no way of knowing what type of timber (structural, facade, interior wall) is
arising from the demolition sites. Therefore, in reality, there could be lesssupply and demand matching than represented in the model, due to amismatch between building component types. A more accurate model
would require a materials dataset that makes a component-level distinction
for each material type - a task yet to be achieved in existing literature.
We assumed that the oldest 16% of buildings (excluding heritage sites)in the future material supply and demand dataset would be demolished, as
older buildings will more likely be demolished ﬁrst, and 5 years is 16% of thestudy period of the original dataset (30 years). However, demolitions are not
evenly distributed in time and space. In reality, demolition sites could beclustered in a certain area, or during a certain time period. Because there is
no exact data on when demolitions will occur, this spatial or temporalclustering is not reﬂected in the model.
This study is also limited to the MRA, which has a unique set of spatialconcerns - it is an urbanized and dense region with high land scarcity andreal estate costs, as well as ambitious goals for circular and timber construction. The optimal number of hubs could vary signiﬁcantly in other
cities either due to the geographic area, real estate costs, or policies related to
the reuse of construction materials. For example, another region could
beneﬁt from larger hubs to ensure supply and demand matching, either
because it has less ambitions for timber construction (and therefore lessfuture demand for timber), or because it is less densely built, requiring hubs
to travel further to collect and redistribute materials.
The optimization algorithm assumes that hubs provide full coverage toall future supply and demand locations for secondary timber. In otherwords, the hubs in the algorithm behave like post ofﬁces, which collectively
cover all possible clients; rather than like chain stores, which only aims tomaximize the coverage of most, but not all, clients. It was also assumed thatthe hubs work independently and do not communicate or share resources
with each other, as this is the case for currently established circular hubs.
However, there could be other models for organizing hubs. For example,
hubs could be organized in a hierarchical network with central hubs
aggregating and sorting materials from more peripheral hubs. In this case,5Articlehttps://doi.org/10.1038/s42949-024-00153-0

Fig. 5 | Diagram showing overall methodology. We iterated through a range ofhubs from 1 to 135 and found the best hub locations for each iteration. The costeffectiveness of the best locations for each iteration was plotted on a cost-effectiveness curve. The lowest point of the curve indicated the optimal number ofcircular timber hubs for the MRA.

the optimization could result in 1–2 large scale hubs for the whole region,
each connecting to a number of smaller hubs that operate at a local scale(3 km). These variations, aligned with management studies, were not a
research topic in this paper.
For the calculation of cost / tCO2eq reduction, a number of assumptions were made based on existing studies on circular construction hubs14,38.
Changing these assumptions could have an impact on the results. This isespecially true for the calculation of storage costs and tCO2eq reduction, as
these parameters are based on more assumptions than transportation costs
and emissions. For more details please refer to the methods section.
In terms of theoretical contributions, this study takes into accountsupply and demand matching when optimizing for spatial scale of resource
reuse, thanks to a novel predictive data set36. Matching future supply anddemand of secondary materials is important for CE research, because it isessential to quantify the possibilities and limitations of resource reuse. As
seen in the dataset for future supply and demand for construction materials,
future demand for timber, 710,000 tons, is more than double of future
supply, 350,000 tons. It is therefore impossible to completely satisfy future
demand for timber construction materials with secondary timber fromdemolitions sites.
Additionally, while industrial ecologists have produced increasingly
accurate datasets predicting locations of future supply and demand of
materials, a connection to spatial planning has not yet been made. By using a
predictive dataset for the Netherlands to calculate the optimal number andlocations of circular timber hubs in the MRA, this study provides anexample of using results from industrial ecology to provide practical spatialplanning recommendations.
In terms of practical contributions, this study presented the optimal number and locations for circular timber hubs in the MRA, as wellas industrial sites that should be prioritized as locations of timber storage and exchange. We provided a concrete vision of how circulartimber hubs might be established in a future where circular timber
construction is the norm: around 30 hubs in total across the region,
congregating around dense urban areas, each working at a local scale ofapproximately 3 km.
Our results also illustrate the important role governments can play inplanning for a CE: If the establishment of circular hubs were completely
market-driven with no governmental intervention, it would lack a top-down
understanding of the collective economic and environmental impact of all
the circular hubs working together as a whole. The results of this study cantherefore show that, when given the right information, policymakers canprovide insights that cannot be obtained by individual companies alone.
Consequently, governmental organizations, such as municipal and provincial bodies, could use our results to prioritize industrial sites for establishing circular hubs, or use incentives and regulations to regulate the scaleand locations of hubs in the region.

Methods

npj Urban Sustainability | (2024)4:13

Overview
We aimed to identify the optimal spatial scale for circular timber hubs in the
MRA using a mathematical optimization method spatial simulated
annealing. The optimal scale was deﬁned as a scale that is most cost-effective, minimizing costs and maximizing emissions reductions through timber reuse. In order to determine the optimal number and locations of hubs,
we iterated through a range of possible numbers of hubs. For each iteration,
an optimization algorithm was used to determine the optimal hub locations,as well as their cost-effectiveness value. The number of hubs with the lowest
cost-effectiveness value was determined as the optimal number of hubs. The
diagram below (Fig. 5) summarizes the overall methodology.
Spatial simulated annealing
We chose between two basic strategies for solving spatial optimisation
problems: exact and heuristic methods. Exact methods involve solving
mathematical models to solve a problem, while heuristic methods use
approximate algorithms that provide good solutions in a reasonable amountof time, but do not guarantee ﬁnding the optimal solution. Exact methods
guarantee ﬁnding the optimal solution but can be computationally intensive, while heuristic methods provide approximate solutions quickly, evenfor large-scale problems39. Given a large number of possible combinations oflocations for circular timber hubs, heuristic methods were chosen to optimize their number and location.
Spatial simulated annealing was chosen as a heuristic optimization
method for this study for its effectiveness in ﬁnding good solutions forcomplex problems within a large search space40,41. The method is inspired by
the process of slow cooling in metallurgy. The algorithm begins by exploring
the solution space broadly, accepting both improvements and occasional
steps backward (worse solutions) to avoid local optima. As the number of
iterations increases, the probability of accepting worse solutions is reduced,
leading the search to converge more tightly around the best solutions found.
Optimization objective: cost-effectivenessThe objective of the algorithm, represented below by Eq. (1), is to choose a
combination of hub locations that are most cost-effective – that minimizes
costs and maximizes CO2eq emission reductions through timber reuse.

Ceff ¼ ðCstor þ Ctrans Þ=ðRCO2eq  Etrans Þð1ÞWhere:
Ceff = cost effectiveness (euros per tCO2eq reduction)
Cstor = storage cost (euros)
Ctrans = transportation cost (euros)
RCO2eq = CO2eq reduction from timber reuse (tCO2eq)
Etrans = transportation emissions (tCO2eq)
6Articlehttps://doi.org/10.1038/s42949-024-00153-0

Cost-effectiveness is an indicator used in sustainability researchthat compares the costs and beneﬁts of different sustainableinterventions42,43. It takes into account the costs of implementing aparticular intervention, as well as the expected environmental beneﬁts,
identifying interventions that can achieve the greatest impact for a given
level of investment. For our case, the cost effectiveness value represents
the collective impact of all chosen hubs within a potential solution,rather than a single hub.
In order to determine the optimal number and locations of hubs, weiterated through a range of possible numbers of hubs: 1–135, which is thetotal number of industrial sites in the area. For each iteration, the spatial
simulated annealing algorithm was used to determine the optimal hub
locations, as well as their cost / tCO2eq reduction value. The number of hubswith the lowest cost-effectiveness value was determined as the optimal
number of hubs.
Cost-effectiveness: contributing factors
The factors contributing to cost effectiveness - storage cost, transportation
cost, CO2eq reduction, and transportation emissions, are explained below.
For more details see the supplementary information document and programming scripts.
Storage cost. The calculation of storage cost is expressed in Eq. (2).
To calculate the storage area, we assumed that the average storage
time of timber is six months38, and that secondary timber will only be
stored if there is demand for it within the same service area. The
building price, 382.51 euros per square meter, was based on datacollected by Statistics Netherlands on building costs of halls, sheds,
greenhouses, and stables 44. The rental price, which varies at eachlocation, was based on governmental data on industrial sites in the
Netherlands35.

Cstor ¼

nX

astor ðpbuild þ prent Þ

ð2Þ

i¼1

Where:
Cstor = storage cost (euros)
astor = storage area (sqm)pbuild = building price per square meter (euros per sqm)
prent = rental price per square meter (euros per sqm)
Transportation cost. The calculation of transportation cost is expressed

below in Eq. (3). We assumed that secondary timber is transported fromsupply locations (demolition sites) to the hub to be stored. Then, thesecondary timber is transported from the hub to the demand locations(construction sites) to be reused. The price for transporting one ton oftimber for one kilometer was based on governmental data on freighttransport in the Netherlands45.
Ctrans ¼ ptrans *nX

d SH *ts þ dHD *tD

ð3Þ

i¼1

Where:
Ctrans = transportation cost (euros)
ptrans = price for transporting one ton of timber for one kilometer (euros)
dSH = transportation distance from supply location (S) to hub
location (H)ts = tons of timber at a speciﬁc supply location (S)dHD = transportation distance from hub location (H) to demand
location (D)tD = tons of timber at a speciﬁc demand location (D)Transportation emissions. Transportation emissions were calculatedusing a similar method as transportation costs, expressed below in Eq. (4).
npj Urban Sustainability | (2024)4:13

The emissions associated with transporting timber were based on a life
cycle analysis for road transportation in Europe46.
Etrans ¼ etrans *nX

d SH *ts þ dHD *tD

ð4Þ

i¼1

Where:
Etrans = transportation emissions (tCO2eq)
etrans = transportation emissions associated with transporting 1 ton oftimber for 1 km (tCO2eq)
dSH = transportation distance from supply location (S) to hub
location (H)ts = tons of timber at a speciﬁc supply location (S)dHD = transportation distance from hub location (H) to demand
location (D)tD = tons of timber at a speciﬁc demand location (D)CO2eq reduction. The CO2eq reduction from timber reuse is expressed
below in Eq. (5). The value is the amount of CO2eq emissions avoided if
future timber demand were satisﬁed by secondary sources (timber waste)rather than primary sources (timber from sustainable forests).
We assumed that when timber demand is satisﬁed from primarysources, timber waste is incinerated, releasing emissions into the atmosphere. For secondary sources, we assumed that waste timber is stored in thenearest circular hub and reused as secondary timber by a construction site
within the same service area. If there is an over-supply of waste timber, theexcess is incinerated. The CO2eq emissions for this scenario are emissions
associated with incinerating excess waste timber that was not reused.

ECO2eq ¼

nX

et *mp  et *ms

ð5Þ

i¼1

Where:
ECO2eq = CO2eq reduction from timber reuse (tCO2eq)
et = tCO2eq emissions associated with incinerating one ton of timber(tCO2eq)
mp = amount of waste timber to be incinerated if no timber was
reused (tons)
ms = amount of waste timber to be incinerated if there is timberreuse (tons)
Constraining conditions: locations of hubs, supply, and demand
The constraining conditions for the spatial optimization were the candidate
hub locations, and future supply and demand locations for secondary
timber. The candidate hub locations were industrial sites within the MRA
with an environmental category34 of 2–3. Environmental category 2–3 refers
to industrial sites that are 30–100 km from quiet residential areas, and
0–50 km from mixed areas. These conditions were chosen based on existing
research ﬁndings on the spatial requirements for circular hubs in the
Netherlands13,14. Industrial sites’ locations, environmental categories, andrental prices were obtained from a governmental dataset35.
Future supply and demand locations for secondary timber were basedon a dataset predicting the supply and demand for secondary construction
materials in the Netherlands from 2022 to 2050, mapped onto a spatial gridwith a resolution of 100 × 100 m36. To ﬁt the conditions of this study, we
ﬁltered the dataset to only include timber supply and demand for our study
period – 2022 to 2026.
To ﬁlter for future supply locations, we needed to determine whichareas will most likely be demolished within our study period. First, gridcells with an average building age of older than 100 years were eliminated, as these were likely heritage areas. Then, the oldest 16% of theremaining grid cells were chosen, as older buildings will more likely be
demolished ﬁrst, and 5 years is 16% of the study period of the original
dataset (30 years).
To ﬁlter for future demand locations, two steps were taken. First, 16%of grid cells were randomly chosen to represent demand during the study
7

Articlehttps://doi.org/10.1038/s42949-024-00153-0

period. Cells were chosen randomly because the dataset has no information
on when future demand will occur. Then, a further 50% of grid cells wererandomly chosen, as the municipality of Amsterdam’s circular strategy aims
to be 50% circular by 20306.
The process of extracting, cleaning, and analyzing the data were written
in the programming languages Python and R. The R package “spsann” wasused to create the spatial simulated annealing algorithm47. Due to the highcomputational demand required by the spatial simulated annealing algorithm, the code was run on a Linux-based high-performance computing
system provided by the Delft University of Technology, Delft Blue48. The
programming scripts are in a GitHub repository.
Reporting summary
Further information on research design is available in the Nature Research
Reporting Summary linked to this article.

10.

11.

12.

13.

Data availability
The data that support the ﬁndings of this study are available from The
Netherlands Environmental Assessment Agency (PBL), but restrictions
apply to the availability of these data, which were used under license for thecurrent study and so are not publicly available. The data are, however,available from the authors upon reasonable request and with the permissionof The Netherlands Environmental Assessment Agency (PBL).

14.

15.

Code availability
All code associated with this study is openly available and can be accessed at
the following GitHub repository: https://github.com/TanyaTsui/
spatialOptimizationCircularHubs.

16.

Received: 2 June 2023; Accepted: 2 March 2024;
17.

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Acknowledgements
This research received funding from the European Union’s Horizon 2020
Research and Innovation Programme under grant agreement No. 821479.

Author contributions
All authors contributed to the design and execution of this project andreviewed and edited the manuscript. T.T. conceptualized the research
design, acquired the data, conducted the spatial optimization, and wrote theﬁrst draft of the manuscript. F.D., T.V., and T.B. contributed toconceptualization, methodological development, and editing of themanuscript.

Competing interests
The authors declare no competing interests.

Additional information
Supplementary information The online version contains
supplementary material available athttps://doi.org/10.1038/s42949-024-00153-0.
Correspondence and requests for materials should be addressed to
Tanya Tsui.
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