Optimal crop distribution in Vojvodina Instructor: Dr. Lužanin Zorana Aleksić Tatjana Dénes Attila Pap Zoltan Račić Sanja Radovanović Dragica Tomašević Jelena Vla Katarina
Introduction • Find optimal crop distribution subject to: – Maximization of the total gross margin – Minimization of the total risk
Constraints • Land constraint • Crop rotation • Budget limit
Start model • Gross margin maximization – Subject to land constraint – Rotational constraints ? !
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
Input Wheat Maize Sunflower Soybean Sugar beet Yield (average) y 1 y 2 y 3 y 4 y 5 Selling price c 1 c 2 c 3 c 4 c 5 Costs t 1 t 2 t 3 t 4 t 5 Parity p 1 p 2 p 3 p 4 p 5
Main idea • Data for crop distribution for last 4 years in terms of 0 -1 3 D matrices if in j th year i th crop was planted on the k th parcel otherwise
To generate ai, j, k for j = 5 (for year 2005) we have to respect: • Rotational constraints If ai, j, k = 1 than ai, j+1, k = 0 If a 3, j-1, k=1 or a 3, j-2, k=1 or a 3, j-3, k=1 than a 4, j, k=0 If a 4, j-1, k=1 or a 4, j-2, k=1 or a 4, j-3, k=1 than a 3, j, k=0 If a 5, j-1, k=1 or a 5, j-2, k=1 or a 5, j-3, k=1 or a 5, j-4, k=1 than a 5, j, k=0, i=1, …, 5 j=1, …, 5 k=1, …, m • Overlapping constraints If ai 0, j, k=1 than ai, j, k=0 for i<>i 0 i=1, …, 5 j=1, …, 5 k=1, …, m
Algorithm - idea • Program eliminates scenarios which don’t satisfy constraints • Calculates objective function for every feasible solution • Output is optimal solution
Output • Optimal distribution of crops • Profit • Graphical presentation of crop distribution MathematicaMatrix. Up. Fill. nb MathematicaMatrix 2_paritet. nb
Modification of Algorithm • Algorithm which calculates optimal distribution for 2 years MathematicaMatrix 2. nb MathematicaModel for two years. nb
Conclusion • Model gives optimal crop distribution, s. t. rotational limits (overlapping) • Some tries for including uncertainty (price, yield) without stochastic
Stochastic model • • Includes risk Yield and price are stochastic Optimal solution respect to risk and profit Use utility function
Model • • • µπi – expected profit σπi – standard deviation of profit σij – covariance of profit R – measure of risk U – utility function
Model
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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