Modeling and Simulating the Italian Wheat Production System:

A Parallel Agent-Based Model to Evaluate the Sustainability of Policies

Gianfranco Giulioni

1 a

, Edmondo Di Giuseppe

2 b

, Arianna Di Paola

2 c

and Alessandro Ceccarelli

Department of Socio-Economic, Management and Statistical Studies “G. d’Annunzio” University of Chieti-Pescara,

Viale Pindaro 42, Pescara, Italy

Institute of BioEconomy, National Research Council, Via Dei Taurini 19, Roma, Italy

Keywords:

Farm Crop Management, Mathematical Optimization, Yield-Gap, Cluster Analysis.

Abstract:

This work presents the modeling steps to build a tool for policymakers to orient policies toward more sustain-

able wheat production. Starting from a sample survey of Italian farms, we identify, with the help of clustering

techniques, the farm types present in the sample. The clustering phase reveals a signiﬁcant heterogeneity

among farms that we handle building an agent-based model. Sampling from the clusters allows for including

a number of farms comparable to those operating in Italy in the agent-based model. Moreover, we build a

mathematical programming model with which farms (i.e., agents) decide the target production level and the

mix of inputs needed to obtain such production. Considered inputs are 1) the use of fertilizers, 2) the use of

herbicides, and 3) the use of pesticides. Policies are introduced as incentives or deterrents, driving production

decisions and the input mix choice towards more sustainable production.

1 INTRODUCTION

The increasing global demand for food, particularly

wheat, highlights its critical role as a staple crop feed-

ing billions of people worldwide. Wheat is central

to human diets and a key ingredient in various pro-

cessed foods (Asseng et al., 2018; Ketema et al.,

2023). Driven by population growth and evolving

dietary preferences, global demand for wheat is ex-

pected to rise signiﬁcantly, necessitating a substan-

tial increase in production to maintain food security

(Sheikh et al., 2014; Tilman et al., 2011; Lethin et al.,

2020; Hannah Ritchie, 2020). However, achieving

this growth is complicated by multiple constraints,

chief among them the limited availability of arable

land due to urbanization, climate change, and envi-

ronmental degradation (Tilman et al., 2011; Costanzo

and B

arberi, 2013).

Decreasing land availability presents a dual chal-

lenge: meeting rising food demand while ensur-

ing environmental sustainability (Fischer and Connor,

2018). Intensiﬁed agricultural practices, if unman-

aged, can lead to soil degradation, biodiversity loss,

https://orcid.org/0000-0003-0946-1738

https://orcid.org/0000-0002-6443-9106

https://orcid.org/0000-0001-9050-4787

and increased greenhouse gas emissions (Liu et al.,

2013; Costanzo and B

arberi, 2013; Poore and Neme-

cek, 2018). Projections indicate that wheat produc-

tion must increase by approximately 70% by 2050 to

meet global demand (Allen et al., 2016; Lethin et al.,

2020). Yet, current agricultural systems are experi-

encing yield plateaus, further intensifying the need

for innovative and sustainable farming strategies (Ray

et al., 2012; Ibrahim and Baqutayan, 2023).

Many wheat-producing countries have introduced

environmental policies promoting sustainable agricul-

tural practices in response to these challenges. The

European Union introduced signiﬁcant changes in the

Common Agricultural Policy (CAP), which became

effective in January 2023. The CAP focuses on ten

speciﬁc objectives, linked to common EU goals for

social, environmental, and economic sustainability in

agriculture and rural areas (EU CAP Network, 2022).

Egypt has adopted strategies to achieve wheat self-

sufﬁciency while addressing climate adaptation and

resource limitations (Asseng et al., 2018). Policy

frameworks increasingly emphasize soil health, eco-

friendly farming techniques, and efﬁcient irrigation

methods to reduce water consumption and enhance

resilience to environmental stressors (Liu et al., 2013;

McMillan et al., 2018). By embedding sustainabil-

ity into agricultural policy, these countries aim to rec-

Giulioni, G., Di Giuseppe, E., Di Paola, A. and Ceccarelli, A.

Modeling and Simulating the Italian Wheat Production System: A Parallel Agent-Based Model to Evaluate the Sustainability of Policies.

DOI: 10.5220/0013568000003970

In Proceedings of the 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2025), pages 337-343

ISBN: 978-989-758-759-7; ISSN: 2184-2841

337

oncile productivity with ecological preservation, en-

suring the wheat supply can meet future demands

without compromising environmental health (Tilman

et al., 2011; Ray et al., 2012).

The effect of a policy introduction depends on

how farmers respond to the measure. Because of the

complexity of the decision process, these responses

are usually heterogeneous. This work uses the agent-

based approach to handle such complexity and hetero-

geneity. Agent-based simulation (ABS) has emerged

as a powerful tool for evaluating policy design due

to its ability to realistically model complex interac-

tions among autonomous agents. The ﬂexibility of

ABS also supports the modeling of diverse agents

with unique decision-making processes, enabling the

exploration of unforeseen consequences of proposed

policies. Beheshti et al. discuss how agent-based

modeling facilitates this exploration, suggesting that

simulations can reveal important insights into the im-

pacts of policy initiatives, particularly in sustainable

decision-making scenarios (Beheshti et al., 2015). By

allowing changes in agent decision rules, researchers

can also simulate various governance models, eluci-

dating behavioral determinants that may signiﬁcantly

affect environmental management efforts (Jager and

Mosler, 2007).

Several studies use agent-based models to tackle

the issue of environmental impacts and for agricul-

tural policy evaluation (see (Kremmydas et al., 2018),

for a survey). According to the authors, the agent-

based approach has the advantage of accounting for

the different effects of policies due to farm hetero-

geneity. Similarly, to investigate sustainable paths of

wheat production, (Khan et al., 2020) uses a compu-

tational approach to predict the economic impact of

climate change-induced loss of agricultural produc-

tivity in Pakistan. In contrast, using an agent-based

model, (Siad et al., 2017) focuses on price formation

in South Italy. This work presents the framework of

an agent-based model built to assess the economic and

environmental sustainability of the wheat production

system in Italy. To this end, we ﬁrst build a model

for individual farmer decision-making based on eco-

nomic principles (Section 2).

In Section 3, we perform a cluster analysis on data

from an Italian sample survey database. This phase

aims to detect the diverse environmental proﬁles of

ﬁrms producing wheat in Italy. It allows the intro-

duction of heterogeneity in our agent-based model by

estimating the parameters of the individual model for

each cluster.

Section 4 details the agent-based model architec-

ture. In particular, aiming to provide a valuable tool to

policymakers, we intend to provide a model similar to

the Italian wheat production system, including a num-

ber of farms comparable to those observed in reality.

Data from the agriculture census is used to initialize

simulations.

Section 5 concludes and describes future direc-

tions for our research.

2 MODELING FARM INPUTS

DECISION

2.1 Farm Crop Management

Modeling a farm’s input decision belongs to the

broader farm management ﬁeld. Farm management

has several aspects: ﬁnancial management, crop and

livestock management, equipment management, la-

bor management, and risk management (see (Kay

et al., 2020) or (Kunz, 2022)). Because we deal

with wheat production, we will build on tools used

in the crop management ﬁeld. In particular, we are

interested in modeling a situation in which a product

(wheat) is produced using several inputs. This choice

is usually analyzed by applying economic principles

((Kay et al., 2020) chapter 8 page 144). Indeed,

the problem of choosing an input combination is a

mathematical minimization, i.e., the farmer selects

the cost that minimizes the input combination. The

dual problem of cost minimization is proﬁt maximiza-

tion (see (Carpentier et al., 2015) for a review of eco-

nomic modeling of agriculture production). We ana-

lyze the problem of maximizing proﬁt for one hectare

of wheat, which is generally posed as follows:

π = p

y(x

,...)−

∑

(1)

where y is yield per hectare, x

are inputs per hectare,

is the price of wheat and p

are the inputs prices.

Because this work focuses on environmental sus-

tainability, we consider fertilizer, herbicide, and in-

secticide relevant inputs for wheat production. A key

role in the economic modeling of input combination

choice is input substitution ((Kay et al., 2020) chapter

8). The input substitution degree has been studied for

several decades (see, for example, chapter 5 in (Heady

and Tweeten, 1963)). When inputs can be considered

substitutes, the Cobb-Douglas or the CES (constant

elasticity of substitution) are used as functional forms

for y(x

In the model developed below, we will provide a

new modelization of the yield function based on the

yield gap concept. Because we are analyzing proﬁt

per hectare, it is reasonable to work under the zero

degree of input substitution. Substitution normally

SIMULTECH 2025 - 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

338

occurs between acreage and other production inputs,

i.e., it is possible to obtain the same production, for

example, by increasing acreage and reducing fertil-

ization. In cultivating a single hectare, each input is

specialized in improving a speciﬁc condition that fa-

vors the plant’s health. Therefore, the Leontief-type

production function models the zero substitution in-

put case.

2.2 Yield-Gap

This approach starts by identifying the potential yield,

the maximum yield obtainable depending on solar ra-

diation, temperature, atmospheric CO2, and genetic

traits. These features govern the length of the growing

period. Thus, the potential yield is location-speciﬁc

because of the climate (see (Fischer, 2015) and (Cli-

maTalk, 2024) for more detailed deﬁnitions and ex-

planations). The yield realized by the farm is lower

than the potential yield, and the difference between

the potential and the actual yield is the yield gap. The

yield gap is caused by limiting factors such as wa-

ter and nutrient availability and reducing factors such

as weeds, pests, diseases, and pollutants. Usually, a

farm’s yield does not exceed 80% Farm management

practices are important to reduce the yield gap. In

Table 2, (Devkota et al., 2024) identiﬁes the manage-

ment factors that primarily affect the yield.

2.3 A Model

We set up a model based on the yield-gap concept as a

tool for management decisions. The model envisages

stress factors and actions to relieve the stress. Each

production input can relieve one speciﬁc stress fac-

tor. Therefore, the farmer’s action consists of weigh-

ing out the input quantity. Let us index stress factors

by i. We denote the conditional yield with y

, i.e., the

yield obtained when only the stress factor i is binding.

Our ﬁrst step is to set up a functional form for y

. Let

us denote the potential yield with ¯y. In addition, we

deﬁne s

∈ (0,1) to identify the share of the potential

yield lost due to the stress and x

as the strength of

the measure taken to counteract the stress. We also

deﬁne g

) ∈ (0,1) as a function of x

that gives

the effectiveness of the undertaken measure. Further-

more, we assume that g

is increasing in x

according

to the functional form g

) = 1 − e

−λ

. We further

introduce the maximum share of yield that can be re-

covered at the maximum effectiveness of the measure.

Let us identify it with ¯s

Under these deﬁnitions, the conditional yield can

be written as

) = ¯y[(1 − s

) + ¯s

(1 − e

−λ

)] (2)

When several stress factors are binding, the real-

ized yield corresponds to the most binding stress fac-

tor: y = min(y

As mentioned above, the economic theory of pro-

duction uses the Leontief type function. Its main fea-

ture is that relieving one stress factor can be ineffec-

tive because of the constraints of the other stress fac-

tors. The optimal strategy in this case is to level out

the conditional yields: y

= ˆy.

Using equation (2), the y

= ˆy condition can be

written as

¯y[(1 − s

) + ¯s

(1 − e

−λ

)] = ˆy (3)

Solving x

, we get:

ˆx

= −



(1 + ¯s

− s

) ¯y − ˆy

¯s

¯y



(4)

With this result, we can go to the proﬁt function

(equation 1), which in our case is

π = p

min( ˆy

) −

∑

ˆx

(5)

Because all the ˆx

deliver a yield equal to ˆy, we have

min( ˆy

) = ˆy and equation (5) simpliﬁes to:

π = p

ˆy −

∑

ˆx

(6)

Remembering that ˆx

depends on ˆy, the whole proﬁt

function depends on ˆy. Therefore, the farmer’s prob-

lem is to maximize proﬁt with respect to ˆy:

max

ˆy

π = p

ˆy −

∑



−



(1 + ¯s

− s

) ¯y − ˆy

¯s

¯y



The ﬁrst order condition (FOC) for a maximum is:

−

∑

(1 + ¯s

− s

) ¯y − λ

ˆy

= 0

Numerical methods can solve the FOC. Let us denote

the solution with ˆy

∗

. Plugging ˆy

∗

in equation (4), we

obtain the optimal level of each input ˆx

∗

The one stress factor case can help understand-

ing because of its analytic solution. In the one stress

factor case, we can drop the i subscript from equa-

tions, and the sum symbol is unnecessary. Solv-

ing the farmer’s maximization problem in this case,

we obtain: ˆy

∗

= (1 + ¯s − s) ¯y − p

/(p

λ) and plug-

ging into equation (4) we get the optimal input level:

ˆx

∗

= −

ln(p

/(p

λ ¯s ¯y)).

3 MODELING THE WHEAT

SYSTEM

The model presented in the previous section will be

used to to shape the behavior of agents in the agent-

based model. As is known, one of the advantages

Modeling and Simulating the Italian Wheat Production System: A Parallel Agent-Based Model to Evaluate the Sustainability of Policies

339

of agent-based models is the possibility they offer to

handle heterogeneity. Even though there are other

ways to allow for heterogeneity in our context (we

will talk about them in the conclusions and future re-

search directions section below), our ﬁrst device is to

identify types of farms in the Italian system. We let

all the farms decide according to the functional forms

displayed in the previous section. Still, the parame-

ters involved in the equations ( ¯y, λ, s, ¯s) are estimated

conditioning on the type. The different types of farms

are identiﬁed by implementing a cluster analysis on

real farm data.

This study utilizes the RICA (Rete

d’Informazione Contabile Agricola) database, a

comprehensive dataset representing 9048 Italian

farms that have cultivated durum wheat for 16

years. The RICA database is essential for evaluating

agricultural production systems, offering detailed

information on farm characteristics, inputs, and

outputs. For the following analysis, the dataset was

ﬁltered to focus exclusively on wheat-producing

farms for 2016, resulting in a dataset encompassing

2140 distinct farms. The choice of 2016 relies on

the fact that seasonal weather conditions strongly

inﬂuence wheat production, input use, costs, and rev-

enues. Favourable agro-climatic conditions in Italy

characterized the year 2016. Thus, we assume—at

least in a ﬁrst approximation—to be working under

stable and favourable climatic conditions, effectively

disregarding the impact of adverse weather. Key

variables extracted from the dataset include: 1)

Produced Quantity (the total quantity of wheat

produced), 2) Crop Acreage (the area dedicated to

wheat cultivation), 3) Herbicide Use (quantities of

various herbicides applied), 4) Nutrient Applications

(quantity per hectare of nitrogen, phosphorus, and

potassium, and 5) Machinery Use (hours of machine

operation per hectare).

A clustering analysis was performed to group

farms into distinct categories based on their input-

use efﬁciency and productivity. Firstly, input-to-yield

ratios were calculated to normalize farm differences

and enable comparison. Then, three key performance

indicators (herbicide ratio over yield, elements ra-

tio over yield, and machinery hours per hectare over

yield) were selected as input variables for clustering.

We refer to the mentioned ratios as inefﬁciency be-

cause they increase as the inputs increase and the

yield decreases, i.e., the farmer obtains less product

with more inputs. A range of cluster numbers (k)

from 2 to 15 was tested using the k-means algorithm.

The elbow method was applied to identify the opti-

mal number of clusters, leveraging the inertia met-

ric, which reﬂects cluster compactness. In particular,

the chosen k maximizes the second difference of the

inertia. Figure 1 displays a visual representation of

the method. In our case, the process suggests k = 5.

The ﬁnal clustering analysis let us classify the Ital-

ian wheat farms into ﬁve distinct clusters, with clus-

ter sizes ranging from 155 to 813 farms. Figure 2

provides boxplots of each cluster’s distribution of the

key inefﬁciency ratios.

Figure 1: Inertia as a function of the number of clusters.

In the ﬁgure, clusters are sorted for increasing in-

efﬁciency levels of fertilizers. The inefﬁciency rank-

ing is conﬁrmed for herbicides and machine use in

the other clusters, except for clusters 1 and 2. Clus-

ters 1 and 2 have a higher dispersion of fertilizer in-

efﬁciency and less regular behavior of the other inef-

ﬁciencies. Prominent is the high level of tractor use

in cluster 1. The interpretation of these odd clusters’

behavior deserves further investigation.

4 DISTRIBUTED AGENT-BASED

SIMULATIONS

The research presented in this paper aims to simulate

the reaction of the Italian wheat production system to

events such as changes in policies or shocks. To have

reliable results, we require the simulation to meet the

features of the Italian system, especially the number

of farms. To this aim, we classify wheat farms in clus-

ters and magnify each cluster so that the total num-

ber of farms in the simulation is comparable to the

number of farms producing wheat in Italy. Accord-

ing to the latest Italian agriculture census holding data

for 2020, the number of grain producers in Italy is

325313 ((Gismondi, 2022) p. 11). Filtering the cen-

sus data by grain type, we count 195735 observations

for durum wheat. The magniﬁcation is implemented

SIMULTECH 2025 - 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

340

Figure 2: The clustering of Italian wheat farms according to

their fertilizer, herbicide, and machinery use.

by estimating the statistical distribution of relevant

clusters’ variables and sampling from these distribu-

tions, keeping the relative cluster size unchanged until

the scale of the Italian system is reached. The magni-

ﬁcation using artiﬁcially generated agents is a practice

needing some care (Roxburgh et al., 2025); however,

in our view, it brings beneﬁt because we could provide

more signiﬁcant simulation results even at a regional

or provincial scale.

The considerable size of the system prompted us

to consider the possibility of running our simulation

in parallel using high-performance computing tech-

nologies. From this point of view, the Repast Suite

(https://repast.github.io) offers interesting opportuni-

ties. Repast provides facilities to run agent-based sim-

ulations. It comes in three different toolkits. The clas-

sic one is “Repast Simphony,” a Java-based toolkit de-

signed for use by personal computers and small clus-

ters. The increase in computer availability led the

development team to release the “Repast for High-

Performance Computing” toolkit, a “C++-based dis-

tributed agent-based modeling toolkit designed for

use on large computing clusters and supercomput-

ers.” The most recent toolkit is Repast for Python.

It is a Python-based distributed agent-based model-

ing toolkit for applying large-scale distributed ABM

methods.

The simulator is currently under development us-

ing “Repast for Python”, which, in addition to other

facilities, builds some of its functions on mpi4py

to ease the management of parallel computation.

Presently, the simulator implements the Farm and

the PolicyMaker classes. The Farm class has the

decide_production_inputs function that performs

the calculations presented in section 2.3. The code

is executed with parameters sampled using the esti-

mated cluster distribution. In other words, the sta-

tistical analysis of the clusters found in section 3 al-

lows the calibration of the model. This preserves

the relevant farm heterogeneity seen in reality. The

PolicyMaker class affects farm decisions by manag-

ing input prices, i.e., by charging taxes on detrimental

inputs. It will be enriched by International, National,

or local policies in the future. To simulate in parallel,

the policy maker is created in the master rank, and

a copy of the original agent is sent to all the other

ranks. In Repast jargon, we say that the original agent

is ghosted to all other ranks. A second important issue

is load balancing among ranks at initialization. To this

aim, we partition clusters between two ranks where

needed to keep proportionality with the n displayed

in Figure 2 among clusters and an equal number of

agents across ranks.

5 CONCLUSION AND FUTURE

RESEARCH

The present work describes the plan to build a model

representing the Italian wheat production system. We

ﬁrst built a model for the single-farm production and

Modeling and Simulating the Italian Wheat Production System: A Parallel Agent-Based Model to Evaluate the Sustainability of Policies

341

input decision. We then identiﬁed the heterogeneity

of farms with a clustering analysis performed using a

sample survey database. Finally, we used the detected

heterogeneity to populate an agent-based model to

evaluate the effects of policy introduction or the oc-

currence of signiﬁcant exogenous shocks. To al-

low the possibility to simulate with as many agents

(farms) as needed, we decided to implement the sim-

ulator using parallel simulation techniques. This will

allows to scale to the Italian system size (which is in

the order of a few hundred thousands), or more in case

the model would be used to analyze wider areas.

The choice to implement in a parallel

computation-enabled environment is convenient

because the model is part of a wider project that

aims to include modules that require additional

computational power.

One of these modules aims to introduce the en-

dogenous computation of the wheat price. As one ex-

pects, this price is heavily affected by international

trade conditions. The module we intend to add rep-

resents the international wheat markets, where agents

are large subcontinental geographic areas. The inter-

national prices are then computed by balancing the

international demand of excess demand areas and the

excess supply of areas with production higher than

domestic demand. We plan to develop this mod-

ule following our previous research (Giulioni, 2019;

Giulioni et al., 2019). This task will allow accounting

for the double-sided interaction between wheat price

and individual farmers’ production decisions. In Sec-

tion 2, the wheat price is a variable affecting wheat

production decisions. In turn, wheat production af-

fects demand and supply in international markets, and

therefore international prices.

A second module allows the computation of the

environmental impact of the wheat production ac-

tivity. We apply the Life Cycle Assessment (LCA)

methodology to the wheat production process. The

methodology can be applied both at the farm and ag-

gregate levels. Performing the LCA individually, we

can endow agents with environmental awareness. As

an example, the ReCiPe LCA methodology outputs

endpoint indicators measuring the damages to human

health in terms of the shortening of healthy life, i.e.,

the “Disability Adjusted Life Years” (DALY), or the

damages to ecosystem quality measured by the num-

ber of local species lost per year. Integrating this

information in the farmers’ decision process could

nudge agents to adopt more sustainable production

strategies. The model presented in section 2 has to

be revised to account for this effect. The LCA at the

aggregate level will mainly inform policymakers of

the potential environmental effects of the policies they

plan to introduce.

As a technical note, we developed the LCA mod-

ule in Python using the Brightway LCA Software

Framework. This fully complies with our choice of

the Repast for Python toolkit and will allow us to de-

liver the whole software bundle in Python.

ACKNOWLEDGEMENTS

This research was conducted as part of the project

“ECOWHEATALY: Evaluation of policies for en-

hancing sustainable wheat production in Italy” funded

by the European Union-Next Generation EU under

the call issued by the Minister of University and Re-

search for the funding of research projects of relevant

national interest (PRIN) grant n. PRIN 202288L9YN.

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