Application of Mathematical Models to Increase the Production and
Productivity in the Indian Agriculture Sector
Suggestion of a Research Project
Background
With a population
of over a billion people, India
depends heavily on its agriculture. The country has made enormous strides since
independence but it still struggles to supply the people with the needed food
products. That the nation has to make strong efforts to increase agricultural
production is imperative. While we search for scientific and technical methods
to accomplish such improvement, the lessons from the manufacturing and the
information technology sectors may be worthwhile to capture and apply to this
sector. Indian manufacturing sector is able to compete internationally both on
cost and quality by applying latest technologies and management techniques.
Hence the appropriate questions relate to identification of the techniques and
their potential for application to the farming sector.
Indian farming
sector is still following the traditional methods except for the introduction
of technologies as a result of the Green Revolution, and White Revolution. It
is quite possible that the various farm inputs are applied in a non-optimal
manner. While the manufacturing sector benefited from statistical process
control methods, the agriculture sector has no such process controls. Private
sector invests its funds in the most profitable and productive manufacturing
ventures in a decreasing order of opportunity to gain on the rate of return.
Being a traditional family run sector, farming businesses have no such resource
and asset allocation policies and perhaps suffer poor returns in terms of
production, productivity, quality, and value.
It is suggested
that these issues should be examined and the application of appropriate mathematical
optimization (Operations Research) and statistical methods and techniques
should be investigated. Three methods are discussed in this paper.
This author
suggests a project to investigate these methods and the Indian farming sector
be given tools to make proper decisions to apply resources and control the
processes with the goal of increasing production, productivity, and value of
the farming sector.
Current Situation
In India , the
farmers are not all free to make their own decisions. It is neither an entirely
free market nor a totally government controlled enterprise. Farmers depend on
the Government for
•
Finance, subsidies, and price guarantees
•
Water, electricity, seeds, fertilizers, and pesticides
•
Latest farming knowledge, technology, and information
•
Supply chain and logistics
•
Reaching customers
•
Access to markets through procurement.
In turn, governments are
•
Driven
by political pressures from framers, laborers, middlemen, and consumers
•
Lacking
in comprehensive knowledge, plan, and a cohesive policy
•
Burdened
by inept governance, inadequate official services, and leaking systems,
•
Saddled
with high levels of subsidies to farmers, unrealized production and
productivity targets, and high prices to customers.
Various
governments have been offering to farmers some combination of free land, power,
water, and knowledge of agricultural practices, subsidized seeds, fertilizers,
pesticides, and insurance with the hope of increasing farm productivity and production.
The governments also provide price support through minimum guaranteed price and
procurement of products. At the same time, governments sell agricultural
products to people who are below poverty level and some above poverty level at
highly subsidized prices. In general there is a long line of bureaucrats in
both the supply chain and the customer logistics.
The impact of
these policies and support schemes cannot be said to be beneficial to the
farming sector despite giant strides made in the availability of agricultural
and faming sciences and technologies and management methods.
First Steps for Remedying the Situation
It is essential
that certain fundamental changes are required in the nation’s thinking about
agriculture. Leaders should agree that basic premises about farming.
•
It is a Business
•
It produces essential food products
•
It creates jobs for millions of rural people
•
It is the backbone of the rural economy
As a business, the farming sector should
•
deliver profits to investors and farmers
•
show continual growth
•
increase production annually
•
rise productivity annually
•
deliver products to consumers at affordable prices with
a high degree of reliability
•
continually improve complete system efficiency
•
be less burdensome on labor by utilizing available
advanced and emerging sciences, technologies, and techniques
•
derive advantage from learning
•
take advantage by applying latest management methods
and techniques
•
satisfy national needs of food supplies
Approaches to desirable solutions will call for the application
of
•
Best technical knowledge & skills
•
Appropriate resources
•
Right policies
•
Identifying optimal sets of inputs
Resource Constraints
As stated earlier, India has a large population and
65% of it depends on the farming sector. The availability of land is not
unlimited. Under these circumstances the utilization of land deserves the best
consideration. There is a great demand from other sectors of development for
various resources (e.g. land, water, power, and finance) from other sectors
also.
Systems View of the Farming Sector
Here is a brief description of the farming sector from a
systems perspective. Figure 1 shows a single farm as a system.
The aim of the system is to obtain the maximum possible
output for minimum input and gain good profits.
Figure 2 shows the system with a variety of typical inputs
and one output.
Figure 2: Farming Operation of a Farm with Typical Inputs and an Output
Figure 3 shows a systems view of the farming sector as a
system.
Figure 3: Farming as a System showing Typical Inputs and
Typical Outputs
Figure 4 shows quantities of inputs to and outputs from the farming system.
Figure 4: Farming as a System showing Quantities of Inputs and Outputs
Resource
considerations will reveal other considerations. For example, land cannot be
allocated to farming exclusively. Industrial, residential, infrastructural, and
forest sectors compete with the agriculture sector for the available land as
shown in Figure 5. Market factors determine the land values and the
agricultural sector will have to provide a competitive rate of return in order
to get a fair allocation of land. When the agricultural sector cannot compete
with other sectors for the right return, governments will have to subsidize the
owners and provide land at a lower price than the markets would offer. Such a
situation is non-optimal and should be avoided if at all possible.
Figure 5: Various Sectors Compete with the Agriculture Sector for Land
The same competitive situation exits for other scarce
resources like water and power. Since labor is an abundant resource in a populous
country like India ,
there can be a tendency to apply the so-called cheap labor in the farming
sector. But this approach is counter productive as it increases labor costs,
decreases agility in the farming sector, and continues to leave the rural population
in poverty. Hence, there is need to upgrade the knowledge, skills, and
abilities of farmers and farm laborers appropriately while keeping in mind the
overall objectives for the sector.
Figure 6 shows a
simplified view of the chain from farm to home. It shows that under current
policies and programs, the governments provide subsidies to farmers as well as
the consumer. If free markets rein, the prices will go up and the farmers will
benefit as the total supplies of most agricultural products are lower than
demands in the country. As the governments cannot afford that situation from a
political point of view, they intervene in the market system. Unfortunately,
such intervention contributes to system inefficiencies. With a highly efficient
system, it is likely that the government intervention can be unnecessary. It is
an appropriate question to ask if we
can eliminate government subsidies and build an efficient production and
marketing system.
Figure 6: Government Subsidizes Farm Inputs as well as the
Consumers
Optimization Problems
The above
discussion should suggest three mathematical (operations research (OR) ) and
statistical methods for investigation. They are:
- Mathematical
Optimization
- Resource Allocation
- Statistical
Process Control.
Mathematical Optimization:
Let us examine the farm system as depicted in Figure 7.
There are several inputs Xi where i = 1 to 9 and an output Y1.
The yield, Y1, from the farm is a function of Xi and we
would like to optimize the inputs (Xi), such that Y1 is
maximized. Depending on the local or other circumstances, we may also place
other constraints on one or the other inputs, (Xi). In order to do
this mathematical formulation of the problem, we need data and information for
functional relationships between inputs and the output for a typical farm in
the region. It is quite likely that the system can be formulated as a linear
programming (LP) problem and a solution obtained. Figure 8 shows the values of
various inputs and that of the output. From a farm business point of view, we
may wish to increase the rate of return.
Figure 7: A Farm with Several Inputs and a Single Output
Figure
8: Values of Inputs and a Single Output
on a Farm (Ci is unit cost of input, Xi and D1
is the unit price of the output)
When we aggregate and represent a farming system (in a
village, region, or the nation) we see a picture as shown in Figure 9.
Figure 9: Composite View of a Regional or National Farming System (C1 to Cn and D1 to Dn are unit costs and prices of inputs and outputs respectively)
We can again apply the optimization techniques to minimize a
selected input or maximize a chosen output or maximize the return on investment
using the cost and price data. It is likely that under certain circumstances,
we may simply wish to minimize a given input if there is scarcity of that item
either locally or globally. Similarly, market demands might dictate that we
maximize a certain output or merely improve productivity or rate of return of
the farming enterprise.
In order to cater to various circumstances, several
different optimization problems can be set up and farmers and other decision
makers may choose the methods appropriate for their case.
With the availability of such optimization tools,
policymakers may ask questions and make intelligent choices as shown below.
For a given geographical region,
what inputs will yield maximum product or maximum value.
For a given geographical region,
•
Determine the best crop(s)
•
High value crops
•
Effect of government subsidies
For a given geographical region
(per acre),
•
Choose the best or high value crop(s)
•
Increase total production
•
Minimize (or target) subsidies appropriately
•
Minimize wastage of resources
Resource Allocation:
Investors look
for maximum return on investment for the funds they have available to invest.
Usually, they will not have inexhaustible opportunities to invest in one high
yielding (ROI) area. A particular opportunity exhausts and the investor has to
find other opportunities to continue investing. In order to take advantage of
such a system, an investor will prioritize the available opportunities in
descending order of the rate of return and invest successively in enterprises
with lower rates of return until the available investment funds exhaust.
Such allocation
methods will be extremely useful in the farm sector as they can be applied to
every input that has limited availability. As stated in the Background section
of this paper, India
Hence one might
ask if it is beneficial to allocate land to the farming sector preferentially
as opposed to such an allocation to the industrial sector or the power
generation sector. Therefore, the best method is to set up the allocation
problem and look for optimal solutions. In this case, it is not simply maximizing
the yield but there may be certain constraints dictated by regional or national
considerations. For example, food security might dictate that certain quantity
of farm products must be produced irrespective of the optimal utilization of a
given input. In such situations it may be possible that we may look for a
combination of production, productivity, and rate of return. Figure 10 shows a
system of allocation of various inputs to the farming sector. In reverse,
Figure 11 shows the competition for a given resource by various sectors.
Figure 10: Systematic Representation Showing the Allocation of various Inputs to the Farm Sector
Figure 11: Systematic Representation Showing the Allocation
of One Resource (e.g. Land) to Various Sectors
Statistical Process Control:
The manufacturing
sector benefited from Statistical Process Controls (SPC) by improving the
quality of products and reducing defects. Indian manufacturers have increased revenues
and profits and gained international acclaim. It may be the right time to set
up SPC in the farming sector. In simple terms, through process control,
operators can determine if a production process is within limits or if the
deviations are out of range. Corrective actions are applied so that the process
deviations do not affect the systems adversely. New standards are established
for the process controls when a new factor is discovered to cause process
improvement. Thus, processes can be constantly improved if possible.
In the case of
the farming sector, the application of SPC may result in improved yields of
products, better quality of products, minimizing inputs of scarce resources,
eliminating waste, and lowering of production costs.
SPC practitioners
use X-Bar R charts, p charts, and C charts. We have to investigate which charts
are applicable under given farming practices in India
Illustrative
sketches of the technique are shown in Figures 12 and 13.
Figure 13: Example Range Diagram to Illustrate the SPC Technique (For a given crop, in a specific region, the range for the minimum yield and/or maximum water requirement can be plotted for various farms.)
Benefits
The suggested
application of the optimization and SPC techniques are highly likely to produce
significant benefits to the Indian agriculture sector. We usually hear that
some farmer was able to produce order of magnitude better yields. These
techniques can determine what set of factors contribute to such yields and by
propagating such knowledge to all the farmers, India
Next
Steps
The author (proposal drafter) has only
made broad suggestions about applying optimization techniques in this white
paper. There is a need to define and explain the problem, the techniques, and
finally, the benefits in greater detail.
Here are some broad next steps.
•
Formulate the problem neatly and
convincingly
•
Send to leaders in India
•
With their sponsorship, develop models
•
Determine for regions, and farms,
suggested optimal choices
•
Recommend to national and state leaders
policy choices
The solution of
the problem relies heavily on obtaining agricultural data from practitioners.
The formulation and solution of the problem requires leadership role from
Operations Research (OR) and SPC (Even Six-Sigma) experts. Some problems can be
solved with PC’s and simple analytical tools. While the national level
optimization and allocation problems will require high performance computing
facilities and help from national agricultural and planning organizations.
References
http://agropedia.iitk.ac.in/openaccess/?q=content/planning-sustainable-agriculture-application-mop-models
Farming pictures from The Hindu online
Contact:
Som Karamchetty, PHD
1400 Stratton Dr., Potomac, MD 20854, USA
(240) 328-6513
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