Orange Grove Management

Rafael Alvarez Sylia Gallegos Juan Carlos Gonzalez Sky Noyd

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

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

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

Revenue

• Options for selling fruit– On tree – Weigh station– Wholesaler

• Price is determined by:– Size

– Quality

– Month of picking

Considerations

• Four Binary Variables– Pesticide, Fertilizer, Tilling, and

Maintenance

• Two Parameters– Revenue and Cost

• Four Constraints– Harvesting seasons of each tree type

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

Analysis of the Model

Example Modelset 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];

Example Data Fileset Month := 1, 2, 3, 4;set Sell := 1, 2, 3;

param Revenue: 1 2 3 4 :=

1 90 90 120 1502 110 110 160 2303 145 145 220 310;

param Cost:1 2 3 4 :=

1 0 0 0 02 20 20 40 803 55 55 100 170;

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

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

Decision Analysis Results with Irrigation

Tree Type Fertilizer Pesticide Maintenance Trimming

Tardias YES YES YES YES

Mayeras YES YES YES YES

Navels NO YES YES NO

Nova NO YES YES NO

Zarzuma NO YES YES YES

Delicias NO YES YES NO

Mars YES YES YES YES

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.

Assumptions

• Given by owner of orange grove• Estimated 30% increase in production

from year to year in the projections

Grade A B

Neither 50% 50%

Fertilizer 70% 30%

Pesticide 90% 10%

Both 100% 0%

Preguntas?