Advances in Science, Technology and Engineering Systems Journal Vol. 5, No. 6, 497-506 (2020)
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ASTESJ
ISSN: 2415-6698
Special Issue on Multidisciplinary Innovation in Engineering Science & Technology
An Economic Theory Perspective for the Fight Against Poverty in the Peruvian Andes
Robert Antonio Romero-Flores*
National University of the Altiplano, Department of Systems Engineering, Puno, 21001, Peru
ARTICLE INFO
Article history:
Received: 31 August, 2020
Accepted: 05 November, 2020
Online: 20 November, 2020
Keywords:
Complex systems
Mathematical modelling
Economic theory of water
Systems simulation
1.
ABSTRACT
The fight against poverty in the Peruvian Andes is a complex task in which various
professionals, such as engineers, economists, anthropologists, among others, participate.
The uncertainty of the decisions taken today, no matter how appropriate they may seem,
such as million-dollar investments in irrigation infrastructure, can result in overproduction and, therefore, in economic recessions. For this reason, a new mathematical
simulation model is proposed using system dynamics to predict recession phenomena that
can occur in months or after a few years of auspicious economic growth, and that can cause
sales prices to be below production costs. The author has developed the conceptualization
of the production system of irrigation improvement projects in several years of
multidisciplinary work in the Cusco region of Peru. The primary objective of irrigation
projects is to improve the socio-economic conditions of the farmer. Techniques as the
fulfillment of goals have been used to quantify qualitative dimensions such as strengthening
organizations and trainings that are key to guaranteeing irrigation improvement projects'
sustainability in the long term. Therefore, it has been possible to identify the variables and
relationships of this type of socio-economic system. To validate the model, we verified that
the simulated data are consistent with the historical data collected. Likewise, if the values
of the various proposed models' variables are adequately modified, these can be applied to
other types of production systems under different market conditions. The dimensions
addressed, such as supply, demand, sale price, land, production volume, public budget, etc.,
enhance the research's importance, making the simulation model formally expressed also
acquire nuances from economic theory for the fight against poverty-based on water. One
of the study's conclusions is to understand the production systems, it is necessary to see
them in the context of their regional economy's behavior.
Introduction
One of the most important policies in the fight against poverty
of the Peruvian government is implementing irrigation
improvement projects. In this paper, we will address issues in
greater depth about the experience of Plan Meriss Inka (PEPMI) to
deal with the social component. We will highlight the
characteristics that make this research an economic theory of water
perspective that could not be exhibited in work originally
submitted in the 2019 IEEE World Engineering Education
Conference (EDUNINE) [1].
The primary nature of the irrigation improvement projects
implemented by PEPMI is multidisciplinary, in which
professionals of different natures such as engineers, economists,
*
Corresponding Author: R.A. Romero-Flores, Urb. Chanu Chanu III S10,
+51951885805, rromero@unap.edu.pe
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https://dx.doi.org/10.25046/aj050659
biologists, anthropologists, among others. One of the
characteristics that stand out from this type of project is the high
social component [2]. Since the first projects' implementation, it
was observed that, despite providing rural communities with
modern irrigation infrastructure. Farmers were reluctant to use it.
A situation that has required social partners to decipher this
peculiar impasse. Anthropologists' role in these cases has been
essential to understanding the farmer's idiosyncrasy in terms of the
intervention of new irrigation projects in their communities it
refers.
From work carried out, it was concluded that the resistance to
using the new irrigation infrastructure was because the farmer only
uses the irrigation infrastructure that they have built and, therefore,
they consider it as their own. So, not having participated in
constructing this new irrigation infrastructure donated by the
government, they did not consider it their own. To overcome this
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problem, Community participation is incorporated as part of the
project's financing, which consists mainly of the farmers’
workforce's valuation in the construction of the irrigation
infrastructure [3]. Similarly, there are cases of projects in which it
has been possible to significantly improve water resources
available without the need to build new irrigation infrastructure; it
was only required to improve water management and irrigation
techniques to increase agricultural productivity. This experience
leaves an important lesson for professionals who are not from the
social area, which is that, to achieve the objectives of the projects,
they should improve their communication skills and understanding
of the farmer idiosyncrasies in the area [3]. The social component
is just one of the many problems. It gives an idea of the complexity
of understanding and managing irrigation improvement projects in
the fight against poverty in the Peruvian Andes. The ability and
experience to face these peculiarities have made the PEPMI to be
considered as a model project in South American by the German
donors German Technical Cooperation (GTZ) and the State
Development Bank of the Federal Republic of Germany (KFW).
In this understanding, the primary objective to be achieved
with social intervention projects is their sustainability in
strengthening the organization of farmers and profitability. In other
words, farmers must manage their own resources without the
accompaniment of PEPMI staff and only through its own
organization and self-financed by the profit that results from the
sale of their products.
In the Peruvian Andes, there is the occurrence of weather
phenomena such as droughts and frosts that cause the loss of crops.
The main effect of having adequate irrigation infrastructure is to
ensure cultivation; firstly, supplying water in case of droughts and
making it possible to recover plants from frosts. So that at least one
harvest per year can be ensured. This is also known as crop safety.
It is possible to increase the number of agricultural seasons per
year by up to two in the best cases. Then, water administration is a
strategy ancestrally used since the Incas to face unpredictable
climatic changes and to guarantee food for the population [4].
To overcome these problems, millions are invested in
infrastructure and training. But in the projects implemented in the
Chumbivilcas-Espinar provinces, it has been shown that this does
not always happen. Due to the overproduction of dairy products,
there was a regional recession. A phenomenon in which supply
exceeds demand and produces a drop in prices. In this case, prices
fell even below production costs. So, the right short-term decisions
can lead to long-term problems [5].
In this research, we are concerned with developing a
production model to understand the factors that participate in it.
The model simulation process has allowed the model to be
validated. However, to know if the production process is
profitable. It is required to evaluate it in the environment of its
regional economy.
Therefore, it is also necessary to conceptualize and formulate
economic factors. This gives greater importance to our research as
it analyzes the Andes' economy from a perspective of fighting
poverty. The methodology used to achieve our objectives is mainly
system dynamics, as it includes the methods of thinking of systems
and servomechanisms. The same ones that are suitable for complex
systems.
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As a result of the research, we have obtained the formulation
of the different production sub-systems such as training,
investment, available water, infrastructure, and others. And we
have also managed to formulate the subsystems of the regional
economy such as supply, demand, sale price, competition, etc. This
makes it possible to project over time the impact of the irrigation
improvement projects' anti-poverty policies. It also allows us to
carry out a sensitivity analysis to know if the decisions we make in
implementing the project are the correct ones, mainly to avoid
regional recessions or falls in products sales prices [1].
2.
Related Works
2.1. System dynamics
System dynamics is a popular simulation methodology
developed by J. Forrester at the Massachusetts Institute of
Technology (MIT). This simulation methodology is based on the
theory of servomechanisms and feedback. It is also related to
areas such as general systems theory and cybernetics. It also uses
methods to study complex systems that act as an interlocutor
between engineering methods and the methods for social systems
[6]. One of the most important applications of System Dynamics
is the world model published in 1970. A simulation of the
behavior of society is shown under current “unplanned” growth
conditions. The results of the simulation of the model show an
over-exploitation of resources and a drop in population. The more
population, the more waste is generated, and the more waste, the
more diseases are generated is one of the conclusions of the model
[7].
In the work of Fifth Discipline, considered to impact the
business world greatly, revalues Forrester's systems dynamics.
The author in [5] considers important for the understanding of
modern organizations the study of dynamic systems, identifying
the system's environment, and feedback mechanisms with it. He
does not consider essential to arrive at the formulation of
mathematical models. As a conclusion to his studies, he proposes
the following disciplines: systems thinking, personal mastery,
mental models, the construction of a shared vision, and team
learning.
For irrigation research, dynamics can also be applied to the
study of water management jobs, as demonstrated in the proposal
for an optimization model for irrigation management in Australia
[8]. In [9], the authors also developed a simulation model for
China’s water transport problem. In both works, positive results
have been obtained using system dynamics.
2.2. Systems thinking
Systems thinking is the fifth discipline; the importance of
systems thinking lies in being the body that unites the other
disciplines of intelligent organizations. This job is incisive in
pointing out that one of the factors for the failure of projects is the
lack of systems thinking in their implementation [5]. Systems
thinking is based mainly on the method of extension or synthesis.
This becomes a premise for troubleshooting, where it is
recommended to first view the system as part of a bigger system
[10]. In this regard, we must comment that the classical scientific
method, as we know, uses the analytical or reductionist method,
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which, contrary to the synthetic method, what it does is studying
the system in its components. The author in [11] categorically
considers as a limitation of the scientific method. However, one
of the most renowned authors on epistemology comments that
systems thinking is an unfounded fashion issue and cannot
generate scientific knowledge [12]. The author in [10] refuted this
position, who maintains that the analytical and synthetic methods
do not replace each other. On the contrary, they complement each
other. In the present work, we show that it is possible to generate
knowledge in the scientific method's formal language, between
the system and its environment (exogenous variables) and the
feedback mechanisms for adjusting the endogenous variables.
appears the next components: consumers, producers, the market
for goods and factors, and government intervention [13]. To
formulate the simulation model of the production system, all these
dimensions have been taken into account. Therefore, in this
document, we will extend the original work to a perspective of
economic theory whose main engine is water. In Figures 1 and 2,
we can see the Sutunta lagoon and the dam built to store 4 million
cubic meters to irrigate 6000 hectares.
2.3. Fight against poverty
Thus, water is the engine for the economy of the Andes,
although its cost is relatively low given its usefulness. To
highlight the importance of water, we will mention the waterdiamond paradox that tries to explain the low cost of water
concerning diamonds that cannot generate life. This explains that,
although the marginal utility of diamonds is much greater than the
marginal utility of water, water's total utility is always greater than
the total utility of diamonds [13].
To eradicate poverty, the author in [14] comments that the
financial system has been saved on a global scale; for example, in
Mexico, the banking system has been saved. Consequently, the
cost of helping the poor is much lower and, in financial terms,
more profitable if they are to be part of the aggregate demand.
And, despite extreme poverty, we seem to have plenty of
resources. At the same time, another study concludes that almost
a billion people go to sleep hungry every day. In comparison,
another billion people suffer from obesity, and 30% of food
production is wasted, even from its mismanagement in harvest,
sales, and post-consumption [15].
3.
Figure 1: Location map of the Sutunta lagoon in the province of Espinar-Cusco
over 4000 m.a.s.l.
Methodology
The experience that served as inspiration for this work was that
of the irrigation improvement projects in the ChumbivilcasEspinar provinces that, due to their height (over 3820 m.a.s.l.) and
geography, these are areas where low temperatures predominate
(even below zero), all this leads to the existence of extreme poverty
in the area [16]. Conditions that, in the first instance, made
interventions in the so-called “high” provinces impractical.
However, initially, they gave unexpected positive results thanks to
the experience of the PEPMI and the adaptation of strategies that
consisted, mainly, in cultivating imported pastures that resisted
low temperatures and that were the main engine of the livestock
industry and its derivatives in the area. Which brought the
economic growth of the area. Despite this, after a few years, there
was overproduction that manifested itself in the drastic decrease in
sales prices. Therefore, it is necessary to manage uncertainty, the
consequence of the decisions we make, and that, at first, seem the
correct ones in the medium and long term, can become
counterproductive. The explanation for this phenomenon was that
an adequate market study was not carried out. Thus, to understand
the interaction of the multiple factors, it was necessary to
understand the behavior of the market and the mechanisms by
which the sale price was mainly obtained. In an economic theory,
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Figure 2: The dam built in Sutunta lagoon
In the conceptualization and formulation of the new production
model, the systems dynamics methodology was used. The same
one is based on the general theory of systems proposed in [11], the
author that deals mainly to provide a general framework for
science. To do this, it recognizes the concept of equilibrium or
homeostatic point. The same that we must reach in the interaction
of supply and demand in the market model also proposed [1].
Nash’s equilibrium abstracts the theory of non-cooperative games
that involve sellers' participation, sets of strategies, and profits
[17].
In the conceptualization phase, approximately 285 variables
have been identified. The same ones have been organized in the
dimensions of investment, training, organization, water for
irrigation, irrigation infrastructure, production, market,
environment, public budget, and water supply. As mentioned
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above, the organizational dimension is primarily qualitative, and
techniques have been used to allow it to be considered and provide
qualitative information. This dimension has been adequate to be
considered in the proposed production model. Another
characteristic is that the production model allows obtaining a
production volume that is considered supply and considering the
existence of competition. Therefore, it is not an empirical model
for educational purposes [6]; otherwise, it can provide information
in a real environment. The number of variables and the
peculiarities described makes it different from the authors'
production models in [18], who propose a model of positive
mathematical programming for models of regional production in
agricultural-environmental programs and the classic spider web
model [13].
The simulation of the production model has been carried out
in the VENSIM program; the simulation results have served to
validate the model. For validation, the Anderson-Darling
normality test was used, whose results have been superior to α =
0.05. As a result of the optimization model, non-linear
programming with restrictions has been used to develop an
optimization model that allows us to find the global optimum
(profit maximization, cost minimization, and equilibrium point).
Likewise, an analysis was carried out on the optimization model
using nonlinear programming and genetic algorithms to determine
the selection operators' efficiency in restricted non-linear
problems.
4.
Discussion
4.1. Conceptualization of the elements of the economic system
for the fight against poverty based on water
In South America, the Inca culture developed. One of the most
important cultures in the world whose cultural richness was based
on values such as community work, also known as the “ayni” and
the “minka”. The Incas built large hydraulic works with the
primary purpose of supplying food to the entire population. The
importance of institutions like the PEPMI lies in need to revalue
the cultural richness that, in some way, was being forgotten. In the
field of intervention, they can be observed as problematic
situations: inadequate irrigation infrastructure (inland canals that
filter water), little farmer organization, and little knowledge of
irrigation techniques [4]. This situation can even be complex if the
following characteristics exist: conflicts, undefined access rights
to water, water scarcity, and geological problems [3].
To solve these problematic situations, PEPMI implements
irrigation improvement projects whose objective is to provide the
population in the project area with the possibility of improving
production and, therefore, improve their quality of life through
access to more and better education, health, etc. services.
4.1.1. Production systems modeling in irrigation improvement
projects
Consistent with the fifth discipline [5], a work in which the
author concludes that one of the causes of project failure is the lack
of a systems approach. If we review the experience of the projects
implemented in Chumbivilcas-Espinar, in which there were
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problems of regional recession, after a few years of economic
growth, it can be seen that, as part of the bigger system, the
“market” is an exogenous component that is always present in the
environment of the system. So, it is necessary to carry out an
adequate market study and, for simulation purposes, to determine
its feedback mechanisms. In figure 1, it can be seen through a block
diagram, the main identified subsystems. Given the complexity of
these projects' implementation, approximately 285 variables and
90 feedback loops have been observed and properly grouped into
subsystems, as shown in Figure 3 [1].
Figure 3: Block diagram of the proposed model for the agricultural production
system
Figure 1 also identifies the necessary elements that participate
in an economic theory (producers, consumers, goods markets, state
intervention, etc.), having, in this case, water as the engine for the
fight against poverty [13] or as “Theory of the economic and social
value of water” states in a perfect market where there are several
buyers and sellers, each commodity in the economy will be given
its value [19]. As previously mentioned, the sustainability of
projects is based on the strengthening of organizations and
profitability. It is, then, necessary to know the profitability to
identify the elements that participate under the economic theory
defended by various authors [13].
4.2. Formulation and validation of the simulation model
The first objective of the work is to know the future behavior
of the production system of the irrigation improvement projects
implemented by the PEPMI. So, the planners will have a tool that
allows them to know if they are making the right decisions or if the
millionaire investments in infrastructure can cause short-medium
or long-term adverse effects such as a recession. These phenomena
have occurred in the provinces of Chumbivilcas-Espinar and the
northern mountain range of Lima [20]. The causal diagrams made
in the conceptualization phase have to be converted to
mathematical logic models based on Forrester diagrams. For which
the Vensim Personal Learning Edition (PLE) software has been
used.
4.2.1.
Subsystems formulation
Each of the subsystems shown in figure 1 are explained below:
A. Water supply
Determining the future supply of water is one of the main tasks
to know. This to guarantee the water supply at the head of the plot.
To achieve this, the historical information of the Pampaconga
project has been considered. After analyzing the information, it has
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been considered to perform a probability function for each month,
using discrete probability distribution functions based on
histograms. Requirements for the Monte Carlo simulation method
[21]. Due to the limitations of Vensim Personal Learning Edition
(PLE), the treatment of each probability function has been carried
out in Excel and the results added in lookup functions in the
implemented model.
multidisciplinary team includes anthropologists, professionals who
serve as important interlocutors between farmers and PEPMI.
In conclusion, the resistance to the change presented to use the
new and free irrigation infrastructure was due; because farmers
only use the infrastructure in whose construction they have
participated. Therefore, project financing includes the community
contribution, which is approximately 15 to 20% of the total project
budget. This amount guarantees the participation of community
members in the works to be built [3].
Another characteristic to take into account is that the Peruvian
government considers irrigation improvement projects as social
programs. And, given the appearance of economic problems, as the
global pandemic caused by Covid-19, these programs are the first
to reduce the public budget.
Figure 4: Projection of water availability due to rainfall
As shown in Figure 4, the hydrological year in Peru begins in
September (month 9), and the high peaks represent the El Niño
phenomenon. With climate change, this phenomenon will be
increasingly present in the Peruvian Andes. When this occurs
within the project's scope, the loss of production, and even
irrigation infrastructure and all kinds of infrastructure is almost
inevitable [22].
In the conceptualization of the production model in its
interaction with the market, the investment subsystem receives
feedback from the market, specifically, of the profit obtained from
the sale of the products and the availability of financing that
predisposes the advance of trainings and irrigation subsystems
infrastructure.
C. Trainings
Training is an essential component to guarantee the
sustainability of the project in its component of strengthening
organizations and in terms of increasing productivity in the
components of water management and the application of irrigation
and cultivation techniques.
The PEPMI, being a state project, depends on the monthly
budget. According to the monthly budget, it has the necessary
factors to carry out the training: operational equipment, material,
and workforce.
Figure 6 shows the Forrester diagram that explains the
availability of resources to conduct the trainings.
Figure 5: Projection of total water availability
The total water availability is made up of the rains and the flow
of the rivers. These are exogenous variables that cannot be
influenced. The projection of water availability is shown in Figure
5.
B. Investment
This subsystem is born from the public budget and external
debt. For external indebtedness, there is German technical
cooperation. According to the experiences of the first works
implemented, the farmers showed resistance to change, to use and
manage the modern irrigation infrastructure implemented by
PEPMI. In addition, there is also the possibility of conflicts
between communities over access to water and/or land. This
demonstrates the high social component of the irrigation projects
implemented [3]. Sometimes the engineer has to act as a
sociologist to meet its goals [12]. To overcome these problems, the
Figure 6: Forrester diagram: Availability of resources for training
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The equations that govern the Forrester diagram in Figure 6
are as follows:
IPER = (BT*WW)/AS
(1)
the farmer achieve 100% adequate water management. Similar
behavior is observed in the variable’s efficiency in applying
irrigation techniques, efficiency in applying cultivation
techniques, and strengthening organizations.
where:
IPER: Personal ratio.
BT: Budget for trainings.
WW: Workforce weight = 0.5.
AS: Average salary = S/ 2000.00.
Percentage for trainings = 0.15.
IOE = (BT*OEW)/ACO
(2)
where:
Figure 7: Advancement in water management
IOE: Operative equipment ratio.
D. Irrigation infrastructure
BT: Budget for trainings.
OEW: Operative equipment weight = 0.3.
ACO: Average cost of operation = S/ 1000.00.
ISUP = (BT*SW)/ACS
(3)
where:
ISUP: Supplies ratio.
BT: Budget for trainings.
SW: Supplies weight =0.2.
ACS: Average cost of supplies = S/ 300.00.
The trainings are carried out according to the availability of
resources. The progress ratio is calculated according to the input
targets programmed versus those available. And the total training
per month predisposes the increase of water management,
efficiency in the application of irrigation techniques, efficiency in
the application of cultivation techniques, and strengthening of
organizations that are governed by the following equations:
WM = 0.065*TPM
(4)
EAIT = 0.06*TPM
(5)
EACT = 0.07*TPM
(6)
SO = 0.065*TPM
(7)
where:
TPM: Trainings per month (the objective is 4 per month).
Irrigation infrastructure is the component with the highest cost,
depending on the size of the project. Its importance lies in the
possibility of transporting water for kilometers without loss due to
seepage and optimizing its storage and availability through dams
and reservoirs. Advantages that the channels made on land do not
have due to the high filtration rate. Irrigation infrastructure is also
important to face adverse weather phenomena such as droughts, as
it allows managing water scarcity, guaranteeing harvest (crop
safety) and counteract adverse weather phenomena such as frost
and hailstorms, since having a permanent water supply crops can
recover, and, in areas where optimal conditions exist, the number
of crops per year can be increased. What is also known as an
increase in land use, which is the first step to fight poverty.
Then, the countries need to provide adequate irrigation
infrastructure to manage the scarce water resource. This is because
the imminent effects of climate change will affect primary sectors
such as fisheries and agriculture, such as by 6% to the Peruvian
GDP for the year 2030. One of the author's conclusions in [23] is
that the emission of polluting gases and, therefore, the effects of
climate change will continue. This situation evidently increases the
total utility of water as part of managing scarcity and climate
variability. Then, new efficient irrigation techniques such as
dripping and sprinkling should also be considered. These aspects
are already being considered in the making of water and irrigation
laws.
Figure 8 shows the Forrester diagram that explains the
availability of resources to carry out the irrigation infrastructure.
The equations that govern the Forrester diagram in Figure 8
are as follows:
WM: Water management.
Percentage for infrastructure = 0.85
EAIT: Efficiency in the application of irrigation techniques.
(8)
ITS = (BI*TSW)/TSS
EACT: Efficiency in the application of cultivation techniques.
SO: Strengthening of organizations.
As can be seen in Figure 7, in month 28, approximately the
objective is achieved. This indicates that the trainings have made
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where:
ITS: Technical stuff ratio.
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BI: Budget for infrastructure.
where:
TSW: Technical stuff weight =0.06.
ICP: Construction personnel ratio.
TSS: Technical stuff salary = S/ 2000.00.
BI: Budget for infrastructure.
CPW: Construction personnel weight =0.59.
CPS: Construction personnel salary = S/ 800.00.
Once the necessary resources are in place to carry out the
irrigation infrastructure, the progress of the works depends on the
availability of resources versus what is programmed and the
weather conditions that allow the construction to continue. The
construction progress is shown in Figure 9.
Figure 9: Progress in the construction of irrigation infrastructure
E. Water for irrigation
Figure 8: Forrester diagram: Availability of resources for irrigation infrastructure
IOE = (BI*OEW)/ACO
(9)
According to the progress of the irrigation infrastructure and
the administration of water, the water for irrigation is determined
according to the water demand calculated in the study phase.
Figure 10 shows the Forrester diagram that explains the
interaction of variables that determine the availability of water for
irrigation.
where:
IOE: Operative equipment ratio.
BI: Budget for infrastructure.
OEW: Operative equipment weight = 0.24.
ACO: Average cost of operation = S/ 4000.00.
ICM = (BI*CMW)/CMC
(10)
where:
ICM: Construction material ratio.
BI: Budget for infrastructure.
CMW: Construction material weight =0.11.
Figure 10: Forrester diagram: Water for irrigation
CMC: Construction material cost = S/ 15.00.
ICP = (BI*CPW)/CPS
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(11)
The equations that govern the Forrester diagram in Figure 10
are as follows:
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IWI = [(D*WMW)*WM] + [(D*IIW)*IPP]
(12)
WF: Water factor.
where:
WWF: Water factor weight (0.6).
Project water demand: 17,172.00 m3
SF: Supply factor.
D=PWD-WI
SFW: Supply factor weight (0.1).
PWD: Project water demand.
TF: Trainings factor.
WI: Water for irrigation.
TFW: Trainings factor weight (0.15)
WMW: Water management weight
MF: Machinery factor.
WM: Water management.
MFW: Machinery factor weight (0.1).
IIW: Irrigation infrastructure weight
HRF: Human resource factor.
IPP: Infrastructure progress percentage
ʃ
Water for Irrigation (t) = IWI(t)dt
where:
IWI: Water for irrigation rate
HRFW: human resource weight (0.05).
(13)
Figure 11 shows the increase in irrigation water until the
project water demand is met, an important parameter that also
serves to design the irrigation infrastructure (channels, reservoirs,
canoes, rapids, etc.). The expansion of the agricultural frontier has
a similar behavior within the project's scope as planned.
PL: Production land.
Note that, in extreme situations, without the water factor,
production will be zero. Otherwise, it will be proportional in terms
of the existence of the other production factors that have been
considered. Figure 12 shows the production achieved. Note that,
starting in month 33, there is a significant increase due to the
already available new irrigation infrastructure, training, supplies,
etc.
Figure 12: Production volume
G.
Figure 11: Increase in water for irrigation
F. Production function
The proposed simulation model for production in irrigation
improvement projects includes the variables of water, supplies,
training, machinery, and the human factor, whose interaction
determines the quality and quantity of the cultivated land [1]. This
is expressed in equation 14:
Adequate land for cultivation =
(14)
0
; WF ≤ 0
[WF*WWF+SF*SFW+TF*TFW+MF*MFW+HRF*
HRFW]*PL
; WF >0
where:
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Market
Once the production model has been obtained to determine
the sustainability of the project, we must determine if there is a
profit for the farmer due to sales in local markets. At this point,
the proposed work requires to know the behavior of the market
whose proposed model is of perfect competition [13].
Therefore, the present research becomes a broader study of
the regional economy and an economic theory approach to
fighting poverty, in this case, based on water as the main engine.
Whose total utility in the medium term will allow farmers to
access better living conditions such as health, housing, education,
etc. Among these factors, we must highlight the greater and better
access to education of the Andean population, as it will allow
access to better economic income. About education, the winner of
the last Nobel Prize in economics, in his work in Kenya,
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concludes that better innovations must be made that allow more
people to benefit economically from education [24].
H. Price determination
The interaction of supply and demand (which we have
considered dividing into current demand and potential demand)
and the seasonality of both allows us to know the product's sale
price. Compared to the original work [1], in the present, we are
going to present a new model described in equation 15.
Price = AP + [AP*(1-(SM+SMF))]
on because it is difficult for producers to influence the sale price.
Who governs us and defines the sale price is the market. Therefore,
it is essential to reduce costs by implementing modern
management techniques within organizations to obtain greater
benefits. To define the optimization models, as observed through
this work, we have the great restriction of the market (competition,
seasonality, weather conditions, etc.). Therefore, it has been
determined that the optimization of production is a restricted
problem of the non-linear type. The objective function to
maximize utility is shown in equation 17.
(15)
Max Z=16εX1 X2 – 11.14X1
where:
Subject to:
AP: Average price.
X3 ≤ 3600+16X1
SM: Satisfied market.
; Stock on the market
X3-16X1 ≤ 3600
SMF: Stocks in the Market Factor.
Satisfied Market = Production volume / Current demand
(17)
(16)
Figure 13 shows the sale price behavior, in which it can be
seen that the price reaches S/ 1.23 in times of scarcity and S/ 1.00
when there is overproduction. To carry out a sensitivity analysis,
a scenario was constructed. The project's production increases by
30%, and due to market capacity (demand) occurs overproduction
and, therefore, the sale price drops to S/ 0.66 per kg. These results,
in a real environment, could occur in a few months or years. Note
that the simulation is for 72 months, and, during the year, there
are various seasons. This has been considered from the
conceptualization of production and the market model. It
represents an advantage and differentiates our proposal in relation
to other production and market models such as the spider web.
X2 ≤ AP+AP*[1-16 X1 ⁄ X3+X4]
; Sale price
Replacing and solving:
Being: AP = S/ 1.10 (Average price)
X2 ≤ 2.2-17.6X1 ⁄ X3+1.1X4
X1 ≤ 400
; Arable area
X4 = 0.1
Solving, it is obtained that the maximum profit is S/ 5
784,000.00 and the sale price results S/ 1.6 (X2).
5.
Conclusions
The new proposed simulation model allows for
understanding the behavior of the production process of irrigation
improvement projects. In this paper, the systems dynamics
methodology has been used mainly for its formulation. The new
model allows the projection of data in the future and, in this way,
determine the impact of the decisions that are made and if they do
not lead to long-term problems. In the conceptualization phase, it
has been possible to identify endogenous and exogenous variables;
Among the exogenous variables, the behavior of regional markets
stands out, determining the sale price of products. For the
validation of the model, the Anderson-Darling normality test has
been used for all the identified subsystems (training,
strengthening of organizations, irrigation water, farmland, etc.).
We obtained from the normality tests values higher than α = 0.05.
Figure 13: Sale price behavior obtained in simulation
4.3. Production optimization
Another aspect contemplated in economic theory is the
maximization of producers' profits, who need to maximize the
difference between total income and total cost. The break-even
analysis allows us to know the minimum level of sales we must
reach to avoid losses. Regarding the minimization of costs, the
author in [25] recommends that this is the area we should focus
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The production factors that we identify for irrigation
improvement projects are water, inputs, training, machinery, labor,
and land. The respective weights can be seen in equation 14. The
irrigation infrastructure and water management determine the
availability of water. All these factors in the model determine the
amount of cropland and the production volume to obtain.
However, to measure the profitability of production, it is
necessary to know its efficiency concerning the regional economy.
That's why we formulate models that allow understanding of the
market's behavior and sales prices in the region. The proposed
models also make it possible to carry out sensitivity analyzes and
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R.A. Romero-Flores / Advances in Science, Technology and Engineering Systems Journal Vol. 5, No. 6, 497-506 (2020)
detect the appearance of regional recession phenomena. All these
models have been expressed in a formal language, a requirement
of epistemology for the generation of knowledge. Then our study
becomes a perspective of economic theory for the fight against
poverty based on water and its correct use.
For the formulation of optimization models, the nonlinear
programming techniques based on objective functions and
restrictions have been considered. The dimensions evaluated were:
profit maximization, cost minimization, and breakeven point. The
proposed production and market models have become constraints
or objective functions as appropriate in the optimization model.
To validate the optimization model, it has been verified that they
comply with the Kuhn Tucker conditions. The optimization
problem has also been analyzed using genetic algorithms, whose
application has made it possible to know that the sexual selection
operator is the most efficient for achieving global and local
optimums.
[20] Ministry of Agriculture and Irrigation, Potato: Characteristics of National
Production and Marketing in Metropolitan Lima, MINAGRI, 2017.
[21] V.P. Singh, System Modeling and Simulation, new age international (p)
limited, 2009.
[22] A Klauer, El Niño La Niña: The ocean-atmospheric phenomenon of the South
Pacific, a challenge for science and history, ISBN: 9972–817–09–1, 2000.
[23] P. Vargas, Climate Change and its Effects in Peru, Central Reserve Bank of
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[24] E. Duflo, P. Dupas, M. Kremer, “School governance, teacher incentives, and
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The difficulties we had were access to information and the
models' calibration, which is a process difficult and slow in which
VENSIM has been very helpful. In future works, we will apply
the proposed models in the Titicaca lake basin, and we will
contrast them with time series.
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