Optimal crop distribution in Vojvodina

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Optimal crop distribution in Vojvodina

• Instructor Dr. Lužanin Zorana
• Aleksic Tatjana
• Dénes Attila
• Pap Zoltan
• Racic Sanja
• Radovanovic Dragica
• Tomaševic Jelena
• Vla Katarina

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Introduction

• Find optimal crop distribution subject to
• Maximization of the total gross margin
• Minimization of the total risk

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Constraints

• Land constraint
• Crop rotation
• Budget limit

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Start model

• Gross margin maximization
• Subject to land constraint
• Rotational constraints ?!

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Discrete model

• Land is divided into m parcels
• There is only 1 crop on each parcel
• Includes some uncertainty for yield
• Rotational constraint
• Budget constraint

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Input
Wheat Maize Sunflower Soybean Sugar beet
Yield (average) y1 y2 y3 y4 y5
Selling price c1 c2 c3 c4 c5
Costs t1 t2 t3 t4 t5
Parity p1 p2 p3 p4 p5
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Main idea

• Data for crop distribution for last 4 years in
  terms of 0-1 3D matrices

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To generate ai,j,k for j 5 (for year 2005) we
have to respect

• Rotational constraints
• If ai,j,k 1 than ai,j1,k 0
• If a3,j-1,k1 or a3,j-2,k1 or a3,j-3,k1
  than a4,j,k0
• If a4,j-1,k1 or a4,j-2,k1 or a4,j-3,k1
  than a3,j,k0
• If a5,j-1,k1 or a5,j-2,k1 or a5,j-3,k1 or
  a5,j-4,k1 than a5,j,k0,
• 
  i1,,5 j1,,5 k1,,m
• Overlapping constraints
• If ai0,j,k1 than ai,j,k0 for iltgti0
• i1,,5
  j1,,5 k1,,m

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Algorithm - idea

• Program eliminates scenarios which dont satisfy
  constraints
• Calculates objective function for every feasible
  solution
• Output is optimal solution

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Output

• Optimal distribution of crops
• Profit
• Graphical presentation of crop distribution
• Mathematica\MatrixUpFill.nb
• Mathematica\Matrix2_paritet.nb

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Modification of Algorithm

• Algorithm which calculates optimal distribution
  for 2 years
• Mathematica\Matrix2.nb
• Mathematica\Model for two years.nb

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Conclusion

• Model gives optimal crop distribution, s.t.
  rotational limits (overlapping)
• Some tries for including uncertainty (price,
  yield) without stochastic

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Stochastic model

• Includes risk
• Yield and price are stochastic
• Optimal solution respect to risk and profit
• Use utility function

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Model

• µpi expected profit
• spi standard deviation of profit
• sij covariance of profit
• R measure of risk
• U utility function

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Model
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Open questions

• Extend constraints for agricultural policy
• When to buy mechanization?
• Involving more stochastic
• Price and yield distribution?
• Measuring of risk
• Utility function?

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