=Paper=
{{Paper
|id=Vol-3944/paper5
|storemode=property
|title=The effect of planning horizon length and green manure on net income in Crop Rotation Problem
|pdfUrl=https://ceur-ws.org/Vol-3944/paper5.pdf
|volume=Vol-3944
|authors=Akouyo Yvette Gbedevi,Kossi Atchonouglo,Sid Ahmed Lamrous,Marie-Ange Manier
}}
==The effect of planning horizon length and green manure on net income in Crop Rotation Problem==
https://ceur-ws.org/Vol-3944/paper5.pdf
The effect of planning horizon length and green manure
on net income in Crop Rotation Problem
Akouyo Yvette Gbedevi1 , Kossi Atchonouglo1 , Sid Ahmed Lamrous2 and Marie-Ange Manier2
1
Université de Lomé, Laboratoire d’Analyse et de Modélisation Mathématiques et Applications (LAMMA), Lomé, Togo
2
Université de Technologie Belfort-Montbéliard , FEMTO-ST , Belfort, France
Abstract
The world population is increasing rapidly, and recent awareness of the limits of natural resources and the
pollution of soil, air and water, is pushing towards a new form of agriculture, sustainable agriculture. Sustainable
agriculture can be defined as an agriculture that combines environmental, social and economic objectives for the
well-being of farmers and the soil. Crop rotation took hold during this decade by emphasizing the management
of soil resources, while improving economic, environmental and social factors. The goal of the crop rotation
planning problem discussed in this paper is to maximize the total net return, with a particular emphasis on
incorporating a plant that contributes green manure to the soil alongside nutrient amendments by choosing the
best horizon for plannification. The rotations generated are of fixed duration for all the plots and the objective is
to maximize the income of the farmers. The results showed that the determined algorithm was feasible.
Keywords
Sustainable Agriculture, Crop Rotation Problem, Mixed-Integer Linear Programming, Optimization
1. Introduction
Agriculture is the main occupation in many countries around the world and with a growing population,
which the UN projects will increase from 7.5 billion to 9.7 billion in 2050 [1]. This means that farmers
will have to do more with less. According to the same survey, food production will have to increase by
60% to feed two billion more people. However, traditional methods are not enough to handle this huge
demand. This drives farmers and agricultural businesses to find new ways to increase production while
conserving soil resources. The challenge is to increase global food production by 50% by 2050 [2] to
feed two billion more people by practicing sustainable agriculture.
Crop rotation is a fundamental feature of all organic farming systems. Crop rotation means changing
the type of crop grown in a particular piece of land from year to year. There are cyclical rotations
that repeat the same sequence indefinitely, and noncyclical rotations that allow for changes in crop
sequence, adapting to management decisions and evolving as market opportunities arise [3]. Greater
soil fertility, fewer pests and crop diseases, and higher yields are just a few of the positive outcomes of
rotation. Compared to continuous monoculture practices, according to [4] , rotation increased crop
yields by 20 % on average and the benefits are highly context-dependent.
The financial stability of the agricultural sector could be improved by including a variety of cropping
strategies. The profits of the farm would not be based solely on a single primary cash crop; rather, they
would be based on a diverse collection of commercial crops that were evenly distributed over a number
of periods. This could eventually lead to an improvement in cash flow by introducing regular incomes
into the agribusiness [5].
In order to assist the farmer in choosing the appropriate crops for the rotation cycle, we proposed
a Mixed-Integer Linear Programming (MILP) model to solve the crop rotation problem by exploring
the benefit of including green manure. We studied the importance of including fertilizer plants in crop
Proceedings of the DAAfrica’2024 workshop
⇤
Akouyo Yvette Gbedevi.
†
These authors contributed equally.
� rosettegbedevi@gmail.com (A. Y. Gbedevi); katchonouglo@univ-lome.tg (K. Atchonouglo); sid.lamrous@utbm.fr
(S. A. Lamrous); marie-ange.manier@utbm.fr (M. Manier)
� 0000-0002-5996-7027 (A. Y. Gbedevi)
© 2025 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
39
rotation schedule by using exact methods such as linear programming to determine the best solution of
the proposed agricultural model and to test it in a real context. The experiment was conducted for a
real planting area of average size with 9 plots, considering 8 crops from different botanical families and
a two-year, three year and four year planting rotation.
2. Literature Review
Maximizing the overall net return is the aim of the crop rotation planning problem that they address in
[6]. The branch and bound approach is used to optimize the crop rotation plans in an integer linear
programming model. In addition to the agronomic, water supply, and seasonal demand constraints, the
suggested model includes a new temporal preference constraint.
In order to optimize the efficiency of organic farming in the Philippines’ second and third largest
agricultural land areas, the authors suggested using a Mixed Integer Programming model as a decision-
making tool. This tool considers a number of organic farming-related factors. With the matching profit
organic farms may make from planting them, the best-selling and most popular produce in the area is
used [7].
Using a mixed integer linear programming model, their work [8] examines the crop rotation problem
with water supply/demand and net return uncertainties that fluctuate within the permitted rotation
cycle. It renders the developed model numerically feasible, mainly when applied to intricate agricultural
issues. Determining the best cropping plans, providing a fair income for the farmer, and strategically
accounting for water uncertainties are the primary goals of this endeavor.
In order to optimize crop rotation in conventional organic farms with plot adjacency constraints
and nutrient amendments, this work [9] makes use of real-world data and the CBC solver. The goal of
the created rotations is to maximize farmers’ income, and they have set durations for each plot. The
suggested agricultural model’s solution is found using a linear programming technique.
In this study [10], the authors examine the Crop Rotation Problem and its applicability to the
combination of farm management and Precision Agriculture. They increased the problem’s appeal for
sustainability by presenting a novel mathematical method for the CRP based on crop requirements and
nutrient balance. To optimize the CRP, a real-encoded genetic algorithm was created. The findings
show that mid- and long-term crop scheduling performed well.
A binary nonlinear bi-objective optimization model is presented in [11] to address the issue of
agricultural cultivation planning that is sustainable by using a meta-heuristic technique based on a
genetic algorithm and constructive heuristics. A planting schedule for crops to be grown in designated
plots to limit the likelihood of pests proliferating and increase the process’s profitability.
An integrated strategic-tactical planning model for the supply chain issue involving sugar beets
is presented by the authors this study. In order to minimize the overall operational costs, including
transportation and inventory of processed and unprocessed beets, a binary integer programming model
is developed . To enable crop rotation planning across many cropping seasons, a special temporal
dimension was introduced to the planning horizon [12]
3. Methodology
3.1. Study Area
According to FAO’s annual report in 2006, nearly 69% of the 56,600 km2 of the Togolese territory is
agricultural land, and 38% of this land is exploited. Rain-fed agriculture is practiced in Togo, and nearly
75% of the country’s working population works as small farmers using traditional farming techniques.
The two principal crops are maize in the south and focus of the nation and sorghum/millet in the north.
70% of the country’s population, or 5.75 million people in 2010, is supported by agriculture, which
also makes up nearly 40% of the country’s GDP. From the south to the north, Togo is divided into five
regions: the Maritime, Plateaux, Central, Kara, and Savanes. From one region to the next, pedoclimatic
40
conditions and the availability of agricultural production factors, particularly land, vary significantly
[13]. Togo’s climate is tropical, and it varies a lot from south to north. The climate is sub-Sahelian (hot
and dry) in the north, sub-Sahelian (rainy) in the center, and Guinea-Sudanian (hot and humid) in the
south. The regions’ intra-annual rainfall distribution is also unique. There are two rainy seasons in the
Maritime and Plateaux regions each year March/April to July and September to mid-November and two
dry seasons August and mid-November to March/April with 900 and 1500 mm of precipitation per year.
There is a dry season from November to April in the Central, Kara, and Savanes regions, with annual
rainfall ranging from 1200 to 1500 mm. As a result, there are two agricultural seasons in the southern
parts of Togo, while there is only one in the northern parts. Despite the significance of agriculture to
the Togolese economy, it has remained traditional and lacked access to organic and mineral fertilizers.
Agricultural production includes:
• Cereals: Maize, Millet, and Sorghum
• Tubers: Yams and Cassava
• Legumes: Beans, Groundnuts, and Soya
Our research focuses primarily on the subtropical climate of the region, taking into account the potential
crops.
3.2. Problem Description
Several factors, including market demands, soil characteristics, and crop nutrient requirements from a
climatic perspective, are taken into consideration when choosing a cropping sequence. Plots are used
to divide an agricultural area. Different kinds of crops can be grown on each plot [14]. Planning crops
on agricultural land while taking into account the primary factors that affect crop yields (economic,
environmental, and ecological) presents a challenge when developing a crop rotation system [9].
Utilizing the principles of crop rotation to make farmers as much money as possible while taking into
consideration restrictions based on demand, crop characteristics, production times, and plot conditions
is the primary objective of this work. The proposed model takes into account the following constraints:
1. Sowing Period : It is essential to observe each crop’s sowing and production times.
2. Cultural continuity among families: Different botanical families contain the cultures. It is not
recommended to grow cultures from the same botanical family in succession on the same plot
[5]. This issue is primarily brought about by the fact that crops in the same family have similar
deficiencies (the risk of acquiring the same diseases or weeds) and nutrient requirements. The
cropping system’s ability to last is jeopardized as a result of this.
3. Crops belonging to the same family’s neighbors: On two adjacent plots, two crops belonging
to the same botanical family cannot be sown simultaneously [5]. Characteristics are shared
by cultures of the same family. Therefore, staking them simultaneously on two plots that are
adjacent to one another is the same as staking the same crop on these two plots. This makes
more resources available to pests, which in turn increases their population and the damage they
can cause.
4. Needs for nutrients: The quantity of soil nitrogen, phosphorus, and potassium required to start
a crop at any given time is referred to as its nutrient requirements. We define the nutrient of
a crop as the quantity of nitrogen, phosphorus, and potassium that this crop requires, and the
nutrient of a plot as the amount of nitrogen, phosphorus, and potassium applied to this plot over
a specific time period.
5. Fertilization with plants: In the same rotation cycle, combining legumes with other crops has
a positive effect on the soil and, as a result, increases yield.
6. Fallow Period: To allow the soil to regain its moisture and fertility, each cycle ought to include
one or more periods of fallowness.
7. Market demand: The distribution of cash crops is significantly restricted as a result of this. Each
culture has a preexisting market; the demand needs to be met.
41
Table 1
List of Index.
Index Description
i relatifs aux cultures
j relatifs aux parcelles
t période de l’horizon de planification
p lié à la famille botanique des plantes
↵ lié à l’intervalle de fertilisation,
↵ 2 ⌦, ⌦ = {↵ 2 N⇤ | ↵ · ✓ T, ✓ 2 N⇤ }
The crop rotation problem is a complicated combinatorial optimization problem that changes de-
pending on the model’s scope, considering the aforementioned constraints. Along the rotation cycle, it
is desirable to determine the best crop combinations to plant in each plot at each time. The problem is
solved using the constructed mathematical model, and the following decisions are made:
• Determine the crop-specific area needed to satisfy demand.
• During the rotation cycle, determine the crop sequence in each plot.
• Obtain the various agricultural operations’ calendar.
The crop rotation problem is a complicated combinatorial optimization problem that changes de-
pending on the model’s scope, considering the aforementioned constraints. Along the rotation cycle, it
is desirable to determine the best crop combinations to plant in each plot at each time. The problem is
solved using the constructed mathematical model, and the following decisions are made:
• Determine the crop-specific area needed to satisfy demand.
• During the rotation cycle, determine the crop sequence in each plot.
• Obtain the various agricultural operations’ calendar.
4. Mathematical Modeling of the problem
The planting area is thought to be divided into plots by us. If two parcels share a boundary that is
not reduced to a discrete set of points, they are neighbors. We will consider the opposite plots to be
adjacent, for instance, if the planting area is divided into four plots.
A crop rotation schedule with a clearly defined planning horizon (T) is established by a producer with
the intention of maximizing profits following an agricultural season. It has a number of crops (N) that
are part of various botanical families (p), where F(p) is the number of crops in the family (p) and surfaces
that are divided into plots (K) and naturally contain certain amounts of nutrients (Nitrogen, Phosphorus,
and Potassium). Profitability (l), production cost (CP), production time (Z), average production (Q) per
hectare, market demand (D), and nutrient requirements are all associated with each crop. Additionally,
the farmer is restricted by the following restrictions: sowing time, continuity and neighbor for crops
belonging to the same family, green fertilization, and fallow time.
The tables define all indices 1, parameters/data, and variables 2 for the proposed model.
The index of fertilization (↵) is determined by the model parameters fertilization interval (✓) and
planning horizon (T). For instance, if the planning horizon is 24 periods and the fertilization interval is
12 periods (✓ = 12), then the set ⌦ is 1, 2 because ↵ = 1 and ↵ = 2 satisfy the definition of ↵ · ✓ T .
The entire model is displayed below. The benefits of crop planning (calendar), the costs of fertilization,
and other production costs (land preparation, transportation, labor) are evaluated by the objective
function in Equation (1). Fertilization costs are also included in, with the goal of reducing reliance on
external chemical fertilizers.
Subject to (1)-(15).
42
Table 2
List of Parameters.
Parameters Description
N number of crops to plant(N>=2)
K number of plots (lot) available
T the horizon (Duration) of planification
V Set of crops for green fertilization
n =N+1 represents a fictitious crop imposing a fallow
FP Set of family cultures p, p= 1, . . . , Nf
Nf Number of crop families
Surfj Area of the plot j in ha
li Crop profitability i per ha (FCFA XOF)
zi Crop production cycle i including the sowing period and the harvest period
Qi Crop Production Average i per ha
Ii Crop sowing interval including earliest and latest period i {Ii 1, . . ., Ii n
Di Crop demand i (unit/period)
Sj Adjacent plots to the plot j
FN ↵ij , FP ↵ij , FK ↵ij Dose of Nitrogen, Phosphorus and Potassium to bring to the plot j on interval ↵ according to crop i .
BN j , BP j , BK j Initial composition of the soil in Nitrogen, Phosphorus and Potassium of the plot j per ha.
RN i, RP i, RK i Crop requirements i in Nitrogen,Phosphorus and Potassium
C N , CP , CK Cost of fertilisation in (FCFA par ha)
Fmini , Fmaxi Limit of fertilization for crop i
✓ Fertilization equilibrium interval (Compensation)
OCi Other production costs incurred on plot j at period t due to crop i. (Preparation of the land,purchase of seeds for sowing, transport, labor)
N X
X T X
K K
XX N X
X T X
K
Surfj ⇤ li ⇤ xitj (FN ↵ij ⇤ CN + FP ↵ij ⇤ CP + FK↵ij ⇤ CK ) OCi ⇤ xitj . (1)
i=1 t=1 j=1 ↵2⌦ j=1 i=1 t=1 j=1
N zi
X X1
xi(t r)j 1. (2)
i=1 r=0
With t = 1, . . . , T ; j = 1, . . . , K.
It is not allowed to plant two crops in the same plot [15, 16, 10]. Indeed, a crop occupies the entire
plot throughout its growth and harvest. The constraint defined in equation (2) forbids scheduling more
than one culture during the same period. There is a spatial constraint.
0 1
X zX i 1 X X zX i 1
xi(t r)v K @1 xi(t r)j A . (3)
i2F(p) r=0 v2Sj i2F(p) r=0
With p = 1, . . . , Nf ; t = 1, . . . , T ; j = 1, . . . , K.
It is not recommended to plant two crops from the same botanical family on adjacent plots at the
same time [15, 9, 16, 10]. The fact that the cultures of the same family share characteristics is the source
of this issue. Therefore, planting them simultaneously on two plots that are adjacent to one another
amounts to planting the same crop on both plots, which does not maximize crop distribution on the
various plots. If a crop i of the same botanical family p has already been sown on plot k, constraint (3)
states that the number of crops on all plots Sj adjacent to plot j during their production periods Zi must
be equal to zero; otherwise, the number of crops is at most equal to the number of independent plots.
zi
X X
xi(t r)j 1. (4)
i2F(p) r=0
With p = 1, . . . , Nf ; t = 1, . . . , T ; j = 1, . . . , K.
On the same plot, cultures belonging to the same botanical family cannot be grown immediately
[15, 16]. This issue is primarily brought about by the fact that crops in the same family have similar
43
deficiencies (the risk of acquiring the same diseases or weeds) and nutrient requirements. The cropping
system’s agronomic viability is jeopardized as a result of this. Constraint in equation (4) sets a maximum
of one crop as the sum of all crops i in the botanical family p over their production period Zi .
T
XX
xitj 1 (5)
i2V t=1
Withj = 1, . . . , K.
Additionally, green manure improves the structure and fertility of the soil while also enhancing its
organic matter enrichment [16]. Green manure adds nitrogen to the rotation by planting legumes [17].
Constraint (5) guarantees that every plot gets at least one implementation of green manure (legumes).
T
X
xntj 1. (6)
t=1
With n = N + 1, j = 1, . . . , K.
The period of frost or fallow enables the plot to restock its production capacity, water reserves,
and other resources. as well as to restrict excessive agricultural production. Constraint defined in
equation (6) ensures that each plot has at least one freezing period. During the frost period, there are
no restrictions on neighborhood and consecutive planting.
K X
X
xitj = 0. (7)
j=1 t2I
/ i
With i = 1, . . . , N.
Following the recommended planting date is critical for allowing the crop to express its yield potential
and lowering crop protection costs. By preventing allocation outside of this window, the constraint
outlined in equation (7) ensures that crop scheduling takes place only during the appropriate sowing
period.
When nutrients are present in sufficient quantities and in mineral forms that can be absorbed by
plants, a soil is more fertile [9]. They deplete the soil of the essential nutrients they require as they
grow.
N
X ↵⇤⇥
X
FN ↵j xitj ⇤ Surfj ⇤ (RN i BN j ) 0. (8)
i=0 t=1+(↵ 1)⇤⇥
With t = 1, . . . , T ; ↵ 2 ⌦.
N
X ↵⇤⇥
X
FP ↵j xitj ⇤ Surfj ⇤ (RP i BP j ) 0. (9)
i=0 t=1+(↵ 1)⇤⇥
With t = 1, . . . , T ; ↵ 2 ⌦.
N
X ↵⇤⇥
X
FK↵ij xitj ⇤ Surfj ⇤ (RKi BKj ) 0. (10)
i=0 t=1+(↵ 1)⇤⇥
With t = 1, . . . , T ; ↵ 2 ⌦.
44
The quantity of nitrogen, phosphorus, and potassium that the soil requires to initiate a crop at any
given time is referred to as the minimum nutrient requirement. A plot’s nutrient amendment is defined
here as the amount of nitrogen, phosphorus, and potassium applied to it over a specific time period. Let
↵ be the size of the interval that is appropriate for sowing crop i, the interval that is used to apply the
amendments FN ↵j ,FP ↵j and FK↵j , BN j ,BP j and BKj , which represent the initial composition of the
Nitrogen, Phosphorus, and Potassium soil of plot j per ha [10, 9] , RN i ,RP i and RKi , which represent
the minimum amount of nutrients that crop i requires.
Equations (8), (9),(10) are used to calculate fertilization balances based on the surface nutrient budget.
K X
X T
Surfj ⇤ Qi ⇤ xitj Di . (11)
j=1 t=1
With i = 1, . . . , N.
Demand from the market is another significant constraint. The farm’s crop yields are constrained by
this constraint to meet the anticipated demand for the crop i. To avoid issues like prolonged product
storage or conservation, which can result in additional costs and increase the risk of income variability,
we believe that the farmer should not exceed the estimated demand. The constraint outlined in the
equation (11) is used to evaluate the crop’s production requirements.
Each of the Boolean decision variables xitj represents the schedule (planning) of crop i during period
j on plot t. When and where crops are planted are tracked by them. The variables of fertilization FN ↵j
,FP ↵j and FK↵j are actual variables.
xitj 2 {0, 1} . (12)
With i = 1, . . . , N ; t = 1, . . . , T ; j = 1, . . . , K.
FN ↵j = FN ↵j 2 R+ | FN max FN ↵j FN min . (13)
With j = 1, . . . , K; ↵ 2 ⌦.
FP ↵j = FP ↵j 2 R+ | FN max FP ↵j FN min . (14)
With j = 1, . . . , K; ↵ 2 ⌦.
FK↵j = FK↵j 2 R+ | FN max FK↵j FN min . (15)
With j = 1, . . . , K; ↵ 2 ⌦.
5. Model discussion and analysis
5.1. Tools
Python-MIP, a collection of Python tools for modeling and solving Mixed-Integer Linear Programs
(MIPs), was used for the model’s implementation and evaluation and CBC Solver as Solver since it does
not require a license unlike Gurobi. The solver uses the branch and bound algorithm to find the optimal
solution for the crop rotation problem. The study will focus on eight crops from five botanical families.
Crop data, as well as production parameters like planting, harvesting dates and nutrient requirements,
are listed in Table 4. The planning horizon is divided into month. At each rotation schedule, each area
adopted at least one fallow period and one green manure crop. The proposed model can be solved in
less than a minute and includes 1998 variables and 23049 linear constraints.
45
Figure 1: Illustration of crop rotation schedule proposed from the model without the addition of
nutrients. The white cells represents fallow period. Yam is cultivated in T = 23 and ended-up in T = 7
of the following year on plot j = 2 for a total duration of 9 months Zyam = 9. As Groundnut and Beans
are from the same botanical family, there is a fallow period of 2 to avoid an immediate succession.
5.2. Study cases
The proposed model will be evaluated in two scenarios. Firstly, we present the impact of including
nutrient amendment in the crop rotation schedule on the net profit (Instance 1). We evaluate the
income and crop rotation schedule in this experiment, taking into consideration whether or not soil
amendments are present. Besides, we present the alteration of the design of the plots on the establishing
region which restricts the crop allocation. Then, we evaluate our model using a variety of two, three,
and four years planning horizons (Instance 2).
5.2.1. Instance 1
Table 4 presents details about the crop, planting and harvest times and Nitrogen, Phosphorus and
Potassium requirement for each crop . In this study, there are a total of eight crops (N = 8) and five
families of crops (Nf = 5). Our planning horizon is two years, divided into 24 periods (T = 24). Table
5 describes the adjacency among plots and the cultivable area of each plot. We do not take into
consideration the main diagonal, but the other positions in the table filled in Green represent the plots
that are adjacent to each other. Details such as number of variables and linear constraint about the two
models are displayed in Table 3.
Table 3
Variables and Linear Constraints of each model
Models Variables Linear Constraints
Without Nutrient Amendment 1944 22995
With Nutrient Amendment 1998 23049
In the first instance of our problem, the solver reached the value of the objective function in 9,66
seconds for the model without nutrient amendments which is 30,639,998 XOF and in 61,21 seconds
for the model with nutrient amendments which is 22,087,660 XOF. Planning is presented differently in
each model. The representation of the CBC solver-derived solutions for the two models is depicted in
Figures 1 and 2. Figures 1 and 2 both demonstrate compliance with the adjacency constraint.
46
Table 4
Crop’s attributes: seeding, harvesting and Nutrient Demand.
Index Crops Botanical Family Sowing Harvest Cycle(Month) N(kg/ha) P(kg/ha) K(kg/ha)
1 Maize Poaceae April-May-September (July-August)-December 4 27-34 10-12 26-37
2 Groundnuts Fabaceae March June 4
3 Beans Fabaceae July-August October-November 4 69 19 51
4 Sorghum Poaceae Mid-June-Mid-July September-October 4 33 10 34
5 Soya Fabaceae Mid-June-Mid-July November-December 6 67-71 16-26 18-53
6 Cassava Euphorbiaceae June-July June-July 12 2-6 1-2 1-9
7 Cotton Malvaceae July-August November-December 5 120-214 43-86 87-223
8 Yam Dioscoreaceae November-March-April-May July-November-December-January 9
Table 5
Plot’s Adjacency matrix corresponding to the given farm.
Plots Plot 1 Plot 2 Plot 3 Plot 4 Plot 5 Plot 6 Plot 7 Plot 8 Plot 9 Area in ha
Plot 1 2
Plot 2 3
Plot 3 1
Plot 4 1
Plot 5 2
Plot 6 3
Plot 7 2
Plot 8 1
Plot 9 3
Figure 2: Illustration of crop rotation schedule proposed from the model including soil nutrients
amendments. The white cells signify fallow periods. Yam is cultivated in T = 23 and ended-up in T = 7
of the following year on plot j = 1 for a total duration of 9 months Zyam = 9. As Groundnut and Beans
are from the same botanical family, there is a fallow period of 2 to avoid an immediate succession.
5.2.2. Instance 2
For instance 2, we want to compare the net returns from the crop rotation planning so we consider for
experiment two-year, three-year and four-year period for the horizon of planning with the same crop
47
(a) Illustration of crop rotation schedule pro- (b) Illustration of crop rotation schedule pro-
posed from the model with a planning posed from the model with a planning
horizon of three years. horizon of four years
Figure 3: Illustration of the crop schedule according to the planning horizon of three and four years
respectively 36 and 48 periods
·108
1
Net Profit XOF/Month
0.8
Net Profit [XOF CFA ]
0.6
0.4
0.2
0
0 12 24 36 48 60
Period [in month]
Figure 4: Variation of net profit based on planning Horizon
data as Table 4 . The Cbc solver respectively a value of 31.366.080 XOF and 88.327.840 XOF after 30
seconds and 28 seconds of running time, and the associated rotation for each plot is given in Figure 3.
As can be seen in Figure 4, the net profit increases with the planning horizon. This necessitates
consideration of the horizon selection and crop selection for the rotation. But planning crops ahead of
time over several years can be risky because there are many things that can affect market demand, like
the weather, and market prices can change a lot from season to season.
48
6. Conclusions
This article highlights the significant role of legumes in modeling a crop rotation system, considering
constraints such as contiguity and the use of mineral fertilizers for soil amendment. To address the
problem of increasing the net income of farmers in a crop rotation system, We used a mixed integer
linear programming model (MILP). Our model proposes the best possible solution by maximizing the
objective, in this case farmers’ income, while respecting a set of constraints, such as crop rotation rules.
The best solution of the proposed model was tested in an experiment conducted for a medium-sized
real plantation area with nine plots, considering eight crops from five botanical families and a two-year
plantation rotation. The results of the study indicate that farmer’s incomes improve when a longer
planning period is considered.
However, the solutions proposed by MILP may lack the flexibility to adapt to rapid changes in the
field, such as a sudden drought or market price fluctuations. This aspect will be taken into consideration
in our future work by introducing a model based on stochastic linear programming model. Additionally,
integrating a dynamic subdivision could further boost farmers’ incomes.
Declaration on Generative AI
Either:
The author(s) have not employed any Generative AI tools.
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