Management Theory and Studies for Rural Business and Infrastructure Development
ISSN 1822-6760 / eISSN 2345-0355. DOI: 10.15544/mts.2016.10
2016. Vol. 38. No. 2: 128–135.
THE EVALUATION OF LITHUANIAN CROP PRODUCERS‘ DECISION
MAKING USING A MULTIOBJECTIVE OPTIMIZATION APPROACH
Andrej Jedikˡ, Virginia Namiotko²,
1
Researcher. Lithuanian Institute of Agrarian Economics. V. Kudirkos str. 18-2. 03105 Vilnius.
Tel. +370 52 622459. E-mail [email protected]
2
Junior Researcher. Lithuanian Institute of Agrarian Economics. E-mail [email protected]
Received 10 05 2016; accepted 01 06 2016
A review of the scientific literature revealed that the use of only one objective, such as the
maximization of gross margin, is not sufficient to interpret farmers’ behavior. The research problem
is to determine whether other attributes such as risk, leisure time also play an important role in their
decision making. The paper aims to evaluate Lithuanian crop producers’ decision making using a
multiobjective optimization approach in relatively small, medium and large farms. The analysis was
performed on data from specialist cereals, oilseeds and protein crops’ farms covered by FADN. The
results of the analysis revealed that Lithuanian specialist cereals, oilseeds and protein crops’ producers aim to achieve multiple goals and those goals are different according to farm size. The research also showed that not all famers consider gross margin as its primary objective.
Keywords: decision making, farmer‘s behavior, multiobjective optimization, utility function.
JEL Codes: C61, D22, Q12.
1. Introduction
The evaluation of the farmers’ decision making has received significant attention in recent years in the scientific literature. The authors agree that farmers’ decisions are influenced by a range of factors, from which one of the most important is
farmers’ objectives. Although most researchers have focused on the gross margin
maximization as the main objective of farmers (Veysset, 2005; Crosson, 2006), some
authors point out that farmers seek not only maximize gross margin, but other attributes such as risk, leisure time, indebtedness, etc. also play an important role in their
decision making.
A. M. Featherstone et al. (1995) investigated behavior of Kansas farms and
identified stronger support for the minimization of cost than for the maximization of
gross margin. Similarly, M. Vandermersch and E. Mathijs (2002) carried out a survey
in Belgium and found that only one-third of all dairy farmers interviewed consider
gross margin maximization as its primary objective.
Copyright © 2016 The Author. Published by Aleksandras Stulginskis University, Lithuanian Institute of Agrarian Economics. This is an open-access article distributed under the terms of the Creative Commons AttributionNonCommercial 4.0 (CC BY-NC 4.0) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The material cannot be used for commercial purposes.
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B. Manos et al. (2007) showed that the most important objective of Bangladeshi farmers is the minimization of labor, and circumstantially the maximization of
gross margin and the minimization of risk. According to the authors, the importance
of the minimization of labor can be explained by the increased interest of farmers to
cultivate extensive crops that are less labor-intensive. In another paper B. Manos et
al. (2009) revealed that Greek cereals and industrial crops’ growers mostly seek to
maximize gross margin, while the minimization of its risk and the minimization of
labor is less important to them.
A. Sintori et al. (2010) analyzed Greek dairy sheep farmers’ decision making
and found that their main objective is to minimize risk. The maximization of gross
margin was the most important objective only in medium farms. Likewise, S. Rozakis
et al. (2012) showed that Greek sheep famers’ behavior is based not only on the gross
margin maximization, but also on the minimization of risk, the minimization of family labor, the minimization of variable cost, and the minimization of the amount of
purchased feed. The results also showed that in some cases gross margin maximization is even less important than other objectives. The authors concluded that such results suggest a link between farm structures and farmers’ objectives.
Gross margin maximization, as primary single objective, was considered in
scientific agricultural researches and applied to farming in Lithuania (Kurlavičius,
2009). However Lithuanian farmers’ behavior according to their multiple objectives
in farming has not been considered or established yet.
The purpose of the present paper is to check following hypotheses:
 the behavior of Lithuanian farmers remains the same in small, medium and
large specialist cereals, oilseeds and protein crops’ farms;
 main objective of Lithuanian producers of specialist cereals, oilseeds and
protein crops’ farms is gross margin maximization.
The object of the research is specialist cereals, oilseeds and protein crops’
farms.
The subject of the research is the behavior of specialist cereals, oilseeds and
protein crops’ producers when alternative objectives are presented.
The paper is structured as follows. Section 2 describes the methodology of
farmers’ behavior evaluation. Section 3 presents the case study and results and discussion. Section 4 provides conclusive remarks of the research.
2. Methodology
The following methodology consists of three parts. The first part describes
general concepts of data grouping into clusters and representative farms selection
from each cluster. The second part presents farmers’ behavior estimation in each
cluster by proposing weighted goal programming as a primary tool. The third part
gives model specification which is necessary to perform farmers’ behavior modelling.
Representative farms selection. The analysis was performed on data from
specialist cereals, oilseeds and protein crops’ farms covered by Farm Accounting Data Network (FADN). The data of specialist cereals, oilseeds and protein crops’ farming type combine 453 farms in the year 2013.
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The specialist cereals, oilseeds and protein crops’ farms have been divided into
three clusters by using K-Means clustering analysis method. The clustering process
has involved technical, economic and social variables such as: farm size, land quality
point, crop distribution in the production plan, variable cost, income and labor input.
According to mentioned conditions three types of clusters were developed: relatively
small, medium and large farm size clusters. The behavior of farm’s holder is considered in representative farm of each cluster (Manos, 2009).
In order to derive the representative farm in each cluster only farms with the
best technical efficiency were considered in further analysis, because rational managerial behavior of farmers leads to efficiency (Manevska-Tasevska, 2011). To estimate farms with the best technical efficiency in each cluster Data Envelopment Analysis (DEA) was engaged. Input-oriented and CRS optimization direction was chosen.
Input variables of DEA model consist of production costs, labor input and land resources and output variable is interpreted as gross production. Taking into account
farms with the best technical efficiency representative farms were derived in each
cluster by applying weighted average technique. Weights of each farms in whole set
were provided by FADN.
Weighted goal programming. Decision making model specification is based
on estimating the utility function of farmers by developing weighted goal programing
model which is proposed as suitable approach of farmer’s behavior in case of multi
objectives (Sumpsi, 1997; Amador, 1998). Such farmers’ behavior modelling was
successfully applied in various agricultural problem fields in different countries
(Amador, 1998; Gomez-Limon, 2000; Andre, 2010; Sintori, 2010; Rozakis, 2012).
To estimate the utility function of farmers in each cluster following steps were performed:
1. The selection of the most important farmers’ target functions 𝑓1 (𝒙), 𝑓2 (𝒙),
… , 𝑓𝑛 (𝒙) - objectives.
2. Determination of a set of constrains which are the same for all objectives.
3. Construction of pay-off matrix for the selected objectives:
𝑜𝑝𝑡
𝑓1
( ⋮
𝑓𝑛1
⋯ 𝑓1𝑛
⋱
⋮ ),
𝑜𝑝𝑡
⋯ 𝑓𝑛
(1)
𝑜𝑝𝑡
where 𝑓𝑖
= 𝑓𝑖𝑖 – i-th optimized objective deriving the production plan x, 𝑓𝑖𝑗 – optimum value of model corresponding to i-th attribute and j-th objective considering
the same set of production plan x and constraints.
4. Weights’ (farmers’ preferences) estimation was performed by developing
weighted goal programming with deviational variables:
5.
𝑛 +𝑝
Min ∑𝑛𝑖=1 𝑖 𝑖
(2)
𝑓𝑖
subject to:
∑𝑛𝑗=1 𝑤𝑗 𝑓𝑖𝑗 + 𝑛𝑖 + 𝑝𝑖 = 𝑓𝑖 , 𝑖 = 1,2, … , 𝑛, (3)
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∑𝑛𝑗=1 𝑤𝑗 = 1,
𝑛𝑖 , 𝑝𝑖 ≥ 0,
where 𝑤𝑗 – j-th objective’s weight, 𝑓𝑖𝑗 – elements of pay-off matrix, 𝑓𝑖 – i-th objective’s
value according to the observed actual production plan x, 𝑝𝑖 – positive deviational variable from i-th objective, 𝑛𝑖 – negative deviational variable from i-th objective.
6. Utility function construction for each cluster, which reflects farmers’
behavior according to determined objectives:
𝑈 = 𝑤1 ∙ 𝑜𝑏𝑗1 + 𝑤2 ∙ 𝑜𝑏𝑗2 + ⋯ + 𝑤𝑛 ∙ 𝑜𝑏𝑗𝑛
(4)
Model specification. Considering crop production plan x = (𝑥1 , … , 𝑥8 ) =
(wheat, rye, barley, oats, triticale, rape, buckwheat, fallow) following most important
farmers’ objectives have been selected (Andre, 2010):
1. Total gross margin (TGM) maximization 𝑓1 (𝒙).
𝑓1 (𝒙) = ∑8𝑖=1 𝐺𝑀𝑖 ∙ 𝑥𝑖 → max ,
(5)
where 𝐺𝑀𝑖 – gross margin of the crop i.
2. Risk (VAR) minimization 𝑓2 (𝒙). The risk in the current study is described as
variance/covariance matrix of gross margin in the cluster. Therefore
𝑓2 (𝒙) = 𝒙′ 𝑐𝑜𝑣[𝐺𝑀]𝒙 → min.
(6)
In order to find optimal production plan x for the target function 𝑓2 (𝒙), quadratic programming model should be solved.
3. Minimization of labor (LAB) input 𝑓3 (𝒙).
𝑓3 (𝒙) = ∑8𝑖=1 𝐿𝑖 ∙ 𝑥𝑖 → min,
(7)
where 𝐿𝑖 – labor requirements of crop i.
The constraint set for all mentioned objectives is based on total cultivating area, rotational considerations, positive values for crop areas and labor constraint. The
condition
∑8𝑖=1 𝑥𝑖 = 100
(8)
ensures that optimal plan x in each cluster is expressed as crop distribution percentage and all objectives can be comparable between clusters.
Clustering, DEA and quadratic programming calculations were performed in R
statistical software. Linear and weighted goal programming were executed by standard solver in MS Excel workbook.
3. Results and discussion
Statistical data show that planting of cereal and rape is becoming more popular
in Lithuania as it needs less labor effort if compared to livestock breeding. Further131
more, this popularity is supported by increase of purchase prices of those crops. During the last few years, the volumes of yield were also growing due to the improved
natural conditions and huge investments in modern tractors, combine harvesters and
farm implements. However, in 2013, farm net income of cereals, oilseeds and protein
crops’ farms was lower as compared to other types farms.
As was mentioned in the methodology section, the specialist cereals, oilseeds
and protein crops’ farms have been grouped into 3 clusters: relatively small, medium
and relatively large farms. Applied DEA method showed that about 25% of relatively
small and medium farms were considered efficient in their clusters. However, the
share of high performance in relatively large farms cluster was much higher – half of
relatively large farms took the lead in efficient production. FADN provided weights
of each efficient farm allow to derive representative farm in each cluster. Table 1
shows estimated cluster characteristics and representative farms’ production plan x of
each cluster, which will be used for further calculations.
Table 1. Characteristics of estimated representative farms
Indicators
Number of farms
Farm size, ha
Structure of crops, %
wheat
rye
barley
oats
triticale
rapes
buckwheat
fallow
Small farms
323
75
Medium farms
112
435
Large farms
18
1170
33.0
1.1
15.6
7.2
25.8
9.4
0.7
7.1
57.5
0.5
8.7
0.4
7.2
23.7
0.0
2.0
55.0
0.7
7.1
0.6
7.8
26.8
0.0
2.1
The optimal crop production plan x of TGM is the same for all clusters because
of the same constraints on crop rotation, labor input and total cultivating area (Table
2). The analogous situation is considered with LAB objective because of the same
reasons.
Table 2. Crop production plan x in small, medium and large farms according to
the objectives
Wheat
Rye
Barley
Oats
Triticale
Rapes
buckwheat
Fallow
TGM
52.0
0
8.0
0
5.0
30.0
0
5.0
Small farms
VAR
0
43.6
2.8
0
7.1
0.5
13.0
33.0
LAB
0
54.0
0
0
0
0
13.0
33.0
Medium farms
TGM
VAR
LAB
52.0
5.2
0
0
19.1
54.0
8.0
0.8
0
0
25.8
0
5.0
0
0
30.0
3.2
0
0
13.0
13.0
5.0
33.0
33.0
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TGM
52.0
0
8.0
0
5.0
30.0
0
5.0
Large farms
VAR
0.8
19.7
1.4
42.1
0.0
2.9
0
33.0
LAB
0
54.0
0
0
0
0
13.0
33.0
However it is more interesting to analyze the VAR objective’s plan production
in different clusters. In order to reduce risk impact representatives of each cluster
behave in different ways. Small farms refuse to produce oats, meanwhile in medium
and large farms it takes largest part. The reason for such behavior of medium and
large farms is one of the smallest variance/covariance of oats with other cultures (the
smallest one is for fallow: that’s why it reaches 33 % upper bound of the rotational
constrain). Small farms would prefer to grow up rye to avoid a risk of gross margin.
After optimization application, objectives were combined into pay-off matrix
for each cluster. The values of pay-off matrix show the relations among different
crops and objectives considered. One can notice the distance between actual situation
and single optimum influenced by crop distribution x (Table 3).
Table 3. Pay-off matrix for relatively small, medium and large specialist cereals,
oilseeds and protein crops’ farms
Objectives
Gross Margin
Small farms
Total Risk
Total labor
Gross Margin
Medium farms Total Risk
Total labor
Gross Margin
Large farms
Total Risk
Total labor
Optimum
VAR
–5546
1.2*107
1022
12663
6.5*106
1023
9164
9.7*106
988
TGM
50505
4.7*108
1415
65916
5.9*108
1415
65520
5.3*108
1415
LAB
–7494
5.5*107
931
26453
9*106
931
8880
3.4*107
931
Observed
25796
1.8*108
1342
63576
5.1*108
1432
62166
4*108
1428
According to constructed pay-off matrix farmers’ utility functions could be
derived in each cluster. Table 4 presents decision making weights.
Table 4. Farmers’ utility functions in relatively small, medium and large farms, %
Small farms
Medium farms
Large farms
TGM weight
37.0
74.9
85.6
VAR weight
63.0
25.1
0
LAB weight
0
0
14.4
The results show that the first hypothesis about the same farmers’ behavior in
relatively small, medium and large specialist cereals, oilseeds and protein crops’
farms should be rejected. Crop producers in small and medium farms take into
account gross margin maximization and risk minimization with different directions of
weights. However, holders of large farms prefer to minimize labor input instead of
risk minimization. Additional FADN data analysis confirms the behavior of large
farms’ holders: the farm net income per 1 AWU of these farms is the largest in the
survey. Such indicator could be reached in two ways: gross margin maximization or
labor input minimization. Although pointed objectives are the same in small and
medium farms, it could be noted that the importance of the objectives differs in
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opposite way: small farms prefer risk minimization and medium farms give the first
place to gross margin maximization. This leads to second hypothesis about gross
margin maximization as the main objective rejection. In general present survey’s
analysis shows that producers of specialist cereals, oilseeds and protein crops’ farms
follow at least two objectives in order to be efficient.
4. Conclusions
1. Lithuanian specialist cereals, oilseeds and protein crops’ producers aim to
achieve multiple goals and those goals are different according to farm size. Crop producers in small and medium farms seek to maximize gross margin and to minimize
risk, however, with different directions of weight. Large-scale farmers’ behavior is
based on gross margin maximization and labor input minimization.
2. Not all Lithuanian specialist cereals, oilseeds and protein crops’ producers
consider gross margin as its primary objective. Maximization of gross margin is the
most important attribute of utility function of medium and large farms. However, the
most important objective of small-scale producers is the minimization of risk.
3. The evaluation of more realistic farmers’ decision making has many practical applications, since it can be used in farm management, but also in agricultural
planning and policy analysis.
4. This research leaves room for further investigation into this field. In this
analysis it was assumed three different structures. However, future research can investigate more farm structures. This would enable to make further conclusions on the
multiplicity of objectives in farmers’ decision making.
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LIETUVOS AUGALININKYSTĖS PRODUKCIJOS GAMINTOJŲ SPRENDIMŲ
PRIĖMIMO VERTINIMAS TAIKANT DAUGIAKRITERINĮ OPTIMIZAVIMĄ
Andrej Jedik, Virginia Namiotko
Lietuvos agrarinės ekonomikos institutas
Įteikta 2016 05 10, priimta 2016 06 01
Santrauka
Mokslinės literatūros analizė rodo, kad ūkininkai, priimdami sprendimus, nebūtinai siekia
vien tik maksimizuoti pelną. Šiame straipsnyje sprendžiama mokslinė problema: ar tokie tikslai
kaip ūkininkavimo rizikos ir darbo laiko kiekio minimizavimas turi įtakos ūkininkų sprendimams?
Šio straipsnio tikslas – įvertinti Lietuvos augalininkystės produkcijos gamintojų sprendimų
priėmimą santykinai mažo, vidutinio ir didelio dydžio ūkiuose taikant daugiakriterinį optimizavimą.
Tyrimui buvo naudoti 2013 metų Lietuvos javus ir rapsus auginančių ūkininkų, įtrauktų į Ūkių apskaitos duomenų tinklą, duomenys. Tyrimas parodė, kad skirtingo dydžio ūkiuose ūkininkų prioritetai yra skirtingi. Be to, buvo nustatyta, kad pelno maksimizavimas nėra vienintelis javų ir rapsų
augintojų tikslas.
Raktiniai žodžiai: sprendimų priėmimas, ūkininkų elgsena, daugiakriterinis optimizavimas,
naudingumo funkcija.
JEL kodai: C61, D22, Q12.
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