it comes under hydrology and irrigation engineering basically a linear approach of allocation of water and land resources. A c program is used here.

1. z
RV College of Engineering
Department of Civil Engineering
LINEAR PROGRAMMING APPROACH FOR OPTIMAL
LAND AND WATER RESOURCE ALLOCATION UNDER
DIFFERENT HYDROLOGICAL SCENARIOS
PRESENTED BY
NANUBALA DHRUVAN (1RV18CV067)
HYDROLOGY PRESENTATION

2. INTRODUCTION
1) 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 .
2)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.
3) 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.
4) 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.

3. OBJECTIVES
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.
2) 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.
3) Optimization techniques emerging out to be an excellent tool for management of water resources
being used and implemented by various researchers across the world Different mathematical
programming techniques are available for optimization of available land and water resources of
which the Linear programming (LP) being the most popular.

4. MATERIALS AND METHODOLOGY
1) LINEAR PROGRAMMING
Linear programming (LP, also called linear optimization)
is a method to achieve the best outcome (such as maximum
profit or lowest cost) in a mathematical model whose
requirements are represented by linear relationships.
Linear Programming 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.

5. RESERVIOR OPERATIONS
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 demand of
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.

6. 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 exceedance.
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.

7. 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)

8. 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 Mm3, Et = Evaporation loss in Mm3, Ot= Spill loss in
Mm3,
St = Storage at a given time t in Mm3, K= Live storage capacity of reservoir in Mm3

9. OPTIMISATION OF CROPPING PATTERNS
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
Where
yi=Yield in Qtl/ Ha
Ri=Revenue in Rs/Qtl
Ci=Production Cost in Rs/Qtl
Subjected to the Constraint

12. STUDYAREA
Hidkal reservoir which is one of the biggest dam in the Belagavi district of Karnataka, created across Ghataprabha River is
considered. This dam is located in the Hidkal village of Hukkeri Taluka.
The salient features of the dam are:
Catchment area : 1412 sq.km
Location :Latitude of 16° 09' 0" North ,Longitude of 74° 38' 0" East
Objectives : to provide water for irrigation ,To satisfy the needs of drinking water, Hydropower
Command area :3 lakh Ha
Average annual rainfall : 553.8 mm
Temperature : varies from 400C to 200C
Type of Dam : Composite

13. Crop 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
Height of Dam : 53.35 m
Gross Storage Capacity : 1443 Mm3
Existing crops : kharif -
Groundnut ,Hybrid maize ,Hybrid jowar
,Local Jowar, Millet : Rabi- Local jowar,
Hybrid maize, Pulses, Sunflower,wheat
seasonal crops – sugarcane, cotton
Existing cropping pattern

14. C PROGRAM FOR LINEAR OPTIMISATION
C is a general-purpose, procedural computer programming language supporting structured
programming, lexical variable scope, and recursion, with a static type system. By design, C provides
constructs that map efficiently to typical machine instructions.
A basic program which represents a linear programming (which optimises the given objective function
with less than 10 variables, subjected to number of given constraints ) is given below:
#include <stdio.h>
#include <math.h>
#define CMAX 10 //max. number of variables in objective function
#define VMAX 10 //max. number of constraints

15. int NC, NV, NOPTIMAL,P1,P2,XERR;
double TS[CMAX][VMAX];
void Data() {
double R1,R2;
char R;
int I,J;
printf("n LINEAR PROGRAMMINGnn");
printf(" MAXIMIZE (Y/N) ? "); scanf("%c", &R);
printf("n NUMBER OF VARIABLES OF OBJECTIVE FUNCTION ? "); scanf("%d", &NV);
printf("n NUMBER OF CONSTRAINTS ? "); scanf("%d", &NC);
if (R == 'Y' || R=='y')
R1 = 1.0;
else
R1 = -1.0;
printf("n INPUT COEFFICIENTS OF OBJECTIVE FUNCTION:n");
for (J = 1; J<=NV; J++) {
printf(" #%d ? ", J); scanf("%lf", &R2);
TS[1][J+1] = R2 * R1;
}

16. printf(" Right hand side ? "); scanf("%lf", &R2);
TS[1][1] = R2 * R1;
for (I = 1; I<=NC; I++) {
printf("n CONSTRAINT #%d:n", I);
for (J = 1; J<=NV; J++) {
printf(" #%d ? ", J); scanf("%lf", &R2);
TS[I + 1][J + 1] = -R2;
}
printf(" Right hand side ? "); scanf("%lf",
&TS[I+1][1]);
}
printf("nn RESULTS:nn");
for(J=1; J<=NV; J++) TS[0][J+1] = J;
for(I=NV+1; I<=NV+NC; I++) TS[I-NV+1][0] = I;
}
void Pivot();
void Formula();
void Optimize();
void Simplex() {
e10: Pivot();
Formula();
Optimize();
if (NOPTIMAL == 1) goto e10;
}
void Pivot() {
double RAP,V,XMAX;
int I,J;
XMAX = 0.0;
for(J=2; J<=NV+1; J++) {
if (TS[1][J] > 0.0 && TS[1][J] > XMAX) {
XMAX = TS[1][J];
P2 = J;
}
}

17. RAP = 999999.0;
for (I=2; I<=NC+1; I++) {
if (TS[I][P2] >= 0.0) goto e10;
V = fabs(TS[I][1] / TS[I][P2]);
if (V < RAP) {
RAP = V;
P1 = I;
}
e10:;}
V = TS[0][P2]; TS[0][P2] = TS[P1][0]; TS[P1][0] = V;
}
void Formula() {;
//Labels: e60,e70,e100,e110;
int I,J;
for (I=1; I<=NC+1; I++) {
if (I == P1) goto e70;
for (J=1; J<=NV+1; J++) {
if (J == P2) goto e60;
TS[I][J] -= TS[P1][J] * TS[I][P2] / TS[P1][P2];
e60:;}
e70:;}
TS[P1][P2] = 1.0 / TS[P1][P2];
for (J=1; J<=NV+1; J++) {
if (J == P2) goto e100;
TS[P1][J] *= fabs(TS[P1][P2]);
e100:;}
for (I=1; I<=NC+1; I++) {
if (I == P1) goto e110;
TS[I][P2] *= TS[P1][P2];
e110:;}
}

18. void Optimize() {
int I,J;
for (I=2; I<=NC+1; I++)
if (TS[I][1] < 0.0) XERR = 1;
NOPTIMAL = 0;
if (XERR == 1) return;
for (J=2; J<=NV+1; J++)
if (TS[1][J] > 0.0) NOPTIMAL = 1;
}
void Results() {
//Labels: e30,e70,e100;
int I,J;
if (XERR == 0) goto e30;
printf(" NO SOLUTION.n"); goto e100;
e30:for (I=1; I<=NV; I++)
for (J=2; J<=NC+1; J++) {
if (TS[J][0] != 1.0*I) goto e70;
printf(" VARIABLE #%d: %fn", I, TS[J][1]);
e70: ;}
printf("n OBJECTIVE FUNCTION: %fn", TS[1][1]);
e100:printf("n");
}

19. void main() {
Data();
Simplex();
Results();
}
For the given problem of optimisation of the water and land resources for the given area,
the objective is to maximise the discharge Z= Z = Σ yi(Ri – Ci) * Ai
Subjected to
Kharif Water Availability : Σ Ai*IRi≤ ΣR 1-4
Rabi water availability: Σ Ai*IRi≤ ΣR5-10
Water Availability for Sugar cane : Ai*IRi≤ ΣR 11
Water Availability for cotton : Ai*IRi≤ ΣR 12
Total Water Availability :Σ GIRi Ai ≤ Σ Ri
Kharif Land Availability : Σ A1-4≤ LAK (138883 Ha)
Rabi Land Availability : Σ A5-10≤ LAR (128078 Ha)
Seasonal Crops land availability : Σ A11-12 ≤ LAS (64039 Ha)

20. RESULTS
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.

21. OPTIMUM 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.

22. AVERAGE SCENERIO :
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.
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 . 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.

24. DRY SCENERIO:
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 respectively
during Kharif season. Similarly during Rabi season optimization model has 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.
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.

26. WET SCENERIO :
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
respectively during Kharif season. Similarly during Rabi season optimization model has
allocated 29.07%, 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 2.17% of actual irrigated land. Two seasonal crops namely Sugarcane and
cotton have been allocated an area of 15.62% and 62.5% respectively.
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.

28. CONCLUSION
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.

29. THANK YOU