# How do human behaviour and infrastructure interact in achieving biowaste policy objectives?

Ammar Hdaifeh, Sylvie Huet, Jean-Denis Mathias

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Ammar Hdaifeh, Sylvie Huet, Jean-Denis Mathias. How do human behaviour and infrastructure interact in achieving biowaste policy objectives?. Journal of Cleaner Production, 2025, 510, pp.145571. 10.1016/j.jclepro.2025.145571. hal-05064547

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# How do human behaviour and infrastructure interact in achieving biowaste policy objectives?

Ammar Hdaifeh* , Sylvie Huet , Jean-Denis Mathias

Université Clermont Auvergne, INRAE, UR LISC, Centre de Clermont-Ferrand, 9 avenue Blaise Pascal CS 20085, F-63178 Aubière, France

## ARTICLE INFO

### Keywords:

- Computational simulation
- System dynamics
- Behavioural change
- Socio-technical systems
- Biowaste management

## ABSTRACT

Effective biowaste management depends on the interplay between household behaviours and infrastructure development, yet many local policy actions overlook this crucial dynamic. This study explores how this inter-action influences the achievement of local policy objectives for biowaste management. We propose a system dynamic modelling approach, applied to a case study where local policy-makers collaboratively set four objec-tives to reach within a given time horizon. Our model analyses the interplay between infrastructure develop-ment, and behavioural dynamics, revealing the following key findings: 1) biowaste production always increases due to population growth whereas decreasing with the application of the anti-biowaste plan, which has positive or negative impacts on reaching the policy objectives; 2) infrastructure development is never sufficient to meet all policy objectives because behavioural shifts are essential; 3) gradual behavioural intentions speed of change, particularly in sorting for home composting, is necessary to meet all objectives without infrastructure capacity constraint and to reach most objectives with infrastructure constraints of capacity; 4) trade-offs exist between sorting for home composting and sorting for dedicated collection behaviours, where faster adoption of the first can hinder the second. This study overcomes the uncertainty of how people will change their behaviours ac-cording to local policy action. By studying the impact of various possible evolutions of behaviours, our work provides policy-makers with insights into the conditions necessary for achieving their objectives, accounting for the dynamic interactions between human behaviours, evolution in the population size, and infrastructure development.

## 1. Introduction

The increase in household biowaste, driven by urbanisation and increased consumption, presents significant environmental challenges, straining waste management systems. Effective biowaste management is crucial for achieving carbon neutrality and supplying renewable energy (Kee et al., 2021). In response, many countries have developed specific policies. For example, the European Union has prioritised waste pre-vention strategies and mandated Member States to provide citizens with viable biowaste sorting solutions, as outlined in directives like 2018/851 (Stankevicius et al., 2020). In France, local authorities must develop solutions to enhance biowaste management systems and maximise the valorisation of collected biowaste (N. Buclet et al., 2000). This task is particularly challenging due to variations in biowaste production be-tween rural and urban areas and the growing population. The complexity of biowaste management arises from its dual nature, encompassing both technical aspects, such as infrastructure

development, and social aspects. Addressing this issue requires an approach that captures the interactions between social behaviours dy-namics and infrastructure developments.

Dynamic modelling techniques, especially the system dynamics model with a stock-and-flow approach, are powerful tools for simulating and analysing different scenarios. These techniques offer a systematic and holistic means to explore the socio-technical dynamics of biowaste management (Mathias et al., 2018; Kollikkathara et al., 2010). For instance, Wang et You (2021) developed an integrated system dynamic model to evaluate the impact of municipal solid waste classification on socio-economic, environmental, and resource aspects, highlighting the importance of these modelling approaches in understanding the com-plex interactions within waste management systems.

Engineering models have shown the importance of infrastructure development in waste management. Meanwhile, behavioural studies by (Knickmeyer, 2020a) underscore the critical role of behaviour change in promoting sustainable waste management practices. However, models

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: ammar.hdaifeh@inrae.fr (A. Hdaifeh), sylvie.huet@inrae.fr (S. Huet), jean-denis.mathias@inrae.fr (J.-D. Mathias).</footnote>
that address both infrastructures and behavioural changes are very rare.

Our approach frames the adoption of biowaste-sorting practices as an
innovation diffusion process (Rogers, 1995; Ryan and Gross, 1950).
While waste management is often implemented as a regulatory obliga-
tion, the French context under the Loi Anti-Gaspillage pour une
Économie Circulaire (AGEC – Anti-Waste Law for a Circular Economy,
2020) creates a different scenario where municipalities are mandated to
provide infrastructure, but household adoption remains voluntary, with
no economic incentives or penalties tied to participation. For most
households, these practices are new, positioning adoption as a socially
driven innovation. This specificity aligns with innovation diffusion
theory, where adoption follows an S-curve shaped by social dynamics
such as imitation, knowledge-sharing, and emerging norms.

Our hypothesis that sorting and recycling practices diffusion can be
modelled by an S-curve is also supported by two bodies of work: (1)
social psychology studies demonstrating that norms are key de-
terminants of household sorting behaviour (Pei, 2019; Knickmeyer,
2020b; Bruno et al., 2022); (2) large surveys made to initialize and
parameterize the dynamics of agent-based models of household prac-
tices (mainly in Chinese contexts) shows knowledge diffusion and
neighbourhood imitation are drivers of adoption (Meng et al., 2016;
Meng et al., 2024; Peng et al., 2021). By modelling adoption speed
through an S-curve, we capture how social influence accelerate uptake
as practices normalise within communities, consistent with Rogers'
(1995) framework.

We propose a generic dynamic approach that integrates both aspects.
By incorporating a stock-and-flow approach, our model visualises bio-
waste accumulation and processing within a defined system boundary,
offering a clear representation of the current and potential future states
of the system.

Policymakers often design infrastructure development plans with the
expectation that they will effectively achieve goals related to food waste
reduction and valorisation. However, they often lack insight into peo-
ple's behavioural intentions to use the infrastructure, as well as how this
intention may evolve overtime. This creates significant uncertainty
regarding the success of their objectives.

Our study addresses this uncertainty by employing our generic dy-
namic approach to simulate a wide range of possible household
behaviour trajectories and their interactions with planned infrastructure
developments. This method, applied to the Valtom territory in France as
a real-world case study, offers policymakers valuable insights into the
conditions required to achieve their policy goals. It accounts for the
evolving relationship between human behaviour and infrastructure
development.

Our work also investigates how the evolution of the population size —rarely considered in the existing models— interacts with an action plan aiming to favour behaviours decreasing household production of biowaste.

The remainder of this paper is structured as follows: Section 2 pre-
sents a literature review on the dynamic modelling of biowaste man-
agement, setting the stage for our proposed approach. Section 3
introduces our materials and methods, including a general overview of
the approach, the Stock and Flow Model for integration and interactions,
and the Valtom territory in France as a case study. The results are pre-
sented in Section 4, followed by a discussion in Section 5. Finally, Sec-
tion 6 concludes our paper.

## 2. Literature review

Waste management systems have been extensively studied through
dynamic modelling, with numerous literature reviews focusing on solid
waste management systems and encompassing all waste streams
(Sancheta, Chaves, et Siman, 2021; Popli, Sudibya, et Kim, 2017;
Berenjkar et al., 2021). However, few dynamic models have specifically
addressed household biowaste management systems (Debray, 2002;
Hénault-Ethier et al., 2017; Inghels et Dullaert, 2011). While some

studies have addressed household biowaste management, most dynamic
models have primarily focused on either infrastructure development
(Babalola, 2019; Kollikkathara et al., 2010) or social behaviour change
(Knickmeyer, 2020a; Scalco et al., 2017) in isolation, often over-
simplifying human behaviour or treating it as a static factor. Babalola
(2019) developed a model considering infrastructure development, but
it did not account for potential changes in household behaviour over
time.

Schmidt et al. (2008) highlight the importance of considering the
mass flow of biowaste in household waste management systems. They
present a method for calculating the potential and collected weight of
kitchen and garden waste, which is crucial for planning and imple-
menting effective biowaste schemes. This approach underscores the
need to incorporate detailed modelling of biowaste flows to improve the
accuracy of waste management strategies (Schmidt et Pahl-Wostl,
2007).

The term 'socio-technical' was used sporadically during the early
20th century, but the foundations of socio-technical systems theory
primarily stem from the work of the Tavistock Institute of Human Re-
lations in the 1950s (Clegg et al., 2017). Socio-technical systems theory
(STS) is a valuable framework for understanding the dynamics of bio-
waste management, emphasising the interplay between the landscape,
actors, institutions, material artefacts, and knowledge (Baxter et Som-
merville, 2011). By applying this theory to the development of a
stock-and-flow model, we can gain a deeper understanding of the
complex interactions between infrastructure development and the
behavioural changes that influence meeting biowaste policy objectives.

The need for more sophisticated models that integrate behavioural
dynamics with infrastructural development is crucial for accurately
predicting biowaste management outcomes. Current models typically
compare simulation results across a limited number of scenarios,
ranging from 2 to 7 (Hénault-Ethier et al., 2017; Kollikkathara et al.,
2010; Eugecirc Nio et Mauri, 2012; Simonetto, 2014; Berenjkar et al.,
2021; Babalola, 2019; Pinha et Sagawa, 2020). While these approaches
provide valuable insights, they may not be sufficient to understand the
key considerations and trade-offs involved in behavioural changes and
infrastructure development for biowaste management. For example,
Kollikkathara et al. (2010) compared two scenarios for municipal solid
waste management in the city of Newark, but their study did not explore
the impact of varying levels of household participation in waste sepa-
ration on the system's performance.

In contrast, the modelling approach proposed in this study focuses on
analysing the interactions between evolving household behaviours and a
predetermined biowaste management infrastructure plan. It considers a
wider range of possible behavioural trajectories, exploring the sensi-
tivity of the studied system to changes in key parameters related to the
evolution of intentions to behave.

Overall, our work proposes a novel modelling approach that in-
tegrates socio-technical dynamics into a stock-and-flow model for bio-
waste management. By incorporating both infrastructure development
and social behaviour change, our approach addresses some of the limi-
tations of existing models and provides a better understanding of the
complex interactions that shape the performance of biowaste manage-
ment systems.

## 3. Materials and methods

We propose a generic model that can be applied to different cases
and tailored to biowaste systems. The global approach is presented in
3.1, while 3.2. gives details about the dynamics. The 3.3 is devoted to
the presentation of the case study. The 3.4 describes the initialisation
and the parametrisation of this case study.

### 3.1. General overview of the approach

We consider a system, called territory, with various inhabitants
living in “waste-collection” territories.

This territory has an already decided detailed biowaste management plan, including:

* Local Policy Objectives for biowaste management (LPO): these objectives are derived from collaborative policy-making over a given time horizon;

* Local Policy Actions (LPA): these actions represent practical measures decided by policy-makers such as the Anti-Biowaste Plan (ABP), —a set of initiatives/actions (e.g., education campaigns) designed to encourage households to adopt reduction behaviours (e.g., meal planning) and thereby reduce biowaste production. The ABP is distinct from valorisation measures, which are modelled separately and include LPAs focused on investments in proximity equipment and large-scale shared infrastructures (e.g., home composters, dedicated collection systems, methanisation units, professional composters). LPAs align with global directives such as the European Union's Directive 2018/851, which promotes waste prevention and valorisation as complementary strategies.

Our territory comprises:

* households that produce biowaste, and adopt some virtuous behaviours (e.g., decreasing their waste, sorting for home-composting, or sorting biowaste for dedicated collection to valorisation) instead of putting all their biowaste in the “classical” collection bin. The number of households (or individuals) living in the waste-collection territories evolves according to the demography parameters (i.e. the population grows or decreases over time).

* a network of proximity equipment located in the waste-collection territories (e.g., home composters, dedicated collection bins for biowastes, and “every other” waste) with a predetermined-by-the-plan capacity evolution (e.g., home composters, dedicated collection bins, sets of trucks collecting the waste, valorisation centres for green waste deposit).

* and large-scale shared infrastructures (e.g., methanisation units, professional composters, incinerators) are also already designed in terms of number and capacities.

The quantities of produced, collected and valorised green and food waste of our territory change over the time according to our generic dynamic model presented in section 3.2. The model captures the dynamic interplay between household behavioural intentions (e.g., decreasing food waste, adopting virtuous behaviours like sorting for home-composting or dedicated biowaste collection) and predetermined-by-the-plan capacity evolution of proximity equipment and large-scale shared infrastructures (according to the LPA). It models how these behavioural intentions and infrastructure capacities create feedback loops that enhance the efficiency and effectiveness of waste management, thereby aiding the achievement of specific local policy objectives.

Our study has two purposes. Firstly, it aims to understand the interplay between the demography and the change in food waste producing behaviours due to the implementation of the ABP, especially in terms of reaching the LPO. Secondly, it aims to understand the impact on the achievement of territorial LPO of the interactions between:

* the change in behavioural intentions (e.g., from putting “everything” in the “classical bin” to sorting for home-composting or sorting for a virtuous collection that is destined to be valorised by the large-scale infrastructure),

* and the network of proximity equipment that changes over time according to the territory LPA.

Indeed, while the actions and the change in equipment and infrastructure are usually known by policy-makers from the plan they have decided, they do not know how people are going to change their

behaviours accordingly. Our work aims to overcome this uncertainty by studying the impact of every possible evolution of the behaviours, giving policymakers the conditions for reaching their objectives.

## 3.2. The stock and flow model

The stock-and-flow model integrates three main stages: (i) household biowaste production, (ii) household biowaste behaviour, and (iii) shared infrastructure, as depicted in Fig. 1. For simplicity, Fig. 1 illustrates the households’ biowaste flows and processing steps within a single waste-collection territory, simply called collection territory in what follows.

Fig. 1 shows, from the left to the right, the three stages of the dynamics.

1. Household biowaste production: this stage represents the volume of household biowaste production based on per-capita biowaste production and population growth rates (including the anti-biowaste plan).

2. Household biowaste behaviour: this stage models how households manage their biowaste, including decisions about sorting for home composting and sorting for dedicated collection. The specific actions taken depend on the characteristics of each collection territory (e.g., some may have dedicated collection for sorted biowaste while others may not). Some proximity equipment such as dedicated collection, home composter, and valorisation centres, are shared across collection territories, adding complexity to the management and coordination of biowaste flows.

3. Large-scale shared Infrastructure: this stage represents the infrastructure where biowaste is processed, including methanisation units, professional composting platforms, and incineration. These infrastructures are shared by one or several collection territories.

The interactions between these stages create feedback loops that influence the overall biowaste management system. For example, increased sorting for home composting intention reduces the volume of biowaste entering the shared infrastructure. In this model, a surplus is defined as the situation where households are constrained by the infrastructure capacity to change their initially intended behaviour. The mathematical form of the dynamics, partly described in Fig. 1, is detailed in the following section.

### 3.2.1. Households’ biowaste production

The household’s food and green waste production from each collection territory are denoted respectively as $B_f^p(t)$ and $B_g^p(t)$. These variables are expressed in terms of mass (tons) and are functions of time $t$, representing the year number in the context of the model. The equation for households’ food and green waste production from each collection territories is given by:

$$B_f^p(t) = b_f^p P(t) \left( 1 - \underbrace{a_f^p(\tau) z(t, m_f^p)}_{\text{Anti-Biowaste Plan effect}} \right) \quad (1)$$

$$B_g^p(t) = b_g^p P(t) \left( 1 - \underbrace{a_g^p(\tau) z(t, m_g^p)}_{\text{Anti-Biowaste Plan effect}} \right) \quad (2)$$

With:

* $b_f^p$ and $b_g^p$ represent the baseline food and green waste production per capita (which vary for each collection territory).

* $P(t)$ This represents the population size of each collection territory at year $t$, calculated as:
<figure><img src="image_3.png" /><figcaption>Fig. 1. Generic simulation stock and flow model for biowaste management: conceptual mapping of household biowaste production, biowaste behaviours, and shared infrastructure (each collection territory may have a different combination of infrastructure). Numbers indicate the order of actions: (1) managing food waste first, (2) managing green waste second. Thus, green surplus is managed first, followed by food surplus. A surplus is defined as the situation where households are constrained by the infrastructure capacity to change their initially intended behaviour. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

$$P(t) = P(0)(1+r) \qquad (3)$$

with $P(0)$ being the initial population size of each collection territory at $t=0$ and $r$ being the annual growth rate of the population for each collection territory.

* The Anti-Biowaste Plan (ABP) aims to encourage households to adopt reduction behaviours (e.g., meal planning to minimize food waste, efficient garden management to reduce green waste). This behavioural diffusion is modelled using S-curve functions $z(t, m_f^p)$ and $(t, m_g^p)$, which represent the gradual adoption of reduction behaviour over time. Parameters $a_f^p(\tau)$ and $a_g^p(\tau)$ denote the ABP's target reduction for biowaste, respectively, to be achieved by the target year $(\tau)$. The ABP's effect models $\tau$ reduced biowaste production (not diversion for valorisation) through behavioural changes. Valorisation measures, such as composting, which divert biowaste from disposal bins, are modelled separately.

* Parameters $m_f^p$ and $m_g^p$ represent time for which the function $z$ is equal to 0.5. The rationale for these sigmoid functions is described further in 3.2.1.4.

For a detailed explanation of the notation system used to represent these variables and parameters, please refer to Appendix A.

### 3.2.2. Households' biowaste behaviour and proximity equipment

Once biowaste is produced by households, we consider four flow destinations for proximity equipment as described in Fig. 1: sorting for home composting, sorting for dedicated collection (to methanisation), green waste to valorisation centre (no sorting), and food waste to residual household's waste (no sorting). These flows are described hereafter.

The first flow of biowaste production is pushed into home composters in each collection territory. The following equations describe the compostable biomass quantities. In what follows, we distinguish between home-compostable biowaste and home-composted biowaste. Home compostable biowaste is the biowaste that people want to compost. However, according to the home composer's capacity, it is not always possible. Therefore, the home composted biowaste corresponds to biowaste that is composted. Therefore, the difference between home compostable and home composted biowaste represents a surplus. Such surplus requires households to behave differently from what they initially intent since the infrastructure limit their composting behaviour. In practice in the model, it means only a part of households can actually compost, while others, from which the waste production corresponds to the surplus, must divert their biowaste by sorting for another proximity equipment.

The biomass of home compostable green and food waste $\hat{B}_g^c(t)$, $\hat{B}_f^c(t)$ at time $t$ for each collection territory are:

$$\hat{B}_g^c(t) = \alpha_g^c(t) B_g^p(t) \qquad (4)$$

$$\hat{B}_f^c(t) = \alpha_f^c(t) B_f^p(t) \qquad (5)$$
with $\alpha_g^c(t)$ and $\alpha_f^c(t)$ being the sorting green and food waste for home
composting intentions since we suppose that, people gradually change
their intention towards sorting for home composting. In order to simu-
late this change, we use the following sigmoidal functions (see 3.2.1.4
for the rationale):

$$
\alpha_g^c(t) = \alpha_g^c(0) + (1 - \alpha_g^c(0)) z(t, m^c) \quad (6)
$$

$$
\alpha_f^c(t) = \alpha_f^c(0) + (1 - \alpha_f^c(0)) z(t, m^c) \quad (7)
$$

The parameters $\alpha_g^c(0)$ and $\alpha_f^c(0)$ are the initial green and food home
composting intentions, respectively. For the computation of the biomass
of home composed green and food waste $B_g^c(t)$ and, $B_f^c(t)$ at time $t$, we
should take into account the limiting capacity $K^c(t)$ of the home com-
posters. We assume that people easily bring their “excessive” green
waste to the valorisation centre and prefer putting their food waste first
in the home composter while it is possible. This is mathematically
translated as follows:

$$
B_f^c(t) = \min[K^c(t), \widehat{B}_f^c(t)] \quad (8)
$$

$$
\hat{B}_g^c(t) = \min[K^c(t) - \hat{B}_f^c(t), \hat{B}_g^c(t)] \quad (9)
$$

The part of the biowaste that cannot be home composted is called
home composting-part surplus and is denoted $U_f^c(t)$ for the food biowaste
and $U_g^c(t)$ for the green biowaste:

$$
U_f^c(t) = \max[\hat{B}_f^c(t) - K^c(t), 0] \quad (10)
$$

$$
U_g^c(t) = \max[\hat{B}_f^c(t) + \hat{B}_g^c(t) - K^c(t), 0] \quad (11)
$$

These possible home composting surpluses are managed through the
second flow.

The second flow of biowaste is directed towards dedicated collection to methanisation after sorting food and green biowaste within each collection territory. As for sorting for home composting, we distinguish the sortable biowaste for dedicated collection from the sorted biowaste for dedicated collection flows. For sortable green waste for dedicated collection, we have an equation similar to the sorting for home composting equations (Eqs (4) and (5)):

$$
\hat{B}_g^s(t) = \alpha_g^s(t) B_g^p(t) \quad (12)
$$

However, for sortable food waste for dedicated collection, we added
the food waste surplus $U_f^c(t)$ that cannot be home composted because of
a lack of home composter capacity:

$$
\hat{B}_f^c(t) = \alpha_f^c(t) B_f^p(t) + U_f^c(t) \quad (13)
$$

Like sorting for home composting, we suppose that we have a pro-
gressive behavioural change in sorting for dedicated collection behav-
iour. However, in the case of sorting for dedicated collection (to
methanisation), we need to take into account two properties. The first
one is that we need to guarantee the intentions are consistent and that no
new biomass is created. Thus, we should have $\alpha_f^c(t) + \alpha_f^s(t) \le 1$ and $\alpha_g^c(t) + \alpha_g^s(t) \le 1$. So, when the inequality is not respected, we assume the
sorting for home composting is prioritised by people. This strong
assumption is in line with the priority defined by the hierarchy of bio-
waste management preconized by (Papargyropoulou et al., 2014;
Kirchherr, Reike, et Hekkert, 2017) Thus, the intentions of practical
sorting for dedicated collection behaviour for green and food waste at
time t, $\alpha_g^s(t)$ and $\alpha_f^s(t)$, are calculated as follows:

For green waste:

$$
\alpha_g^s(t) = 1 - \alpha_g^c(t) \quad \text{if} \quad \alpha_g^c(t) + \alpha_g^s(t) \ge 1 \quad (14)
$$

$$
\alpha_g^s(t) = \alpha_g^s(0) + (1 - \alpha_g^s(0)) z(t, m^s) \quad \text{if } \alpha_g^c(t) + \alpha_g^s(t) < 1 \quad (15)
$$

For food waste:

$$
\alpha_f^s(t) = 1 - \alpha_f^c(t) \quad \text{if} \quad \alpha_f^c(t) + \alpha_f^s(t) \ge 1 \quad (16)
$$

$$
\alpha_f^s(t) = \alpha_f^s(0) + (1 - \alpha_f^s(0)) z(t, m^s) \quad \text{if } \alpha_f^c(t) + \alpha_f^s(t) < 1 \quad (17)
$$

The parameters $\alpha_g^e(0)$ and $\alpha_f^e(0)$ are the initial intentions for practical sorting of green and food waste for dedicated collection. Once biowaste flows have been sorted, they are valorised if the dedicated collection capacity is sufficient. This constitutes the third flow. Similar to sorting for home composting flow, for the computation of the biomass of sorted green and food waste in dedicated collection $B_g^s(t)$ and, $B_f^s(t)$ at time $t$, we should take into account the limiting capacity $K^s(t)$ of the dedicated collection (proximity equipment). Thus, the dedicated collection is first filled with food waste up to its capacity. It is then filled with green waste up to the remaining unused capacity. Like home composting equations (Eqs (8) and (9)), this is mathematically translated as follows:

$$
B_f^s(t) = \min[K^s(t), \widehat{B}_f^s(t)] \quad (18)
$$

$$
\hat{B}_g^s(t) = \min[K^s(t) - \hat{B}_f^s(t), \hat{B}_g^s(t)] \quad (19)
$$

Like home composting-part surplus (Eqs (10) and (11)), the part of
the biowaste that cannot be sorted is called sorting-part surplus and is
denoted $U_f^s(t)$ for the food biowaste and $U_g^s(t)$ for the green biowaste:

$$
U_f^s(t) = \max[\hat{B}_f^s(t) - K^s(t), 0] \quad (20)
$$

$$
U_g^s(t) = \max[\hat{B}_f^s(t) + \hat{B}_g^s(t) - K^s(t), 0] \quad (21)
$$

The third flow of biowaste involves green waste directed to the green valorisation centres $B_g^v(t)$, and the fourth flow of biowaste involves food waste directed to the residual household waste $B_f^v(t)$ in the household residual bin (“classical bin”). The following equations represent these flows:

For the volume of green waste sent to the valorisation centre in each
collection territory at time t, $B_g^v(t)$:

$$
\hat{B}_g^v(t) = 1 - \alpha_g^e(t) - \alpha_g^s(t) B_g^p(t) + U_g^c(t) + U_g^s(t) \quad (22)
$$

In the absence of dedicated collection infrastructure in the collection
territory the equation will be:

$$
\hat{B}_g^v(t) = 1 - \alpha_g^e(t) B_g^p(t) + U_g^c(t) \quad (23)
$$

For the volume of food waste ending up in the residual household waste (“classical bin”) in each collection territory at time , $B_f^r(t)$:

$$
B_f^r(t) = 1 - \alpha_f^e(t) - \alpha_f^s(t) B_f^p(t) + U_f^s(t) \quad (24)
$$

And in the absence of dedicated collection infrastructure in the
collection territory the equation will be:

$$
\hat{B}_f^r(t) = 1 - \alpha_f^e(t) B_f^p(t) + U_f^c(t) \quad (25)
$$

3.2.3. Large-scale shared infrastructure

Once biowaste has been collected, it is treated in the large-scale
shared infrastructure, which is common to *n* collection territories. In
this step, we consider three possible destinations for the biowaste flow:
methanisation units, incineration, and professional composting.

The first flow is directed from total sorted in dedicated collection
biowaste stocked in the *n* collection territories from step 1 towards the
methanisation unit, which we called digestible methanised biowaste
$\hat{B}^m(t)$:
$$ \hat{B}^m(t) = \sum_{j=1}^{n} \left( B_{f,j}^s(t) + B_{g,j}^s(t) \right) \qquad (26) $$

This can be further broken down into:

$$ \hat{B}^m(t) = \hat{B}_f^m(t) + \hat{B}_g^m(t) \qquad (27) $$

Where: $\hat{B}_f^m(t)$ is the digestible methanised food waste, calculated as:

$$ \hat{B}_f^m(t) = \sum_{j=1}^{n} B_{f,j}^s(t). $$

$\hat{B}_g^m(t)$ is the digestible methanised green waste, calculated as: $\hat{B}_g^m(t) = \sum_{j=1}^{n} B_{g,j}^s(t)$.

$\sum_{j=1}^{n}$: is the summation symbol for the sorted biowaste flows, j represents each individual collection territory from 1 to n, and n is the total number of collection territories.

The computation of the biomass of methanised green and food waste $B_g^m(t)$, $B_f^m(t)$ at time t, considers the limiting capacity $K^m(t)$ of the methanisation unit. When the methanisation unit reaches its full capacity, we first prioritise the adjustment of the digestible methanised green waste, followed by the digestible methanised food waste. This sequential adjustment ensures that the total biomass processed does not exceed the unit's capacity:

$$ B_f^m(t) = \min \left[ K^m(t), \hat{B}_f^m(t) \right] \qquad (28) $$

$$ B_g^m(t) = \min \left[ K^m(t) - B_f^m(t), \hat{B}_g^m(t) \right] \qquad (29) $$

Thus, the total methanised biowaste calculated as:

$$ B^m(t) = B_f^m(t) + B_g^m(t) \qquad (30) $$

The part of biowaste that cannot be methanised is called methanising part surplus and are denoted $U_f^m(t)$ for the food biowaste and $U_g^m(t)$ for the green biowaste (these surpluses will be directed to professional composting as we will see in the next flow):

$$ U_f^m(t) = \max \left( \hat{B}_f^m(t) - K^m(t), 0 \right) \qquad (31) $$

$$ U_g^m(t) = \max \left[ B_f^m(t) + \hat{B}_g^m(t) - K^m(t), 0 \right] \qquad (32) $$

The professional composting infrastructure is assumed to have infinite capacity. The second flow is directed from total green waste stocked in the n collection valorisation centre territories from step 1 towards the professional composting plus any possible surplus from methanisation unit $U_f^m(t)$ and $U_g^m(t)$ which we called total composted biowaste in professional composting $B_g^{c+}(t)$:

$$ B_g^{c+}(t) = \sum_{j=1}^{n} \left( B_{g,j}^v(t) + U_g^m(t) \right) \qquad (33) $$

$$ B^{c+}(t) = B_f^{c+}(t) + B_g^{c+}(t) \qquad (34) $$

with $B_f^{c+}(t) = U_f^m(t)$

The third flow is directed from food waste stocked in residual household waste of each of the n collection territories from step 1 towards the incinerator $B^i(t)$ as follow:

$$ B^i(t) = \sum_{j=1}^{n} \left( B_{f,j}^r(t) \right) \qquad (35) $$

### 3.2.4. Infrastructure capacity evolution

One measure of the local action plan is to develop infrastructure to achieve local policy objectives. In our model, it means that home composter and dedicated collection capacities are increasing over time. The principle of the linear update is used to present the evolution of

infrastructure capacity.

The general form is:

$$ K(t) = K(0) + (a(\tau) - K(0)) \frac{t}{d} \qquad (36) $$

Where $K(0)$ is the initial capacity, $a(\tau)$ is the planned capacity for the target year $\tau$, $t$ is the number of years since the beginning of the expansion and $d$ is the total number of years over which the expansion is planned to occur.

In our use case, as detailed in section 3.4, we consider infrastructure development that consists of proximity equipment, specifically home composters and dedicated collection equipment. These are updated according to planned actions in the LPA. For each type of equipment, the value of $a(\tau)$ represents the decided capacity in the target year. This approach ensures that the equipment capacity evolves in line with the planned action for each equipment in the collection territory.

### 3.2.5. The innovation diffusion for modelling households' biowaste behavioural changes

The adoption of new practices or innovations within a population often follows a characteristic pattern known as the diffusion of innovations (Rogers, 1995; Ryan and Gross, 1950). This theory describes how an innovation is communicated and spreads over time among the members of a social system. This pattern is mathematically represented by the S-curve function, where the rate of adoption starts slowly, accelerates as the innovation progresses, and eventually levels off as the innovation becomes widely accepted (Rogers, 1995; Ryan and Gross, 1950). In our model, we apply the principles of innovation diffusion theory to capture the evolution of behavioural intentions for three key aspects of household biowaste management:

* Adoption of the biowaste reduction behaviours promoted by the actions of the Anti-Biowaste Plan (ABP): modelling how households gradually adopt the biowaste reduction behaviours (e.g., meal planning, repurposing leftovers, etc.).

* Adoption of behaviours that favour valorisation of biowaste:

* Sorting for home composting Intention: modelling the increasing willingness of households to compost their biowaste.

* Sorting for dedicated collection Intention: modelling the increasing willingness of households to sort their biowaste for dedicated collections (destined for professional composting or methanisation).

The S-curve of innovation diffusion reflects the gradual acceptance of an innovation, starting with a small group of early adopters, followed by a more rapid uptake by the early and late majorities, and eventually reaching a saturation point (Rogers, 1995). We define the mathematical function representing this S-curve as:

$$ z = \frac{t^5}{(t^5 + m^5)} \qquad (37) $$

Where: z represents the proportion of the population that has adopted the behaviour (or intention to adopt) at a given time. t is the number of periods (e.g., years) since the introduction of the innovation. m signifies the time it takes for half the population to adopt the behaviour, leading to z = 0.5. In our model, parameters $m_f^p$ and $m_g^p$ represent the speed of change of behavioural intention for ABP for food and green waste, and parameters $m^s$ and $m^c$ represent the speed of change of behavioural intention of sorting for home composting and sorting for dedicated collection (destined for methanisation), respectively. The specific functional form z was chosen as it closely approximates the observed patterns of innovation diffusion in various domains (Chatterjee et Eliashberg, 1990). The use of exponents captures the acceleration and deceleration phases characteristic of the S-curve.

In our analysis, we model the diffusion of sorting for home
composting and sorting for dedicated collection intentions simulta-
neously, recognizing that households have limited resources and time to
adopt new practices. To reflect this, we introduce a constraint where the
combined weight of sorting for home composting and sorting for dedi-
cated collection intentions equals one. As the intention to sort for home
composting increases, the intention to sort for dedicated collection must
decrease proportionally (only when the sum of both intentions is higher
than one), representing the trade-offs and choices households make in
allocating their efforts towards biowaste management. This approach
allows us to model the distinct processes of sorting for home composting
and sorting for dedicated collection (and therefore to methanisation)
while accounting for their interdependencies in household behaviour.

Fig. 2 illustrates the S-curves for different values of m, representing the time to reach 50 % adoption of the intended behaviour. For instance, m = 3 years corresponds to a high speed of change in behavioural intention, with half the population intending to adopt the behaviour within 3 years, while m = 5 years represents a low speed of change in behavioural intention, taking 5 years to reach 50 % intention. These parameter values are adjusted to reflect the specific characteristics and dynamics of each biowaste management behaviour. It's important to distinguish between behavioural intention and actual adoption behav- iour. While behavioural intention reflects the willingness to adopt a practice, the actual adoption of behaviour is dependent upon the availability and accessibility of infrastructure. Therefore, our model considers both behavioural intentions and infrastructure capacity con- straints to analyse the overall dynamics of household biowaste management.

3.3. The use case of Valtom territory

3.3.1. The Valtom territory

We apply our generic stock-and-flow model to the specific case study of the Valtom territory in France, which is described hereafter. The Valtom, a “syndicate for the valorisation and treatment of household waste and similar waste”, has nine collection territories responsible for the management and collection of domestic waste. These nine collection territories are located in the Puy-de-Dôme and northern Haute-Loire departments of France (Fig. 3), and cover 531 municipalities. The de- mographic distribution reveals a predominantly rural composition, with two major urban collection territories, CAM<fnref n="1" /> (42 %) and SBA (24 %), while the remaining seven collection territories (ALF, TDM, SCB, SCZ, SIB, SDC, SHD) have lower population densities ranging from 2 % to 14 %. This heterogeneity among the nine collection territories not only manifests in population density disparities but also in the variety of biowaste reduction efforts, social attitudes towards biowaste practices,

<figure><img src="image_4.png" /><figcaption>Fig. 2. Speed of change in behavioural intentions.</figcaption></figure>

and infrastructure capabilities for biowaste management (see section 3.4 for details). These territories have collectively defined a Local Policy Actions (LPA) plan to reach Local Policy Objectives (LPO). The document containing the LPA and LPO is called STGDO (“Schéma Territorial de Gestion des Déchets Organiques” which means in English “territorial scheme for the management of biowaste”) (Valtom, 2018, 2019 a and b). This scheme is built on a diagnosis realised in 2017, and runs from 2018 to 2024, the year at which the LPOs are expected to be achieved.

Each collection territory has its own proximity equipment; home composters, valorisation centres and dedicated collection infrastructure. They share three common large-scale shared infrastructures: a large methanisation unit, a large professional composting platform, and an incinerator. Thus, the flows coming from each collection territory are summed up to enter the large-scale shared infrastructure common to the nine collection territories.

3.3.2. The Valtom's local policy objectives (LPO) and local actions plan (LPA) for biowaste management

The Local Policy Objectives (LPO) are quantitative objectives to be achieved by 2024 across Valtom's nine collection territories. Specifically, the four LPO are:

* LPO1. The amount of food waste digested in the methanisation unit by 2024 should be at least 5700 tons. This is expressed mathematically as:

$$
B_f^m(2024) \geq 5700 \text{ tons} \tag{38}
$$

* LPO2. The total amount of digested food and green waste in the methanisation unit should exceed 12000 tons by 2024. This is expressed as:

$$
B^m(2024) \geq 12000 \text{ tons} \tag{39}
$$

* LPO3. There should be a 12 % decrease between 2017 and 2024 in the flow of green waste received at the valorisation centres from all nine collection territories. This is mathematically represented as:

$$
\sum_{j=1}^{n} B_{g,j}^{y}(2024) \leq 0.88 \sum_{j=1}^{n} B_{f,j}^{y}(2017) \quad (40)
$$

* LPO4. There should be a 50 % decrease between 2017 and 2024 in the flow of food waste in the residual waste from all nine collection territories. This is expressed as:

$$
\sum_{j=1}^{n} B_{f,j}^{r}(2024) \leq 0.50 \sum_{j=1}^{n} B_{f,j}^{r}(2017) \quad (41)
$$

While these LPOs provide a unifying policy framework, the diverse
characteristics of the Valtom collection territories necessitate various
Local action plans LPA to possibly meet these objectives. They have been
defined by the local stakeholders in terms of a progressive increase of
infrastructure's capacities for home composters and dedicated collec-
tion. The value of the capacities is chosen to reach the LPO, assuming
that these capacities would be fully utilized by people at the time they
are available. The local policy action (LPA) also involves an Anti-
Biowaste Plan (ABP), applied to everybody in Valtom's territory, aim-
ing for a 50 % reduction in lost food waste.

By applying the generic stock-and-flow model structure to the spe-
cific context of the Valtom territory, the simulation aims to better un-
derstand how these LPA may achieve the LPO by unveiling the
complexity of the social-technical dynamics of biowaste management
across the nine collection territories.

Each collection territory has been supplied with home composters K<sup>c</sup>, while only SBA and CAM have been provided with collection infra-

<footnote n="1">¹ Note that all territories are designated by 3 letters in the main text for the sake of clarity. The full names of the nine territories are given in Table 1.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Demographic and Administrative Overview of the Valtom Territory. Municipalities with more than 3000 inhabitants (Legend of the right figure: Valtom border: Outlined in red, Population of municipalities: <3000 inhabitants in White, >3000 inhabitants in Orange). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

structure $K^s$—SBA for food waste and CAM for both food and green waste.

Only SBA and CAM collection territories have the potential to contribute to the LPOs concerning methanisation objective, which is filled from the collection infrastructure flows, defined by their sorting behaviour, their collection infrastructure capacity, and possibly their food composting-part surplus $U_f^c(2024)$.

All collection territories have the potential to contribute to the LPO of reducing green waste deposited at the valorisation centre through their sorting for home composting behaviour and their compost infrastructure capacity $K^c$. Additionally, only CAM can contribute through its sorting behaviour and its collection infrastructure capacity $K^s$. However, their contributions are negatively impacted by the surplus of every collection territory from green composting $U_g^c(2024)$ and, in CAM's case, the green sorting-part surplus from dedicated collection $U_g^s(2024)$, both of which are sent to valorisation centres.

Similarly, all collection territories have the potential to contribute to the LPO of reducing food waste in residual household waste through their sorting for home composting behaviour and infrastructure capacity. SBA and CAM also contribute through their sorting behaviour and collection infrastructure capacity. Nonetheless, the surplus from food composting-part $U_f^c(2024)$ from the rest of collection territories and the food sorting-part $U_f^s(2024)$ from SBA and CAM collection territories negatively affect this contribution, as these surpluses end up in residual household waste.

### 3.4. Initialisation and parameterization of the model for the Valtom territory

Initial values and parameters are initialised according to the data from the STGDO's diagnosis, which has been done by the stakeholders to define their LPA and LPO (Valtom, 2018, 2019a, 2019b). They differ for each collection territory.

#### 3.4.1. Initialisation of the model for the Valtom territory

The parameters and initial state variables in 2017 are given in the following table for each collection territory.

Demographic values correspond to data from the French census, as well as *r*, corresponding to the linear evolution of the collection territories' population during the two last censuses. The initial per capita waste production and the proximity capacities (home composter and dedicated collection) are chosen according to the Valtom report's values, which are built from the estimated or measured flows.

Since we lack information about the actual behavioural intentions (sorting for home composting and sorting for dedicated collection) at this initial time, we assume that the initial behavioural intentions are at the minimum values necessary to explain the estimated or measured

flows, considering the infrastructure capacities (for individual composter and collection) are fully used. This means we assume there is no surplus at the beginning of the simulation. However, it is possible that the initial behavioural intentions were higher than the values we used for simulation in this study.

In other words, it is possible that part of the real observed flow in 2017 was explained by a surplus due to a higher behavioural intention compared to the infrastructure capacity. Indeed, in such a case, a part of the flow potentially generated by the intention is redirected to another infrastructure, such as the residual waste bin.

#### 3.4.2. The experimental design to study the interplay between infrastructure implementation and behavioural intentions

The LPA has been defined by local stakeholders, assuming that an increase in capacity is sufficient to reach the LPO. We argue that the intricate socio-technical dynamics of the Valtom territory's biowaste management system require taking into account both the technical aspects (e.g., infrastructure capacity) and the behavioural aspects (e.g., the behaviours reducing the production of food waste, the household sorting for home composting and sorting for dedicated collection behaviours intentions). That is why we adopt in this paper an analytical approach that distinctly addresses its infrastructure (soft such as advertising and training actions to help household reducing their food waste of the ABP, hard such as the increase of the capacity of the collection equipment for example), and the behavioural elements. To better understand this complex interplay, the research studies two sets of scenarios presented further.

We start with the presentation of the parameter values of the dynamics which are not changed in the experimental design. Then we describe the tested scenarios through the varying parameters.

The simulation runs from 2017 to 2030, checking for the LPO in $\tau = 2024$. The fixed LPA parameters are those related to the anti-biowaste plan (ABP). They are described in Table 3. This means that the adoption of the anti-biowaste plan is expected to reach 50 % in 3.5 years (i.e., $m_f^p = m_g^p = 3.5$) after its introduction. The capacity of the methaniser is set at $K^m = 20,000$ tons while the capacities for the incinerator and professional composting are considered infinite. Table 3 presents the set of all fixed parameters used in our results.

A first experimental design aims to understand how the change in behaviours due to the Anti-Biowaste Plan (ABP) on the one hand, and the demographic dynamics on the other hand, influence the achievement of policy objectives. We consider a business-as-usual scenario, in which only the size of the populations of the collection territories evolves over time, changing the quantity of produced biowaste (see Table 2 for the values of *r*, the growth rate of the populations). A second scenario adds to this first one, the ABP and its associated behaviour change (i.e. increase of behaviours reducing food waste). The
<table><caption>**Table 1**
Population Distribution and Communal Structure in the VALTOM Territory: Source STGDO n°1.</caption><thead><tr><th>Code</th><th>Collectivity</th><th>Population</th><th>Total number of Communes</th><th>Number of communes with more than 3000 inhabitants</th><th>Urban/Rural Classification</th></tr></thead><tbody><tr><td>ALF</td><td>Community of Communes Ambert Livradois Forez</td><td>28,197</td><td>58</td><td>1</td><td>Rural</td></tr><tr><td>CAM</td><td>Clermont Auvergne Métropole</td><td>284,672</td><td>21</td><td>18</td><td>Urban</td></tr><tr><td>SCB</td><td>SICTOM of Combrailles</td><td>17,804</td><td>41</td><td>1</td><td>Rural</td></tr><tr><td>SCZ</td><td>SICTOM of Couzes</td><td>26,516</td><td>46</td><td>0</td><td>Rural</td></tr><tr><td>SIB</td><td>SICTOM Issoire-Brioude</td><td>93,225</td><td>144</td><td>6</td><td>Rural</td></tr><tr><td>SDC</td><td>SICTOM Pontaumur-Pontgibaud</td><td>18,216</td><td>33</td><td>0</td><td>Rural</td></tr><tr><td>SHD</td><td>SMCTOM of the Haute-Dordogne</td><td>16,001</td><td>35</td><td>0</td><td>Rural</td></tr><tr><td>SBA</td><td>Syndicat du Bois de l'Aumone</td><td>165,000</td><td>123</td><td>11</td><td>Urban</td></tr><tr><td>TDM</td><td>Thiers Dore Montagne</td><td>37,559</td><td>30</td><td>2</td><td>Rural</td></tr><tr><td></td><td>VALTOM Total</td><td>687,190</td><td>531</td><td>39</td><td>Mixed</td></tr></tbody></table>

comparison of the quantity of food waste yearly produced for each of these two scenarios allows understanding of the effect of the interplay of the demography and the Anti-Bio Waste Plan (ABP) on the achievement of the Local Policy Objectives.

The second experimental design aims to understand the effect of the interplay of behavioural intention changes related to sorting (for home-composting or dedicated collection), and the change in the capacity of the proximity equipment due to the Local Policy Actions. Then, starting from the simulation of both the demography and the ABP, we investigate the following scenarios:

- Scenario n° 1 considers that there is no change in intention regarding sorting for composting and sorting for dedicated collection, but the investment is made to increase the capacities of proximity equipment (home composters and dedicated collection) over time. This corresponds to infinite value of $m_f^c$, $m_g^c$, $m_f^s$, $m_g^s$ implying the speed of change is so low that behavioural change over the time of the plan is not

significant. It means that sorting for home composting and sorting for dedicated collection are constant over time and are equal to their initial values. Indeed, here, we investigate the influence of the home composter and dedicated collection capacities evolution according to Table 4 describing the LPAs for the development of proximity equipment.

- Scenario n° 2 considers that there is no limitation on proximity equipment and large-scale shared infrastructure capacity, while intentions related to sorting for home composting and sorting for dedicated collection are changing. Then it manipulates the values of $m_f^c$, $m_g^c$, $m_f^s$, $m_g^s$, varying them from 1 year to 14 years by step 1 year with the hypothesis that the speed of change in intention is different for sorting for home composting and sorting for dedicated collection, but the same for green and food waste, i.e. $m_f^c = m_g^c$ and $m_f^s = m_g^s$.

- Scenario n° 3 aims to illuminate the simultaneous change of behaviours and capacities. In other words, we tested changes in sorting for home composting and sorting for dedicated collection intentions, and in home composter and dedicated collection capacities.

For the second and third scenarios, we track the behavioural changes, focusing on the critical inflexion points of sorting for home composting and sorting for dedicated collection behaviours depending on the initial intentions, which are instrumental in assessing the progress toward the local policy objectives set for 2024. Focusing on the year 2024, we tested a spectrum of $m^c$ and $m^s$ values, ranging from 1 year to 14 years, cumulatively simulating the system's trajectory across 196 distinct parameter configurations (14 × 14). Each configuration embodies an intention of adoption scenario for sorting for home composting and sorting for dedicated collection behaviours, and their compounded effect on achieving the local policy objectives. Through this experimental design, we manipulated the speed of change of the behaviour intention for sorting for home composting and sorting for

<table><caption>**Table 3**
Fixed parameters used in the simulations.</caption><thead><tr><th rowspan="3">Collection territories<br>Anti-biowaste<br>characteristics</th><th colspan="3">Anti-biowaste production ABP</th></tr><tr><th>Policy action on<br>food reduction's<br>values</th><th>Policy action of<br>green reduction's<br>values</th><th>intention<br>diffusion half-<br>time (green and<br>food)</th></tr><tr><th>a<sub>f</sub><sup>p</sup></th><th>a<sub>g</sub><sup>p</sup></th><th>m<sub>f</sub><sup>p</sup>, m<sub>g</sub><sup>p</sup></th></tr></thead><tbody><tr><td>SBA</td><td>0.3</td><td>0.106</td><td>3.5</td></tr><tr><td>CAM</td><td>0.5</td><td>0.049</td><td>3.5</td></tr><tr><td>TDM</td><td>0.5</td><td>0.080</td><td>3.5</td></tr><tr><td>ALF</td><td>0.3</td><td>0.155</td><td>3.5</td></tr><tr><td>SCZ</td><td>0.5</td><td>0.169</td><td>3.5</td></tr><tr><td>SIB</td><td>0.5</td><td>0.124</td><td>3.5</td></tr><tr><td>SCB</td><td>0.5</td><td>0.091</td><td>3.5</td></tr><tr><td>SDC</td><td>0.5</td><td>0.094</td><td>3.5</td></tr><tr><td>SHD</td><td>0.5</td><td>0.092</td><td>3.5</td></tr></tbody></table>

<table><caption>**Table 2**
Initial state variables and parameters, shared infrastructure capacities $K^m = 20000$, $K^c + K^g$ and $K^i$ are infinite, note:"-" indicates no infrastructure.</caption><thead><tr><th rowspan="2">Collection territories</th><th colspan="2">Demographic parameters</th><th colspan="2">Initial per capita waste production in Kg/year</th><th colspan="4">The initial intention expressed in % (sorting for home composting and sorting for dedicated collection)</th><th colspan="2">Proximity capacities (home composter and dedicated collection)</th></tr><tr><th>P</th><th>r</th><th>b<sub>g</sub><sup>p</sup></th><th>b<sub>f</sub><sup>p</sup></th><th>α<sub>g</sub><sup>c</sup></th><th>α<sub>f</sub><sup>c</sup></th><th>α<sub>g</sub><sup>s</sup></th><th>α<sub>f</sub><sup>s</sup></th><th>K<sup>c</sup></th><th>K<sup>s</sup></th></tr></thead><tbody><tr><td>SBA</td><td>165000</td><td>0.006</td><td>92</td><td>71</td><td>12.7</td><td>20.1</td><td>0</td><td>0</td><td>4255</td><td>0</td></tr><tr><td>CAM</td><td>284672</td><td>0.009</td><td>78</td><td>77</td><td>3.3</td><td>4</td><td>36</td><td>3</td><td>1617</td><td>8660</td></tr><tr><td>TDM</td><td>37559</td><td>0.004</td><td>100</td><td>75</td><td>4.1</td><td>5.5</td><td>0</td><td>0</td><td>304</td><td>-</td></tr><tr><td>ALF</td><td>28197</td><td>-0.001</td><td>61</td><td>89</td><td>16.2</td><td>13.5</td><td>0</td><td>0</td><td>614</td><td>-</td></tr><tr><td>SCZ</td><td>26516</td><td>0.004</td><td>46</td><td>75</td><td>18.5</td><td>13.4</td><td>0</td><td>0</td><td>495</td><td>-</td></tr><tr><td>SIB</td><td>93225</td><td>0.003</td><td>80</td><td>91</td><td>13</td><td>14.3</td><td>0</td><td>0</td><td>2152</td><td>-</td></tr><tr><td>SCB</td><td>17804</td><td>0.004</td><td>86</td><td>91</td><td>9.6</td><td>10.7</td><td>0</td><td>0</td><td>318</td><td>-</td></tr><tr><td>SDC</td><td>18216</td><td>0.001</td><td>83</td><td>89</td><td>10.5</td><td>11.2</td><td>0</td><td>0</td><td>346</td><td>-</td></tr><tr><td>SHD</td><td>16001</td><td>-0.002</td><td>84</td><td>107</td><td>7.8</td><td>7.5</td><td>0</td><td>0</td><td>230</td><td>-</td></tr></tbody></table>
<caption>**Table 4**</caption>

Values of the proximity equipment capacities development (home composter, and dedicated collection unit) reached in 2024 in the simulations for scenario 1 on the left, the scenario 2 on the right, with methanisation unit capacity at 20,000 since 2017. Note:"-" indicates no infrastructure in the corresponding territory.

<table><thead><tr><th rowspan="2">Collection territories</th><th colspan="5">Scenario n° 1</th><th colspan="5">Scenario n° 2</th></tr><tr><th>K<sup>c</sup></th><th>K<sup>s</sup></th><th>K<sup>m</sup></th><th>K<sup>c+</sup></th><th>K<sup>i</sup></th><th>K<sup>c</sup></th><th>K<sup>s</sup></th><th>K<sup>m</sup></th><th>K<sup>c+</sup></th><th>K<sup>i</sup></th></tr></thead><tbody><tr><td>SBA</td><td>6918</td><td>2214</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>infinite</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CAM</td><td>4228</td><td>10360</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>infinite</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TDM</td><td>1178</td><td>-</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ALF</td><td>1279</td><td>-</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SCZ</td><td>836</td><td>-</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SIB</td><td>4310</td><td>-</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SCB</td><td>740</td><td>-</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SDC</td><td>663</td><td>-</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SHD</td><td>642</td><td>-</td><td>-</td><td>-</td><td>-</td><td>infinite</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Shared infrastructure</td><td>-</td><td>-</td><td>20000</td><td>infinite</td><td>infinite</td><td>-</td><td>-</td><td>infinite</td><td>infinite</td><td>infinite</td></tr></tbody></table>

dedicated collection ($m^c$ and $m^s$) to ascertain the minimum required behaviour intention in 2024 to meet local policy objectives by $\tau = 2024$.

## 4. Results

### 4.1. Synthesis of influential factors on achieving policy objectives for biowaste management

This section presents an overview of the main results about the influence of the various modelled processes and/or scenarios on the achievement of the LPO for biowaste management. The purpose is then to detail these results in the following section. Table 5 synthesizes the impacts of different factors and contrasts scenarios on the achievement of the LPO in 2024 as follows:

1. **The impact of the anti-biowaste plan:** The reduction of the production of waste associated with the anti-biowaste plan (ABP) has globally a positive impact on the achievement of the objectives of reduction and a negative one on the objectives of increase. Overall, the ABP is never sufficient to reach the reduction objectives.

2. **The impact of infrastructure dynamics without behavioural dynamics:** this hypothesis explores a scenario in which there is no change in behaviour regarding sorting biowaste for home composting and sorting for dedicated collection intentions, but the investment is made to increase the capacity of the proximity equipment (home composters and dedicated collection) over time. The purpose is to test the influence of infrastructure characteristics alone on biowaste management and to analyse how the dynamics of biowaste production and investment in infrastructure interact. However, the simulation results demonstrate that improvements in proximity

equipment have no impact on achieving any of the LPOs because existing infrastructure has sufficient capacity in the absence of behavioural changes. The results are detailed in Section 4.2. A parallel evolution in behaviour (sorting for home composting and sorting for dedicated collection intentions) is therefore essential for the realisation of LPOs, which is the purpose of the next factor exploration.

3. **The impact of behavioural intentions dynamics without infrastructure constraints:** this hypothesis explores a scenario where there are no limitations on infrastructure capacity while behaviours related to sorting biowaste for home composting and sorting for dedicated collection intentions are changing. The purpose is to focus on behavioural intentions in a context where infrastructure is not a limiting factor. In such a context, intentions always become actual behaviours. Table 5 shows that all LPOs can be achieved in this case, even if the objectives implying an increase of methanised flows require these behaviours to reach a certain intention value. More details will be provided in Section 4.3.

4. **Socio-technical dynamics:** this approach integrates the evolution of both proximity equipment (home composters and dedicated collection) and behavioural intentions. The purpose is to focus on how social behavioural and technical dynamics interact to achieve LPOs. The results suggest the desired reduction of green waste in the valorisation centre can't be satisfied. The three other LPOs are reached, even if the increase of total methanised biowaste requires a certain level of behavioural intentions. More details about these dynamics are elaborated in Section 4.4.

<caption>**Table 5**</caption>

Impact of various processes and/or scenarios on the LPOs.

<table><thead><tr><th>Factors<br>LPOs</th><th>The impact of ABP without any<br>change in behavioural intentions<sup>a</sup><br>and capacities<sup>b</sup></th><th>infrastructure dynamics<br>(Unchanged behavioural<br>intentions<sup>a</sup>, increasing<br>capacities<sup>b</sup>)</th><th>Behavioural intentions<br>dynamics (Changing<br>behavioural intentions<sup>a</sup>,<br>infinite capacities<sup>b</sup>)</th><th>Social-Technical<br>Dynamics (Changing<br>behavioural intentions<sup>a</sup>,<br>increasing capacities<sup>b</sup>)</th></tr></thead><tbody><tr><td>Objective: Enhance the food waste entering in the<br>methanisation unit B<sup>m</sup><sub>f</sub>(2024)<br>≥ 5700 tons</td><td>Negative impact<br>Not achieved</td><td>Not achieved</td><td>Can be achieved</td><td>Achieved</td></tr><tr><td>Objective: Enhance the total biowaste in the<br>methanisation unit B<sup>m</sup>(2024) ≥ 12000 tons</td><td>Negative impact<br>Not achieved</td><td>Not achieved</td><td>Can be achieved</td><td>Can be achieved</td></tr><tr><td>Objective: reduce the green waste received at<br>valorisation centres<br>∑<sup>n</sup><sub>j=1</sub> B<sup>v</sup><sub>gj</sub>(2024) ≤ 0.88 ∑<sup>n</sup><sub>j=1</sub> B<sup>v</sup><sub>gj</sub>(2017)</td><td>Positive impact<br>Not achieved</td><td>Not achieved</td><td>Achieved</td><td>Not achieved</td></tr><tr><td>Objective: reduce the food waste in residual waste<br>streams. ∑<sup>n</sup><sub>j=1</sub> B<sup>fj</sup><sub>fj</sub>(2024) ≤ 0.50 ∑<sup>n</sup><sub>j=1</sub> B<sup>fj</sup><sub>fj</sub>(2017)</td><td>Positive impact<br>Not achieved</td><td>Not achieved</td><td>Achieved</td><td>Achieved</td></tr></tbody></table>

<footnote>a Intentions are sorting for home composting and sorting for dedicated collection intentions $\alpha_f^c(t)$, $\alpha_f^s(t)$, $\alpha_g^c(t)$, $\alpha_g^s(t)$, $\alpha_g^v(t)$, while.</footnote>

<footnote>b 'Capacity' relates to the size in tons of the proximity equipment (home composters and dedicated collection) $K^c(t)$, $K^s(t)$.</footnote>
## 4.2. How do ABP, demographics and infrastructure dynamics influence the achievement of the policy objectives?

In this section, we analyse the dynamic effects of the Anti-Biowaste Plan (ABP), demographic changes, and proximity equipment developments (home composters and dedicated collection) on achieving the LPOs for biowaste management. The ABP is an action plan aimed at reducing household biowaste production through its timeline implementation and its reduction amplitude that implies shifts in household behaviours. We address the critical role of biowaste production, analysing the impact of the ABP in conjunction with the changing demographic landscape of the Valtom collection territories.

In our trajectory analysis, we investigate the dynamics of food waste $B_f^p(t)$ and green waste $B_g^p(t)$ production across the Valtom collection

territories. We evaluate the influence of ABP in terms of limitations of food and green waste production ($a_f^p(\tau)$ and $a_g^p(\tau)$ parameters), along with the implementation timeline (represented by parameter $m_f^p$, $m_g^p$ in Eq. (1) and (2)), and demographic parameters such as initial populations size $P(2017)$, growth rates $r$, and per capita biowaste productions $b_f^p$, $b_g^p$. These parameters are given in section 3.4.1 (in Tables 2 and 3), enabling a comparative analysis of SBA, CAM, rest of collection territories, and total Valtom collection territories.

Fig. 4 visualises the biowaste production with and without the implementation of the ABP, highlighting the biowaste production due to behavioural change. The 'Behaviour-Driven Waste Reduction Phase' is indicated in green, showing periods where ABP's impact is dominant, while the 'Population Growth Dominant Phase' is shown in red, marking periods where population growth counteracts the ABP's effects.

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Temporal dynamics of biowaste production with and without ABP behavioural interventions (2017–2030) in the VALTOM territory: (a) food waste trajectory, (b) green waste trajectory. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
The transition between these phases is marked by the critical time point *t*\*, representing the inflexion point where initial ABP-driven waste reduction benefits are counteracted by population growth. The determination of *t*\* is based on the intersection of ABP plans and the demographic parameters within each collection territory. For example, in urban collection territories like SBA and CAM, the shift to the 'Population Growth Dominant Phase' occurs earlier (2023 and 2022 for green waste, and 2025 for food waste), reflecting their higher population growth rates. Conversely, rural collection territories encounter a delayed transition to this phase (2026 for green waste and 2029 for food waste), indicating a prolonged period of effective ABP-driven waste reduction, as synthesised in Table 6 for food and green waste productions.

The timing of the critical point, *t*\*, is crucial, especially considering the benchmarks set by the local policy objective for 2024. This year, we evaluated how well the Anti-Biowaste Plan (ABP) aligns with the later stages of the local policy objectives. To do so, we use simulation analysis to determine when *t*\* occurs and how it influences the outcomes of the ABP in 2024. This analysis helps us understand how the ABP's distinct objectives in each collection territory interact with demographic factors, either advancing or impeding the achievement of local policy objectives. For instance, Fig. 4a shows a significant reduction in food waste by 41.25 % by 2024 (31900 tons), which occurs within the Behaviour-driven Waste Reduction Phase (*t*\* = 2026). This reduction is mainly due to the demographic characteristic of the broader Valtom collection territories and the ABP's amplitude in encouraging households to decrease food waste, positively impacting the local policy objective to minimize residual food waste. However, this reduction also poses a challenge for enhancing methanisation of food waste, as the effective reduction in available biowaste may reduce the feedstock needed for food methanisation processes. Conversely, Fig. 4b shows only a 4.71 % reduction in green waste by 2024 (53342 tons), occurring within the Population Growth Dominant Phase (*t*\* = 2023). This lower impact is due to the objective amplitude of the ABP on green waste reduction at the household level, which negatively affects the LPO to minimize green waste at valorisation centres. However, it contributes positively by providing a larger quantity of green waste for methanisation, enhancing the methanised green waste portion.

The broader Valtom collection territories analysis reveals a quicker transition to the 'Population Growth Dominant Phase' — *t*\* = 2023 for green waste and *t*\* = 2026 for food waste — resulting in aggregate demographic growth rates. This shift from green to red shading is visualized in Fig. 4a and b.

The previous results unveiled the dynamic effects of the ABP and demographic changes on biowaste production, as well as their impact on achieving the local policy objectives for biowaste management. Building upon these findings, our analysis now turns to the combined influence of proximity equipment developments (home composters and dedicated

collection) on meeting LPO.

In proximity equipment development, we explore a scenario where behavioural intentions related to sorting biowaste for home composting and sorting for dedicated collection remain unchanged across collection territories (people do not change their habits), whereas there is a progressive investment to expand the capacity of proximity equipment including home composters and dedicated collection equipment. This investigation aims to investigate the interplay between the initial unchanging behavioural intentions characteristics across Valtom collection territories and infrastructure characteristics—such as type, initial capacity, target capacity, and location—on meeting the local policy objectives. This approach is intended to reveal the infrastructure's influence and how it might synergize with ABP initiatives to advance policy objectives.

Table 7 shows that the development of the proximity equipment has no impact on the achievement of the LPOs. The fourth and fifth columns of the table contain the same values, indicating that progress towards the LPOs is exclusively due to the ABP. This is expected, as the initial capacities are assumed to be sufficient for the flows, and the initial behavioural intentions are chosen at the minimum value to explain the flow. This means we assume there is no surplus at the beginning of the simulation. Therefore, increasing capacity does not affect the results regarding LPO achievement, while flows decrease due to the ABP. If a surplus had existed initially, the results would have been different. The existing infrastructure is sufficient for managing biowaste in this case, therefore.

Based on the infrastructure and behavioural intentions characteristics within Valtom collection territories, all collection territories are equipped with home composters, yet only CAM and SBA feature biowaste dedicated collection equipment. Thus, the initial intentions are heterogeneous between collection territories, particularly sorting for dedicated collection (CAM's green sorting intention for dedicated collection is 36%, and food sorting for dedicated collection is 3%; both are zero in SBA). This difference in intentions between collection territories influences the effectiveness of these infrastructural elements.

This section has disentangled the impact on the achievement of LPOs of ABP and infrastructure dynamics without change in sorting for home composting and sorting for dedicated collection intentions. In the next section, we investigate the specific impact of the evolution of behaviours in the absence of constraints linked to the infrastructure capacities.

<caption>**Table 7**</caption>

The evolution of flows and stocks in comparison to the LPOs without household behavioural change regarding sorting for home composting and sorting for dedicated collection. As shown by the last column, proximity equipment development does not affect the achievement of the objective in the presence of ABP. It means that the existing infrastructure is sufficient and that intention changes are required.

<table><caption>**Table 6**</caption><thead><tr><th>Biowaste Category</th><th>Initial State (2017, tons/ year)</th><th>LPO (2024)</th><th>Impact of ABP in LPOs without proximity equipment development</th><th>Impact of ABP in LPOs with Proximity equipment development</th></tr></thead><tbody><tr><td>Food waste in residual household waste</td><td>47,944</td><td>-50 %</td><td>-41.61 %</td><td>-41.61 %</td></tr><tr><td>Green waste in valorisation Centres</td><td>43,261</td><td>-12 %</td><td>-5.59 %</td><td>-5.59 %</td></tr><tr><td>Methanised food waste</td><td>662</td><td>+5700 tons</td><td>-298 tons</td><td>-298 tons</td></tr><tr><td>Methanised total biowaste (food and green)</td><td>8662</td><td>+12,000 tons</td><td>-175 tons</td><td>-175 tons</td></tr></tbody></table>

Critical times (*t*\*) occurrence and biowaste production in 2024 across Valtom Collection Territories.

<table><thead><tr><th>Collection territories characteristics</th><th>Results</th><th>SBA (Urban)</th><th>CAM (Urban)</th><th>Rural collection Territories</th><th>Total collection territories</th></tr></thead><tbody><tr><td>Critical time for food waste trajectory</td><td>t*</td><td>2025</td><td>2025</td><td>2029</td><td>2026</td></tr><tr><td>Food waste production in 2024</td><td>B<sup>o</sup><sub>f</sub> (2024)</td><td>8698</td><td>11958</td><td>11242</td><td>31900 (-41.25 %)</td></tr><tr><td>Critical time for green waste trajectory</td><td>t*</td><td>2023</td><td>2022</td><td>2026</td><td>2023</td></tr><tr><td>Green waste production in 2024</td><td>B<sup>o</sup><sub>g</sub> (2024)</td><td>14198</td><td>22560</td><td>16583</td><td>53342 (-4.71 %)</td></tr></tbody></table>
### 4.3. Influence of behavioural intention dynamics: exploring behaviour change without infrastructure limitations

This section examines the influence of behavioural intention dynamics in achieving local policy objectives (LPOs) in a hypothetical scenario where there is no limitation on infrastructure capacity for the infrastructures expected to be present in 2024. Accordingly, every collection territory has an infinite composter capacity, and only SBA and CAM, the urban collection territories, have an infinite collection capacity.

In this context, intention directly translates to actual behaviour adoption, as there are no physical constraints preventing households from sorting for home composting or sorting for dedicated collection according to their intentions. This equivalence is assumed for modelling purposes and does not imply that underlying behavioural processes—such as social interaction, norms, attitudes, or perceived control—are explicitly simulated.

Specifically, we analyse how varying sorting for home composting and sorting for dedicated collection behavioural intentions (represented by $\alpha_g^c(t)$; $\alpha_f^c(t)$, $\alpha_g^v(t)$, $\alpha_f^v(t)$) impact the achievement of LPOs. These intentions are modelled using the innovation diffusion framework, with parameters $m^c$ and $m^s$ representing the time it takes for 50 % of the population to adopt the intention to compost and sort, respectively (see 3.2.1.5 for details), meaning that lower values of $m$ indicate faster change of intentions.

We recall that sorting for home composting is prioritised over sorting for dedicated collection when the two intentions sum higher than one, meaning in such a situation, significant sorting for dedicated collection intention is dependent on lower levels of sorting for home composting intention behaviour (see Eqs (15) and (17)). This relationship is crucial as it influences the overall effectiveness of achieving all LPOs. The adoption dynamics between sorting for home composting and sorting for dedicated collection intentions are interlinked, with sorting for dedicated collection intention influenced by the sorting for home composting intention. Faster sorting for home composting intention (lower $m^c$) restricts the development of sorting for dedicated collection intention because of its prioritisation, as explained before.

Fig. 5 illustrates how different combinations of sorting for home composting and sorting for dedicated collection behavioural intentions influence the achievement of LPOs in 2024 when there are no

infrastructure limitations. It shows that, regardless of the speed of change of behavioural intentions $m^c$ and $m^s$ values, two objectives are consistently met:

1. The minimum 50 % reduction in food waste in residual household waste streams, is due to two factors. The first one (and the strongest) corresponds to the effect of the Anti-Biowaste Plan (ABP). As we have seen in Section 4.2, the ABP contributes to a considerable reduction in food waste (41.25 %), further supporting the achievement of this objective. This means that only small behavioural complementary efforts are needed to meet this LPO which corresponds to the second factor explaining that this LPO is met. This small effort is realised helped by the prioritisation of sorting for home composting over sorting for dedicated collection when the combined both behaviours exceed one. This leads to a significant diversion of food waste from residual household waste streams to composters. This diversion is effective even when the speed of change of sorting for home composting behavioural intentions is slow ($m^c = 14$), with a minimum sorting for home composting behavioural intentions value of 0.52 for all collection territories due to high enough initial behavioural intentions of sorting for home composting (see section 3.4.1: Table 2 for the exact values). For a detailed analysis of the food sorting for home composting behavioural intentions values see Appendix B section B.2.

2. The minimum 12 % reduction in green waste at valorisation centres. This reduction is firstly explained by the prioritisation of sorting for home composting over sorting for dedicated collection which ensures a substantial diversion of green waste away from valorisation centres. The achievement of this LPO across all $m^c$ and $m^s$ values is secondly explained by the moderate initial sorting green waste for home composting behavioural intentions (from 3.3 to 18.5 % of the produced flows depending on collection territories see section 3.4.1: Table 2 for the exact values), and the ABP's impact on green waste reduction (i.e., -4.71 % of production). For a detailed analysis of the sorting food waste for home composting behavioural intentions values see Appendix B section B.3.

However, meeting the objective of total methanised biowaste, to which only CAM and SBA contribute, requires a trade-off between sorting for home composting and sorting for dedicated collection speeds

<figure><img src="image_7.png" /><figcaption>Fig. 5. Influence of the sorting for home composting and sorting for dedicated collection to methanisation behavioural intention on achieving Local Policy Objectives (LPO) in 2024. The green colour and corresponding symbols mean that the objective is met, whereas the red colour means that the objective is not met. This matrix displays outcomes across different $m^c$ and $m^s$ values, representing the midpoints (in years) of sorting for home composting and sorting for dedicated collection to methanisation behavioural intentions, respectively, highlighting the effectiveness of household's behaviour changes in achieving LPOs when there is no infrastructure limitation. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
of adoption. The rapid adoption of sorting for home composting (low $m^c$) can restrict sorting for dedicated collection due to the prioritisation of sorting for home composting. Thus, as shown in Fig. 5 a $m^c$ higher than 10 years is required to reach this objective.

Regarding the objective of methanised food waste, a more trade-off approach between the speed of change of sorting for home composting and sorting for dedicated collection behavioural intentions is necessary: a minimum $m^c$ = 10 years is required with a corresponding maximum sorting behavioural intention when $m^s$ = 10. For this objective and larger $m^c$, we observe a change of regime during the temporal evolution of the sorting for dedicated collection behavioural intentions compared to the sorting for home composting behavioural intentions. In the first years, the sorting for dedicated collection behavioural intentions is computed from Eqs. (15) and (17) without being constrained by the sorting for home composting behavioural intentions. Since a critical year, that we call y\*, for which the sorting for home composting and the sorting for dedicated collection behavioural intentions sum higher than 1, the sorting for dedicated collection behavioural intentions become constrained by the sorting for home composting behavioural intentions (computed from Eqs. (14) and (16)). The value of y\* depends then of both minimum $m^c$ and $m^s$. Reaching the objective of methanised food waste implies sufficient sorting behavioural intentions in 2024, the date of the objective. Such sufficient behavioural intentions can be reached in 2024 only when y\* is higher than 2024. Indeed, a small value of $m^s$ implying a quick increase of the sorting behavioural intentions, and thus reduce the date of y\*. For a more detailed analysis of the data and models underlying these findings, refer to Appendix B.

However, when the sorting for home composting behavioural intentions is lower ($m^c$ > 12), it does not hinder sorting for dedicated collection and LPO of methanised food waste is always met whatever the value of $m^s$ mainly due to the contribution of CAM collection territory.

These behavioural intentions combinations are essential because the anti-biowaste plan (ABP) in the local policy action (LPA) restricts achieving the objective of increasing the food waste portion in methanisation, while its impact on green waste is lower. Therefore, both higher sorting for home composting behavioural intentions and ABP restricts this objective, while even with the constraints of sorting for home composting intention, the green waste volume is sufficient to achieve the total biowaste objective due to lower impact of ABP on green waste production.

These results underscore the need for a policy that dynamically promotes either sorting for home composting or sorting for dedicated collection intentions based on specific objectives. By adjusting $m^c$ and $m^s$ values (the speed of change in intention adoption), policy-makers can manage the transition toward enhanced biowaste management practices, ensuring the achievement of all LPOs, especially those related to methanisation.

### 4.4. Influence of socio-technical dynamics: exploring behavioural intentions change with infrastructure limitations

This section examines the influence of behavioural intentions dynamics in achieving local policy objectives (LPOs) when there is infrastructure limitation. Specifically, we analyse how varying sorting for home composting and sorting for dedicated collection intentions under limited infrastructure capacity impact these objectives.

Similar to the previous analysis of behavioural intentions dynamics, sorting for home composting intentions are prioritised over sorting for dedicated collection. This means that faster adoption of sorting for home composting (lower $m^c$) can limit the development of sorting for dedicated collection intentions, significantly influencing the effectiveness of achieving all LPOs. When infrastructure limitations are considered, faster adoption of behavioural intentions leads to reaching capacity quickly, generating composer-part surplus and collection-part surplus of green waste first (see Eqs. 11 and 21).

Composter-part surplus of green waste from all collection territories

is directed to valorisation centres. For CAM, the only collection territory collecting green waste, the collection-part surplus of green waste also ends up at these centres, directly impacting the objective of reducing green waste at valorisation centres. Fig. 6 illustrates the influence of sorting for home composting and sorting for dedicated collection intention on the achievement of LPOs in 2024, with green indicating met objectives and red indicating unmet objectives.

Results from Fig. 6 show that regardless of $m^c$ and $m^s$ values, two objectives are consistently met:

1. The minimum 50% reduction in food waste in residual household waste streams. Even with infrastructure limitations, this objective is met as it was when there were no infrastructure limitations (see the previous section). The adoption of sorting for home composting and sorting for dedicated collection behaviour decreases food waste in residual household waste. Besides, the introduction of a limiting capacity of infrastructure (and the associated surplus) does not impact this result because the composer-part surplus of food waste is redirected to collection infrastructure, however, this surplus part goes to residual household waste when there is no collection infrastructure. No food waste from the collection part-surplus has been observed in the simulation. Only a small part of food waste from the composting-part surplus ends up in residual household waste. Therefore, this small part does not influence the achievement of the food waste reduction objective. For more details about the quantity of these surpluses see Appendix C section C2.

2. The minimum of 5700 tons of food waste in methanisation units. With infrastructure limitations, there is a limiting capacity for composters that cannot absorb all compostable food waste, even for low sorting for home composting behaviour. This surplus goes to the collection until reaching the collection capacity. Therefore, the maximum sorted food waste is reached, enabling the achievement of the food waste in methanisation unit objective. For more details about the quantity of this surplus see Appendix C section C1.

However, the objective of reducing green waste at valorisation centres is challenging to meet because faster sorting for home composting adoption generates a composer-part surplus of green waste first, which is directed to valorisation centres. Moreover, the sorting-part surplus of green waste from CAM further contributes to this challenge. Achieving the target for total methanised biowaste is only met when there is significant sorting and low composting, in order to divert green waste towards the methanisation centre.

For a more detailed analysis of the data and models underlying these findings, refer to Appendix C.

### 5. Discussion

We investigate the properties of a territorial biowaste management plan through a system dynamic modelling approach, focusing on the Valtom territory in France. By integrating both infrastructural development and behavioural dynamics, we analyse how these factors interact to influence biowaste management outcomes and meet local policy objectives. Our model simulates the evolution of biowaste production, infrastructure development and behavioural shifts, providing policymakers with key insights into conditions for reaching their biowaste policy objectives. These findings align with previous research highlighting the importance of considering both social and technical factors in waste management (Canali et al., 2016; Chia et al., 2024; Wang et al., 2021; Soma, Li, et al., 2020).

Our work focuses on understanding systemic dynamics, particularly the interplay between behavioural intention diffusion (e.g., speed of change in sorting for home composting or collection) and infrastructure implementation (capacity development). Though tested on the Valtom case study, the framework is designed to apply generically to waste management systems with capacity limits and evolving population
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Influence of sorting for home composting and sorting for dedicated collection to methanisation on achieving Local Policy Objectives (LPO) in 2024. Green colour means that the objective is met whereas red colour means that objective is not met. This matrix displays outcomes across different *m*<sup>c</sup> and *m*<sup>s</sup> values, representing the midpoints or speed of change of sorting for home composting and sorting for dedicated collection to methanisation intention, respectively, highlighting the effectiveness of household's intention changes in achieving LPO when there is infrastructure limitation. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

dynamics.

Our results show that the adoption of biowaste reduction behaviours by households promoted by the Anti-Biowaste Plan (ABP, while contributing to overall food and green waste reduction, reveals a critical interaction with demographic trends and affects local policy objectives. While effective in the short term, the impact of this adoption is limited by population growth in the mid-term. The critical time (t*) appears due to the relative speed of change between demographic characteristics (population size, population growth rate) and anti-biowaste plan (ABP) effectiveness. This splits an initial "behaviour-driven waste reduction phase" from a subsequent "population-growth dominant phase" during which waste production increases. A decision-maker comparing their own system with our case study can conclude that in a system with faster population growth, this inflection point will emerge earlier, making the achievement of local policy objectives difficult or impossible. Conversely, in a system with lower or negative population growth rate, this critical point might appear very late or not appear at all, potentially supporting the achievement of local policy objectives.

Furthermore, our results also demonstrate that solely relying on infrastructure development is insufficient. Even with significant capacity increases for home composters and dedicated collection equipment, the effectiveness of these upgrades is constrained by pre-existing behavioural intentions. Specifically, when behavioural intentions generate a lower or equal flow to the infrastructure capacity, the proximity equipment development has no impact on achievement of local policy objectives (LPOs), as observed in our study. Conversely, when household intentions exceed infrastructure capacity, the limitations of infrastructure can influence the achievement of LPOs. For example, if home composters capacities are too small in comparison of the households' intentions to compost green waste, households actually compost less than they intent to do, and must divert the rest of their green waste to the valorisation centre. Such diversion can hinder the achievement of LPOs.

Policymakers are often unable to identify the true cause of failure to meet LPOs. The usual conclusion is that “households are acting less than expected.” Our study acknowledges this as one possible explanation, but

also highlights those other reasons may exist for non-achievement. By pointing out these additional possibilities, our work enables decision-makers to conduct surveys to identify the true reason and acting accordingly. For example, asking households whether they have sufficient composting capacity. If the answer is no, then expanding capacity would be the appropriate action rather than focusing on changing household intentions (e.g., through education campaigns).

The framework's primary utility lies in enabling policymakers to evaluate their systems against generic critical times which arise from relative speeds of change between population dynamics, infrastructure development and behavioural intention diffusion. In Valtom, parameterization revealed specific conditions under which critical points emerge. These points represent generic issues applicable to other bio-waste systems with varying demographic profiles, behavioural intention diffusion, and infrastructure implementation speeds. By identifying these issues and explaining how they occur, our work offers actionable insights for decision-makers.

It is important to note that calibration of the model presents significant challenges due to the nature of the data required. Indeed, while we have accessed and calibrated some technical parameters using Valtom reports, comprehensive calibration would require simultaneous data on infrastructure capacity, household behavioural intentions, and the interactions between them. Such integrated data are rarely, if ever, collected in practice. Indeed, the only available data are trajectories of waste volumes collected for a territory. However, it is impossible to determine the underlying causes for a given volume: whether it results from low sorting intention, high sorting intention limited by bin capacity, or diversion through home composting. Furthermore, the evolution of household behavioural intentions over time is never measured directly. For these reasons, we adopted an exploratory approach, testing various parameters related to the relative speeds of change. This ensures that at least one trajectory aligns with real-world conditions, even though these conditions cannot be precisely known from available data.

Our model treats biowaste-sorting adoption as an innovation diffusion process (Rogers, 1995), aligned with the Loi Anti-Gaspillage pour une Économie Circulaire (AGEC – Anti-Waste Law for a Circular
Economy). In this context infrastructure provision is mandatory for municipalities, but household participation is voluntary and decoupled from economic incentives. This creates a setting where adoption hinges on social dynamics—imitation, peer influence, and norms. Our modelling approach is informed by studies showing that norms and knowledge-sharing drive household behaviour (Pei, 2019; Knickmeyer, 2020b; Bruno et al., 2022). It is also informed by large-scale surveys used to initialize and parameterize the dynamics of agent-based models of household practices where knowledge diffusion and neighbourhood imitation are drivers of adoption (Meng et al., 2016; Meng et al., 2024; Peng et al., 2021).

While this work offers valuable insights in biowaste management, it's important to acknowledge its limitations, many of which stem from the simplifying hypotheses made. Our model, while capturing key system components and interactions, makes certain assumptions regarding household behaviours and infrastructure warranting further investigation. For example, our model assumes homogeneous households within each collection territory, with behavioural intentions considered independent of each other, or of infrastructure factors, such as the distance between households and infrastructure, the influence of other behaviours, and the final fate of the biowaste. This simplification, while allowing for a tractable analysis, does not fully capture the complexity and heterogeneity of the real world.

Further, our system dynamics approach aggregates social causality and does not model individual behavioural mechanisms explicitly. While we model behavioural intentions and their diffusion at a population level, we do not capture the micro-level social processes that drive individual decision-making. Our framework treats intention diffusion as an aggregated outcome of multiple underlying social factors (such as norms, attitudes, perceived behavioural control, and social learning) without explicitly modelling these factors or their causal relationships. In this context, behavioural intention in our model directly translates to actual behaviour adoption only when there are no physical constraints preventing households from acting according to their intentions.

To address these limitations, future research should use Agent-Based Modelling (ABM) to better capture individual-level heterogeneity and the social influence (Chen et Gao, 2020; Xu et al., 2020; Misslin et al., 2022). ABM allows for better representation of causal relationships between infrastructure, social networks, and behavioural adoption (Meng et al., 2016; Meng et al., 2024; Peng et al., 2021). Such models would complement our system dynamic insights by simulating micro-level decision-making and social interactions. This dual approach would improve understanding of biowaste management dynamics and offer more granular policy guidance (Cohen, Gil, et Rosado, 2025).

## 6. Conclusions

This work highlights the importance of an approach to household biowaste management that considers the complex interplay between infrastructure development and behavioural changes. Our dynamical model demonstrates the value of such a tool in exploring the interactions between infrastructural development, and behavioural intentions changes, and their impact on biowaste management outcomes and policy objectives. The insights gained from this model can guide policymakers in understanding the conditions needed to meet their biowaste policy objectives, considering the uncertain evolution of household behaviours and their interaction with planned infrastructure capacities. Moreover, our case study reveals that underachievement of objectives may stem not only from insufficient behavioural intentions but also from inadequate infrastructure capacity that constrains households from acting on their intentions. While our model provides insights, it has limitations, including assumptions about household homogeneity and simplified behavioural dynamics. These limitations should be addressed in future research through advanced modelling techniques. We recommend refining the ABP's plans and implementation timelines based on each collection territory's unique demographic characteristics and long-

term population growth projections. Moreover, our findings highlight the need to combine infrastructure development and behavioural interventions. While infrastructure development is essential, they must be complemented by efforts to encourage changes in sorting behaviours, whether for home composting or dedicated collection to methanisation. These recommendations aim to enhance the territorial biowaste management especially in regions with shared and independent infrastructures.

## CRediT authorship contribution statement

**Ammar Hdaifeh:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Sylvie Huet:** Supervision. **Jean-Denis Mathias:** Supervision.

## Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Ammar HDAIFEH is a PhD student at Université Clermont Auvergne and works at the Engineering Laboratory for Complex Systems (LISC-INRAE). His research is supported by Clermont Auvergne Métropole (CAM) and ADEME as part of the BEECOME 2 project.

## Acknowledgements

This work was supported by Clermont Auvergne Métropole (CAM) [grant number 2021/194/003]; and the ADEME [grant number 2306D0005] as part of the BEECOME 2 project.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jclepro.2025.145571.

## Data availability

The code has been shared as a supplementary file during the Attach File step.

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