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Linear Programming Approach- Application in Agriculture

January 2020

Authors:

St.Xavier's College Jaipur

In real scenario farm planning in terms of water management, the type of crop to be grown, the crop combination and different agricultural techniques applied to increase the farm production are the challenges faced by decision makers. These challenges are further being associated with socio -economic development and the scarcity of resources in particular region. To overcome these problems faced by farm linear programming technique is applied in order to optimize the farm’s returns by allocating the available farm resources optimally. The aim of the study is to develop a farm model for Jaipur District of Rajasthan by using linear programming in order to determine the feasible optimal crop combination and how these crops will be allocated to increase the production

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Linear Programming Approach- Application in

Agriculture

[1]Mahak Bhatia, [2] Prof. G.M.J.Bhat

[1]Research Scholar, [2] Professor of Mathematics

Abstract— In real scenario farm planning in terms of water

management, the type of crop to be grown, the crop

combination and different agricultural techniques applied

to increase the farm production are the challenges faced by

decision makers. These challenges are further being

associated with socio -economic development and the

scarcity of resources in particular region. To overcome

these problems faced by farm linear programming

technique is applied in order to optimize the farm’s returns

by allocating the available farm resources optimally. The

aim of the study is to develop a farm model for Jaipur

District of Rajasthan by using linear programming in order

to determine the feasible optimal crop combination and how

these crops will be allocated to increase the production.

Index Terms—crop combination, farm planning, linear

programming

INTRODUCTION

Agriculture sector plays a vital role in social and economic

development of India. The overall development of a sector

depends on available land and water resources. Proper

utilization of land and water resources is very important for

optimum agricultural production. This requires proper

allocation of resources in a farm. Farmers have to take a

complex decision as to what to grow, suitable season,

available farm techniques and the required quantity.

Decisions are made subject to the prevailing physical and

financial farm conditions but an uncertainty still prevails in

a planning horizon ahead in this sector. Uncertainty may

arise in the yield, cost of resources such as labor, seeds,

manures and fertilizers. Due to the complexity of the

agricultural sector a mathematical programming approach is

applied to develop a farm model that represents complete

farm subject to the constraints in terms of mathematical

equations. Farm planning can assist the farmers in

allocating the available resources in an optimal manner.

Management of water resources and allocation of land

under limited resources such as labor, fertilizers, seeds,

etc.is one of the major issues in farm model that needs to be

optimized. Generally, allocation of land under each crop is

based on the land area that is used to be cultivated in

previous season, depending on the availability of resources.

Hence, both land and water resources for different crops

needs to be optimized by allocating the resources efficiently

to obtain the maximum production. But maximization of

production does not guarantee the maximization of profit

Thus, it can be concluded that linear programming approach

is one of the tools to optimize the decision variables that

provide us with the combination of farm enterprise that is

feasible with respect to the set of fixed farm constraints.

Fig1: Farm Model

II.

LITERATURE REVIEW

Linear programming is an optimizing technique which is

widely used to allocate the resources optimally in order to

increase the production. Pap Zoltan [1] [2008] Developed a

linear programming model for an agricultural farm to

maximize the total gross margin by adopting crop rotation

policy The results of the study reveals that the income obtain

by applying linear programming model is more than that

obtain by binary crop rotation model. Raniraghavay & Dr.

Rao Tirupathi P. [2] [2012] develop three multi objective

mathematical model for two seasons depending upon the

availability of water resources and the results reveals that

optimization approach improves the annual net benefits of

the farm under study. MajekeF.et.al. [3] [2013] develops a

linear programming model to overcome the problem of

allocation of resources faced by the resettled farmers in

Bindura, Zimbabwe in order to enhance the farm’ income.

Sofi, N. A. et.al. [4] [2015] use simplex algorithm to determine

the solution of a linear programming model developed to

determine the allocation of land to optimise the farm

productivity. A linear programming crop mix model for a

finite time planning horizon under limited available

resources such as budget and land acreage, acrop-mix

planning model was formulated in order to maximize the

total returns at the end of planning horizon

[5] [Mohamad Hj. Nordin and Fatimah Said]. Kulshrestha

S.K [6] observes that the growth of cereals depends on the

wheat. The wheat production in Rajasthan is double than

the cropped area shows that the yield had improved over

a time.

III.

STUDY AREA

Jaipur District is located at 26°55′10″ N to 75°47′16″ E Total

geographical region of the state is 1106148 ha .Most of the

people are engaged in primary sector especially those that

resides in rural regions. Net sown area of the district is about

663167 ha and gross sown area is about 848313 ha. Major

Kharif crops of the region includes Groundnut, Bajra, Kharif

Pulses and the crops cultivated in Rabi season are Wheat,

Mustard, Barley & Gram.

Tomato, Pea, Chili, Brinjal, Cabbage, Cauliflower etc. are

Farm model

Crop Allocation

Resource

Allocation

Water resources

Allocation

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cultivated. Ber, Aonla, Bael, Guava, Lemon etc. are important

fruit crops of the district [7].

Jaipur has a semi-arid climate. Temperatures vary in different

seasons. In the summer months of April to June, average

daily temperature of around 35oC. May and June are the

hottest months in Jaipur. Temperature reaches up to 40-45oC

in these months. Annually the rainfall is concentrated in the

monsoon months between June (Last of June) and September.

It receives over 500 mm (approx 20 inch) of rainfall an

average. The winter months of November to February are

mild and pleasant, with average temperatures in the 15-18oC

range and little or no humidity. December and January are the

coldest months in Jaipur. Temperature varies between 5-10oC

in these months. There are however occasional cold waves

that lead to temperatures near freezing [8].

Table 1: Area, Production and Productivity of major

crops cultivated in the district [7]

IV.

METHODOLOGY

A Linear programming problem with “n “decision variables

and “m “constraints is formulated as:

Max.Z=∑ cixi i=1,2,3,…,n

s.t. ∑ ai xi ≤ ∑ bj j=1,2,3,…,m

xi ≥ 0

xi= represents the decision variables (to be determined by

policy makers)

ci= represents the cost vector

ai= represents activity coefficient

bj= represents the available resources

The objective function is:

Max.Z = 3190 x1+ 1023 x2 + 2139 x3 +726 x4

Subject to constraints:

Land: 157649 x1+ 114503 x2 + 9064x3 +118627 x4 ≤ 663167

Seeds & fertilizers: x1+ x2 + x3 + x4 ≤ 100000

Labor: x1+ x2 + x3 + x4 ≤ 200450

Non-negativity conditions:

x1, x2 , x3 , x4 ≥ 0

x1, x2, x3 and x4 are the decision variables for wheat,

rapeseed & mustard, peas and gram respectively .

Mathematical Formulation

The objective of the study is to maximize the farm returns by

allocating the resources optimally. Only the crops grown in

Rabi season i.e. wheat, rapeseed & mustard, peas and gram is

considered for the study. The problem is to determine the

suitable crop combination in order to get maximum profit.

The land available for cultivation is 663167 hectares. Proper

allocation of crops and the available resources is very

important in order to increase the productivity and also for the

efficient utilization of resources as Jaipur district of Rajasthan

receives erratic rainfall. Therefore, the variation in cropping

pattern is observed within district depending upon the

availability of water resources. Farms with sufficient water

prefer to cultivate peas and wheat more whereas the farms

with less availability of water grow mustard and wheat as a

major crops. Moreover, in order to increase the production

farmers adopt different farming patters such as crop rotation,

inter cropping and mixed cropping. It is observed that there is

increase in production to about 25% by adopting theses crop

policies Farmers especially the small farmers prefer to adopt

mixed cropping that includes both livestock as well as

cultivation of crops within the same farm. Livestock rearing

contributes to increases the farm returns to great extent.

Crop

Area

(ha)

Production

(ton)

Productivity

(kg/ha)

Pearl millet

297162

486981

1639

Sorghum

40478

23175

573

Green Gram

76260

35740

469

Cowpea

8532

4342

509

Sesamum

6396

1682

263

Groundnut

36080

68333

1894

Cluster-bean

59525

61050

1026

Wheat

157649

502927

3190

Barley

60542

187003

3089

Gram

118627

86174

726

Pea

9064

19390

2139

Rapeseed

Mustard

114503

117090

1023

Taramira

9988

4549

455

Onion

3551

8436

2376

Fenugreek

2554

2510

983

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157

Results

Fig2: Process of Linear Programming

Kulshrestha, S. K. (2017). An Analysis of Growth of

Area, Production and Yield of Wheat Crop in

Rajasthan.

Krishi Vigyan Kendra, Chomu (Jaipur), VPO – Tankarda,

Dist - Jaipur (303 702) - (Rajasthan) INDIA Retrived

From:http://jaipur1.kvk2.in/district-profile.html

Jaipur geography and climate Retrieved From:

http://www.jaipurthepinkcity.com/geography/geogr

aphy_climate.htm#.XJlFLIhuaUk

Taha A. Hamdy (2014) Operations Research an

Result of the developed linear programming farm model is

obtained by using EXCEL. Result of the problem shows that

farmer can get a profit of 15,6499 Rs. The solution of the

problem yields the following results:x1= 0, x2=0, x3=

73.164938 and x4=0

References

Pap, Z. (2008, September). Crop rotation constraints

in agricultural production planning. In Intelligent

Systems and Informatics, 2008. SISY 2008. 6th

International Symposium on (pp. 1-5). IEEE

Rani, Y. R., & Rao, P. T. (2012). Multi objective crop

planning for optimal benefits. International Journal

of Engineering Research and Applications

(IJERA), 2(5), 279-287.

Majeke F.et.al. (2013) “A Farm Resource Allocation

Problem: A Case Study of Model A2 Resettled

Farmers in Bindura, Zimbabwe”.International

Journal of Economics and Management Sciences

Vol. 2, No. 7, 2013, pp. 01-04.

Sofi, N. A., Ahmed, A., Ahmad, M., & Bhat, B. A.

(2015). Decision making in agriculture: A linear

programming approach. International Journal of

Modern Mathematical Sciences, 13(2), 160-169

Mohamad Hj. Nordin and Fatimah Said (2011) “A

mathematical programming approach to crop mix

problem.”African Journal of Agricultural Research

Vol. 6(1), pp. 191-197.Retrieved from: DOI:

10.5897/AJAR10.028

Introduction .Ninth Edition. United States. Dorling

Kindersley Pvt. Ltd

Optimization

Decision

Variables

Objective

Function

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The solution of the problem yields the following results:x1= 0, x2=0, x3= 73

Rs. The solution of the problem yields the following results:x1= 0, x2=0, x3= 73.164938 and x4=0

Decision making in agriculture: A linear programming approach

Jan 2015
160-169

N A Sofi
A Ahmed
M Ahmad
B A Bhat

Sofi, N. A., Ahmed, A., Ahmad, M., & Bhat, B. A. (2015). Decision making in agriculture: A linear programming approach. International Journal of Modern Mathematical Sciences, 13(2), 160-169

Linear Programming Approach- Application in Agriculture

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