FUZZY NONLINEAR PROGRAMMING IN MULTIOBJECTIVE ENVIRONMENT FOR IRRIGATION PLANNING

Page 1

SESSION II

EFFICIENT MANAGEMENT OF MULTIPURPOSE AND MULTISTAKEHOLDER WATER PROJECTS

D. V. MORANKAR ASST PROF, FACULTY OF CIVIL ENGINEERING, COLLEGE OF MILITARY ENGINEERING, PUNE, INDIA dineshmorankar@ gmail.com

K.SRINIVASA RAJU PROF, DEPARTMENT OF CIVIL ENGINEERING, BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI, HYDERABAD CAMPUS, HYDERABAD, INDIA

D.NAGESH KUMAR PROF, DEPARTMENT OF CIVIL ENGINEERING, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA


INTRODUCTION

Three Phases of Irrigation Water Management  Planning  Operation  Evaluation 

Sustainable Use of fresh Water Resources


CASE STUDY


CASE STUDY Panshet Dam GS 303 Mm3 LS 294 Mm3

Warasgaon Dam GS 374 Mm3 LS 362 Mm3 Temghar Dam GS 108 Mm3 LS 105 Mm3

Khadakwasla Dam GS 86 Mm3 LS 56 Mm3 Spill in Mutha River

Mutha River

DRCB

PMC PCMC

KCB PCB

Pavna Dam

Pavna River

Mula River

PUNE CITY NMRBC Capacity 58 m3/s

Mulshi Dam

PIMPRI – CHINCHWAD CITY

Legend: GS : Gross Storage ; LS: Live Storage; Sources from where Waste water is generated PMC: Pune Municipal Corporation Limits; PCMC: Pimpri Chinchwad Municipal Corporation Limits; KCB: Khadki Cantonment Board Limits; DRCB: Dehu Road Cantonment Board Limits; PCB: Pune Cantonment Board Limits; Indicates Waste Water Sources Treated Waste Water to be lifted to New Mutha Right Bank Canal (NMRBC)


MATHEMATICAL MODEL Objectives 1.Maximizing Benefits

36

12

12

12

i =1

t =1

t =1

t =1

BM = ∑ Bi Ai − PGW ∑ GWt +PDW ∑ DWt +PIND ∑ INDt 36

2.Maximizing Production

PM = ∑ PM i Ai i =1

36

3.Maximizing Labour Employment LM = ∑ LM i Ai i =1

Constraints of the System 1.Continuity Equation

S t +1 = S t + I t − DWt − IRt − EVt − SPILLt − INDt − JS t ;

2. Crop Water Requirements 11

∑ A * CWR

− IRt − GWt − 0.5WWt = 0;

∑ A * CWR

− JSt − 0.5WWt = 0;

t = 1, 2,..,12.

∑ A * CWR

− SPILLt − ( 20.49 − WWt ) = 0;

t = 1, 2,..,12.

i =1 23

i =12 36

i = 24

i

i

i

it

it

it

3. Canal Capacity Restrictions

IRt + INDt + WWt + JSt ≤ CCt ;

t = 1, 2,..,12.

t = 1, 2,..,12.

t = 1,2,..,12.


MATHEMATICAL MODEL Fuzzy Decision The imprecisely defined goals and constraints are presented as fuzzy sets in the space of alternatives. The confluence of fuzzy Objectives(G) and fuzzy constraints(C) is defined as the fuzzy decision(Z) . Z = G ∩ C Fuzzy Membership Function 0  β  Z − Z L  µ Z ( X ) =   Z − Z L   U 1 

GJ

Ci

(X )

(X )

]

]

β

≥λ

β

≥λ

0 ≤ λ ≤ 1

for

Z ≤ ZL

for Z L < Z < Z U for

Z ≥ ZU


INPUT DATA 1. Inflow : 1980-2006: M onthly Inflows at Khadakwasla Reservoir 2. Net Benefit/ ha from various crops: As per Agriculture Department 3. M onthly Crop Water Requirement using Modified Penman’s M ethod 4. Avg M onthly Evaporation Loss from Khadakwasla Reservoir 5. Monthly domestic demands, Industrial demands Avg Values 6. Labour Requirement per crop per ha: As per Rahuri Krishi Vidyapeeth 7. Crop Yield Variation and M arket Price Variation 8. Ground Water Potential in Khadakwasla Command: GSDA, Pune


RESULTS AND DISCUSSIONS Characteristics

β1=β2=β3 =1

β1=β2=β3 =3

β1=β2=β3 =5

β1=β2= β3 =7

Area Under Crop in Khadakwasla ("100" ha) Intensity of Irrigation in % Area Under Crop in JSLIS ("100" ha) Intensity of Irrigation in % Area Under Crop in Purandar ("100" ha) Intensity of Irrigation in % Total Area Under Crop ("100" ha) Intensity of Irrigation in % Benefits in ‘Million Rs’

675.61

675.61

723.95

720.78

66.44 196.25 99.59 335.10 83.44 1206.95 74.71 2296.754

66.44 196.25 99.59 335.10 83.44 1206.95 74.71 2296.755

71.19 197.40 100.18 236.10 58.79 1157.45 71.64 2266.371

70.88 197.57 100.26 194.51 48.43 1112.86 68.88 2208.558

Production in ‘Metric Ton’

2365184

2365184

2312342

2222871

Labour in ‘Man Days’

7952016

7952016

7822995

7604542

0.61

0.23

0.01

0.00

Degree of Satisfaction ‘λ’


RESULTS AND DISCUSSIONS


CONCLUSION  Changing scenarios, must be evaluated through integrated reservoir planning.  There is 8.72%, increase in Khadakwasla command, 26.70% increase in JSLIS command and 32.19 % increase in PLIS command.  Uncertainty in the crop yield, crop prices and labour availability from socio-economic point of view can be handled using Fuzzy Non Linear Multiobjective Programming concept.  Careful selection of exponent of nonlinear membership function is essential for possible implementation of the methodology to real world planning problems. Acknowledgements

Authors are grateful to all the officials of Pune Irrigation Circle, Pune ,GSDA, Pune and Agriculture Directorate, Pune Division for providing necessary data, practical inputs and encouragement for the study. They are thankful to farmers for providing valuable suggestions during response survey.


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