Orange Grove Management

1. Orange Grove Management Rafael Alvarez Sylia Gallegos Juan Carlos Gonzalez Sky Noyd

2. Orange Grove Overview • Orange Grove located in Alamo Veracruz, Mexico • 28.9 acre property, including 3,932 new orange trees • Seven different varieties of oranges: • Tardias • Navels • Mayeras • Zarsuma • Delicias • Mars • Nova

4. Objective • Maximize profit by analyzing the revenues and costs of production • Develop an IP model • Solve for the Revenue • Solve for the Costs • Profit = Revenue – Costs • Irrigation System? • Solve the model using AMPL

5. Costs • The cost factors we will be analyzing are: • Fertilizer • Pesticide • Maintenance • Worker Salary • Tilling • Transportation (Shipping) • No previous records regarding costs • Used 3 sources to find costs • Juan and his family • Local engineer • Concitver.com

6. Revenue • Options for selling fruit • On tree • Weigh station • Wholesaler • Price is determined by: • Size • Quality • Month of picking

7. Considerations • Four Binary Variables • Pesticide, Fertilizer, Tilling, and Maintenance • Two Parameters • Revenue and Cost • Four Constraints • Harvesting seasons of each tree type

8. Designing the Model • There will be production movement from month to month • Each node represents a month • There will be three basic costs associated with sales • All types of oranges will follow the Figure 1 generic production and sales model

9. Analysis of the Model

10. Example Model set Month; set Sell; param Revenue{Sell, Month} >= 0; param Cost{Sell, Month} >= 0; var X{Month} >= 0; var Y{Month} >= 0; var Z{Sell, Month} >= 0; var P binary; var F binary; var T binary; var M binary; maximize Profit: sum{i in Sell, j in Month} (Revenue[i,j] - Cost[i,j])*Z[i,j] - 390*F - 700*P - 225*T - 400*M; subject to Start: X[1] = 1932*(5 + 20*F + 10*P + 7.5*T + 7.5*M)/1000; subject to Balance{i in 1..3}: X[i] = Y[i] + X[i+1]; subject to Balance4: X[4] = Y[4]; subject to Selling{i in Month}: Y[i] = sum{j in Sell} Z[j,i];

11. Example Data File set Month := 1, 2, 3, 4; set Sell := 1, 2, 3; param Revenue: 1 2 3 4 := 1 90 90 120 150 2 110 110 160 230 3 145 145 220 310 ; param Cost: 1 2 3 4 := 1 0 0 0 0 2 20 20 40 80 3 55 55 100 170 ;

12. Projected Solution • Without irrigation total projected profit is estimated at $597,974 for the year • Tardias, Mayeras, and Mars trees • all activities are recommended • Navels, Nova, and Delicias trees • model recommends only using Pesticide and Maintenance for the return on fertilizer and pesticide would not cover their costs

13. Projected Solution cont. • With irrigation the total projected profit is estimated at $881,506 for the year • Tardias, Mayeras, and Mars trees • all activities are recommended • Navels, Nova, and Delicias trees • model recommends only using Pesticide and Maintenance for the return on fertilizer and pesticide would not cover their costs

14. Decision Analysis Results with Irrigation

15. Irrigation System • The net present value of the projected profit to be gained over the next five years is $192,791. • When considering whether or not an irrigation system should be installed, at a price of $60,000 the estimated gain is still $132,791.

16. Assumptions • Given by owner of orange grove • Estimated 30% increase in production from year to year in the projections

17. Preguntas?