linear programming approach for optimal … · 2017-11-01 · this dam is located in the hidkal...

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International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 10, October 2017, pp. 1500–1512, Article ID: IJCIET_08_10_151

Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=8&IType=10

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

LINEAR PROGRAMMING APPROACH FOR

OPTIMAL LAND AND WATER RESOURCE

ALLOCATION UNDER DIFFERENT

HYDROLOGICAL SCENARIOS

Shakuntala G. Vadde

Post Graduate Student, VTU, Belagavi, Karnataka, India

Shreedhar R

Associate Professor, GIT, Belagavi, Karnataka, India

Chandrashekarayya G. Hiremath

Assistant Professor, VTU, Belagavi, Karnataka, India

ABSTRACT

This study proposes application of Linear Programming Optimization technique

for the optimization of reservoir release followed by optimal allocation of land and

water resource for the maximization of net annual farm income from the study area.

The study is conducted in Ghataprabha Command area, a significant portion of

Krishna river basin situated in Northern part of Karnataka, India. Two distinct

scenarios have been considered in the study involving four different hydrological

years which is very essential for scheduling of irrigation water supply and better

management of existing water resource. Scenario-I representing average weather

condition whereas Scenario-II consists of different hydrological years such as dry, wet

and normal corresponding to probability of exceedence P80, P20 , P50 respectively. The

net benefit incurred from command area for Scenario-I was about 5740 Million

Rupees. The results of Scenario-II demonstrated that the net income for dry, wet and

normal years was 4201, 5912 and 5386 Million Rupees respectively.

Key words: Optimization, Linear Programming, Reservoir operation, optimal land

allocation.

Cite this Article: Shakuntala G. Vadde, Shreedhar R and Chandrashekarayya G.

Hiremath, Linear Programming Approach for Optimal Land and Water Resource

Allocation under different Hydrological Scenarios. International Journal of Civil

Engineering and Technology, 8(10), 2017, pp. 1500–1512.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=10

Shakuntala G. Vadde, Shreedhar R and Chandrashekarayya G. Hiremath


1. INTRODUCTION

Water is the fundamental and most vital resource for the existence of lives on the planet earth.

Since the water resources across the world are unevenly distributed both temporally and

spatially and inspite of plentiful water resources, numerous regions are facing the scarcity of

water [9].

The monetary advancement of a nation is specifically reliant on the accessibility of water

in view of its utilization in industrial supply, household agriculture and local usage. In order

to maintain the balance among ecosystem, environment, hydrological integrity and water

demand of the society there is serious need for efficient and sustainable water management

system. The hydraulic structures are designed and constructed to serve various objectives viz.

satisfying needs of domestic and industrial areas, irrigation, hydropower, flood protection,

fishery development navigation etc.[1].In Karnataka agribusiness consumes about 94% of

existing water resources because of uneven scanty and unreliable nature of rainfall. This

emphasizes a need for a well-planned and operated efficient water management system.

In order to accumulate the surplus water various Reservoirs have been built across the

country so as to use it as and when required to serve the various purposes. The conventional

practice of reservoir operation highly relies upon the experience and judgment of the

managers of reservoir system which vary from person to person founded on the empirical

methods. These practices will not assure of optimal operational decisions. In the current era

with the advancement in the science and technology and evolution of various computer

models have made it possible to assess the consequences of an operating decision well in

advance by simulation of river system and reservoir operation on real time basis [5]. Hence to

gain maximum benefit from the command areas, it is imperative to form an effective reservoir

release policy for optimal allocation of water to the fields in required quantity. Optimization

techniques emerging out to be an excellent tool for management of water resources being

used and implemented by various researchers across the world such as A. B.Mirajkar et

al.,(2016)[1],A. D. Teixeira et al., (2002) [2],S. Kumari et al.,(2015) [10].H. R. Safavi et al.,

(2017)[6] used Optimization for conjunctive use of surface water and Ground water.

Different mathematical programming techniques are available for optimization of

available land and water resources of which the Linear programming (LP) being the most

popular. U. Mandal et al., (2013)[11] applied LP technique for Hirakud canal command area

for maximizing the net benefit out of command area. Similar works were carried out by A.

Singh et al.,(2014)[3]and Sabouni et al., (2014)[7].S. Devi et al., (2005)[8] employed LP for

optimal water allocation in large river basin system of transboundary Subarnarekha River in

India. Similarly S.Kumari et al., (2015)[10], S. J. Pereira-Cardenal et al., (2015)[9],C.

Davidsen et al., (2015)[4] successfully used dynamic programming technique for

management of water resources.

This paper proposes a Linear Programming technique for optimizing monthly release from

the Hidkal reservoir. The releases so obtained used for optimal allocation of water and land

resources so as to maximize the net return from Ghataprabha command Area (GCA).

2. STUDY AREA

The proposed study is intended to propose a reservoir release policy for the Hidkal reservoir

which is presently the biggest dam in the Belagavi district of Karnataka, created across

Ghataprabha River. This dam is located in the Hidkal village of Hukkeri Taluka. It is having a

catchment area of 1412 sq.km, situated at a Latitude of 16° 09' 0" North & 74° 38' 0" East

Longitude. The salient features of the reservoir are as mentioned in the Table 1 below. The

Linear Programming Approach for Optimal Land and Water Resource Allocation under different

Hydrological Scenarios


specific objective behind construction of this dam was to provide water for irrigation and

satisfy the needs of drinking water and Hydropower. The Ghataprabha command area which

is currently spread over an area about 3 lakh Ha comprising seven talukas of Belagavi district

(Athani, Chikkodi, Gokak, Hukkeri, Raibag, Ramdurg, Savadatti) and six talukas of Bagalkot

district (Badami, Bagalkot, Bilgi, Hungund, Jamkhandi and Mudhol). The command area

receives an average annual rainfall of 553.8 mm. The temperature in the area varies from a

maximum of 40oC to 20

oC.

Table 1 Salient features of Hidkal Dam

SALIENT FEATURES OF HIDKAL DAM

1 Location Hidkal

2 Taluka , District Hukkeri, Belagavi

3 Type of Dam Composite

4 Height of Dam 53.35 m

5 FRL / MWL 662.9 m

6 Reservoir Storage Capacity

(i)Gross Storage Capacity 1443 Mm3

(ii) Live Storage Capacity 1388 Mm3

(iii) Dead Storage Capacity 57 Mm3

7 Canals

Length G.R.B.C. 202 km

G.L.B.C. 109 km

8 Irrigated area

G.R.B.C. 155559 Ha

G.L.B.C. 161871 Ha

9

Power Generation Capacity

(Two units) each 16MW

32 MW

Figure 1 Location map of study area.

The most crucial part of operations is the arrival of right quantity of water at the perfect

time to water system zones. This study uses the Linear programming approach for the

optimization of monthly release from the Hidkal Reservoir. The present cropping pattern in

the study area is given in Table 2 below.



Table 2 Existing cropping pattern in the command area

Season Crop Area in

Hectares

Percentage

Area

Kharif

Groundnut 34721 25%

Hybrid maize 52081 37.50%

Hybrid jowar 24305 17.50%

Local jowar 10416 7.50%

Millet 17360 12.50%

Total 138883

Rabi

Local jowar 32019 25%

Hybrid maize 16010 12.50%

Pulses 16010 12.50%

Sunflower 16010 12.50%

Wheat 48029 37.50%

Total 128078

Two

Seasonal

Sugarcane 32020 50%

Cotton 32019 50%

Total 64039

3. MATERIAL AND METHODOLOGY

Linear Programming is an optimization technique widely used by water resource engineers

for maximizing the net revenue from the command area. The excel solver tool has been used

for optimizing the monthly release from the reservoir followed by optimizing the cropping

pattern for the associated command area.

3.1. Reservoir Operation

The proposed study aimed at the formation of optimal monthly release for the Hidkal

reservoir analyzing the monthly demands of the crops in the GCA, flow data and evaporation

loss data of past 30 years. The analysis has been done for different Hydrological scenarios.

• Scenario (I): This criterion involves formation of monthly reservoir releases for average

condition by using mean monthly inflow and evaporation data of past 30 years.

• Scenario (II): Past 30 years mean monthly inflow and evaporation data and irrigation

demandof crops have been processed to form reservoir operation policies for three

hydrological scenarios namely Dry, Wet and Normal corresponding to probability of

exceedence of P80, P20 ,P50 respectively.

It involves calculation of Inflow, evaporation and monthly crop demand values at 80%,

50% and 20% probability.

Pi dry = Pi avg * (P dry / P avg) (1)

Where Pi avg = Average monthly Inflow for month ; Pi dry= monthly Inflow dry year for

month I;P avg = Average yearly Inflow and P dry = yearly Inflow at 80% probability of

exceedence

Similarly the monthly Inflow values for normal and wet year are calculated. The same

procedure has to be followed for processing of Evaporation and irrigation water demand of

crops into dry, wet and normal scenarios.

The system of reservoir is as shown in the Fig. 2. It consists of four major components

viz. inflow, storage, evaporation and outflow which largely influence the functioning and




effective operation of any reservoir. During storms, the runoff gets stored in reservoirs and a

part of stored water might be lost as evaporation. The stored water is released as and when

required. Such releases from the reservoir system need to be optimized.

Figure 2 System of Reservoir

3.2. Objective Function

The objective function of the model is to maximize the monthly release from the reservoir

which can be given as

Max Z= ∑Rt (2)

It is subjected to constraints

St+1 =St+ Qt – Et –Rt - Ot (3)

It implies that the end of year storage is equal to the beginning of the next year’s storage.

Rt ≤ Dt (4)

The monthly releases of water should be less than or equal to the irrigation demand from

the command area.

St ≤ K (5)

The storage should be less than or equal to the live storage capacity of the reservoir

Rt≥ 0 (6)

St ≥ 0 (7)

Equations (6) and (7) are the non-negativity constraints

Where

Rt= Releases in Mm3, Qt = Inflows in Mm

3, Et = Evaporation loss in Mm

3, Ot= Spill loss in

Mm3,

St = Storage at a given time t in Mm3, K= Live storage capacity of reservoir in Mm

3

3.3. Optimization of cropping pattern

The objective function is to maximize the net benefit from the command area by optimal

allocation of water and land resources.



Max Z = Σ yi(Ri – Ci) * Ai (8)

Where

yi=Yield in Qtl/ Ha

Ri=Revenue in Rs/Qtl

Ci=Production Cost in Rs/Qtl

Subjected to the Constraint

(1)Kharif Water Availability

Σ Ai*IRi≤ ΣR1-4 (9)

(2)Rabi water availability

Σ Ai*IRi≤ ΣR5-10 (10)

(3)Water Availability for Sugarcane

A11*IR11≤ ΣR1-12 (11)

(4)Water availability for Cotton

A12*IR12 ≤ ΣR4-10 (12)

(5) Total Water Availability

Σ GIRi Ai ≤ Σ Ri (13)

(6)Kharif Land Availability

Σ A1-5 ≤ LAK (138883 Ha) (14)

(7) Rabi Land Availability

Σ A6-10 ≤ LAR (128078 Ha) (15)

(8) Seasonal Crops land availability

Σ A1-12 ≤ LAS (64039 Ha) (16)

Where

LAK = Land Availability for Kharif crops from existing cropping pattern.

LAR = Land Availability for Rabi crops from existing cropping pattern.

LAS = Land Availability for Two seasonal crops from existing cropping pattern.

Table 3 Designation of crops in GCA.

Season

Crop

Area

designation

Irrigation

Requirement

designation

Kharif

1.Groundnut A1 IR1

2. Hybrid Maize A2 IR2

3. Hybrid Jowar A3 IR3

4.Local jowar A4 IR4

5.Millet A5

IR5

Rabi

6.Local jowar A6 IR6

7. Hybrid maize A7 IR7

8.Pulses A8 IR8

9.Sunflower A9 IR9

10.wheat A10

IR10

Two Seasonal

11.Sugarcane A11 IR11

12.Cotton A12 IR12




Table 4 Monthly Release designation from reservoir.

4. RESULTS AND DISCUSSION

4.1. Reservoir Operation

The releases for different scenarios are as shown in Table5.The objective function was set to

maximize the monthly release from the Hidkal reservoir. The monthly releases are highest

during dry years (Probability of exceedence P80) and lowest during wet years. The releases for

average scenario are well approached by that in normal scenario.

Table 5 Releases for different Scenarios

Month

Releases

for different Scenarios in (Mm3)

Average Dry Normal Wet

May 49.13 50.23 49.51 48.12

June 122.30 130.86 124.47 113.05

July 278.61 288.36 280.54 266.19

Aug 195.43 215.23 199.97 172.38

Sept 107.82 145.48 120.53 76.34

Oct 361.99 390.12 385.38 333.49

Nov 129.48 136.62 134.32 121.70

Dec 369.57 259.14 371.49 366.85

Jan 464.00 0.00 270.85 463.35

Feb 30.93 0.00 0.00 192.99

Mar 0.00 0.00 0.00 0.00

Apr 0.00 0.00 0.00 0.00

4.2. Optimal Allocation of Area and water resource

LP model has been employed to gain most promising net benefit from the Ghataprabha

command area by optimal allocation of area and water resource in the vicinity of command

area. The existing cropping pattern in the command area is as shown in the Table 2. The land

availability constraint was employed for Kharif, Rabi and seasonal crops from the existing

cropping pattern. The water availability constraint was set depending upon water demand for

each crop in the command area during its growing period.The optimal results for irrigated

land allocated to each crop and net benefit gained under each scenario are explained as

follows.

Month

Release

Designation

May R1

June R2

July R3

August R4

September R5

October R6

November R7

December R8

January R9

February R10

March R11

April R12



*Average Scenario: The global optimal solution under average scenario for maximum benefit

is as shown in Fig. 3. The LP model has allocated 25%, 46.87%, 13.13%, 5.62% and 9.37%

of actual irrigated land to Groundnut, Hybrid Maize, Hybrid Jowar, Local Jowar and Millet

respectively during Kharif season. Similarly during Rabi season optimization model has

allocated 23.32%, 15.63%, 15.63%, 9.38% and 28.12% of the actual irrigated land to local

Jowar, Hybrid Maize, Pulses, Sunflower and wheat respectively. The unirrigated land during

Rabi season is around 7.93% of actual irrigated land. Two seasonal crops namely Sugarcane

and cotton have been allocated an area of 9.37% and 62.5% respectively.

Figure 3 Optimal Area allocation for Average Scenario

Out of total water availability of 2109.25 Mm3during average scenario, nearly 6.43%,

19.85% of water is allocated to sugarcane and cotton respectively as shown in Fig. 4 below.

Kharif and Rabi crops have got a share of 28.13% and 45.59% respectively. The maximum

net benefit for the average scenario is 5740 Million Rupees as shown in Table 6.

Figure 4 Optimal water allocation for Average Scenario

* Dry Scenario: The global optimal solution under dry scenario for maximum benefit is as

shown in Fig. 5. The LP model has allocated 17.5%, 37.41%, 12.25%, 5.25% and 8.75% of

actual irrigated land to Groundnut, Hybrid Maize, Hybrid Jowar, Local Jowar and Millet

593.41

961.51

135.68

418.65

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

Kharif

Rabi

Sugarcane

Cotton

Optimal water Allocation in Million cubic meter

Optimal water allocation for Average Scenario

347.2

651.0

182.3

78.1

130.2

298.6

200.1

200.1

120.1

360.2

60.0

400.2

0 200 400 600 800

GroundnutHy maizeHy jowar

Local jowarMillet

Local jowarHy maize

PulsesSunflower

WheatSugarcane

Cotton

Optimal Area of crop in Million sq.mts

Cro

ps

Optimal Area allocation for Average Scenario





allocated 17.5%, 8.75%, 8.75%, 8.75% and 26.25% of the actual irrigated land to local Jowar,

Hybrid Maize, Pulses, Sunflower and wheat respectively. The unirrigated land during Kharif

and Rabi seasons found to be 18.83% and 30% of actual irrigated land respectively. Two

seasonal crops namely Sugarcane and cotton have been allocated an area of 4.68% and

39.04% respectively.

Figure 5 Optimal Area allocation for Dry Scenario

Out of total water availability of 1616.04 Mm3

during dry scenario 4.4%, 16.48% of water

is allocated to sugarcane and cotton respectively as shown in the Fig. 6 below. Kharif and

Rabi crops have got a share of 33.22% and 45.9% respectively. The maximum net benefit for

the average scenario is 4201 Million Rupees as shown in Table 6.

Figure 6 Optimal water allocation for Dry Scenario

*Wet Scenario: The global optimal solution under wet scenario for maximum benefit is as

shown in Fig. 7. The LP model has allocated 25%, 46.87%, 13.13%, 5.62% and 9.37% of

actual irrigated land to Groundnut, Hybrid Maize, Hybrid Jowar, Local Jowar and Millet




243.0

519.6

170.1

72.9

121.5

224.1

112.1

112.1

112.1

336.2

30.0

250.0

0.0 100.0 200.0 300.0 400.0 500.0 600.0

Groundnut

Hy jowar

Millet

Hy maize

Sunflower

Sugarcane


Cro

p

Optimal Area allocation for Dry Scenario

536.82

741.80

71.06

266.35

0.00 200.00 400.00 600.00 800.00

Kharif

Rabi

Sugarcane

Cotton


Optimal water allocation for Dry Scenario





Figure 7 Optimal Area allocation for Wet Scenario

Out of total water availability of 2154.47 Mm3during wet scenario, nearly 9.89%, 19.09% of

water is allocated to sugarcane and cotton respectively as shown in Fig. 8. Kharif and Rabi

crops have got a share of 28.84% and 45.18% respectively. The maximum net benefit for the

average scenario is 5912 Million Rupees as shown in Table 6.

Figure 8 Optimal water allocation for Wet Scenario

*Normal Scenario: The global optimal solution under normal scenario for maximum benefit

is as shown in Fig. 9. The LP model has allocated 25%, 46.87%, 13.13%, 5.62% and 9.37%

of actual irrigated land to Groundnut, Hybrid Maize, Hybrid Jowar, local jowar and Millet






347.2

651.0

182.3

78.1

130.2

372.3

200.1

200.1

120.1

360.2

100.0

400.2

0 200 400 600 800

Groundnut

Hy jowar

Millet

Hy maize

Sunflower

Sugarcane

Optimal Area of crop in Million sq.mts.…

Cro

ps

Optimal Area allocation for Wet Scenario

513.61

1016.37

213.12

411.36

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

Kharif

Rabi

Sugarcane

Cotton


Optimal water allocation for Wet Scenario




Figure 9 Optimal Area allocation for Normal Scenario

Out of total water availability of 1937.07 Mm3during normal scenario nearly 5.9%,

15.56% of water is allocated to sugarcane and cotton respectively as shown in Fig. 10. Kharif

and Rabi crops have got a share of 31.46% and 47.08% respectively. The maximum net

benefit for the average scenario is 5386 Million Rupees as shown in Table 6.

Figure 10 Optimal water allocation for Normal Scenario

The net benefit evaluated for different scenarios in the study area is given in Table 6

below. This indicates that the Net benefit incurred from the command area is higher for

average and wet scenario compared to normal and dry scenario.

Table 6 Net benefit for different scenarios in the command area

Net benefit for different Scenarios in Million Rs

Crop Average Wet Normal Dry

Groundnut 821 821 821 574

Hybrid maize 1652 1652 1652 1319

Hybrid jowar 140 140 140 130

Local jowar 129 129 129 120

Millet 113 113 113 106

Local jowar 493 615 397 370

Hybrid maize 508 508 508 284

Pulses 436 436 436 244

347.2

651.0

182.3

78.1

130.2

240.1

200.1

200.1

120.1

360.2

50.0

286.8

0 200 400 600 800

Groundnut

Hy jowar

Millet

Hy maize

Sunflower

Sugarcane


Cro

ps

Optimal Area allocation for Normal Scenario

609.4

912.1

114.3

301.4

0.0 200.0 400.0 600.0 800.0 1000.0

Kharif

Rabi

Sugarcane

Cotton


Optimal water allocation for Normal Scenario



Sunflower 110 110 110 103

Wheat 399 399 399 373

Sugarcane 75 125 63 38

Cotton 863 863 619 539

Net benefit 5740 5912 5386 4201

5. CONCLUSIONS

In this study two scenarios have been formulated to optimize the reservoir release and the

Cropping pattern using Linear Programming technique for the Ghataprabha command area

located in Karnataka, India. The releases in average years are well approached by those in

normal scenario.The unirrigated land during Rabi season found to be around 7.93% of actual

irrigated land for average scenario and the net benefit incurred was about 5740 million

Rupees. The results of scenario II involving Dry, wet and normal years demonstrated that the

releases are higher for dry scenario than wet scenario and the net benefit was found to be

4201, 5912 and 5386 million Rupees for dry, wet and normal scenarios respectively. The

unirrigated areas during Rabi season for wet, normal scenario are 2.17%and 12.5% of actual

irrigated land. The unirrigated land during Kharif and Rabi seasons for dry scenario found to

be 18.83% and 30% of actual irrigated land respectively.The consideration of different

hydrological years as two different scenarios expected to be very useful for programming of

irrigation water supply and management.

ACKNOWLEDGMENT

The authors convey their sincere thanks to Shri. Alok Shetty, Assistant Executive Engineer

Karnataka Neeravari Nigam Limited, CBC, Sub Div., No.2 Hidkal Dam, Belagavi for his

kind assistance in providing all the required data and information for the successful

completion of proposed work.

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linear programming approach for optimal … · 2017-11-01 · this dam is located in the hidkal...

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