Step 1 – Land constraints : using the first paragraph of the problem statement, the first step is to write the land constraints, one of them concerning grassland, the other concerning arable land (or total UAA).
Step 2 – Animal feed : the needs and food availabilities must be expressed in terms of tons for each food category (silage maize, hay, grazing, wrapped bales). A series of equations indexed by F will therefore be written, and using data from tables X / Y.
Step 3 – Herd management : two equations are written. One concerning prolificity, the other concerning renewal.
Step 4 – Dairy quota
Step 5 – Objective function : crop production income (calculated using gross margins as per usual) must be distinguished from animal production. Animal production proceeds include milk sales, the sales of calves and cull cows, and its expenses include fixed costs and the price of purchased soya-bean.
Here is a suggestion of names to use for the data and variables :
| SET | A | Cattle present |
| C | crops | |
| CA(C) | Annual crops | |
| F | Fodder products | |
| CO | Concentrates purchased | |
| R | type of ration | |
| SCALAR | TERlab | Available arable land in ha |
| pp | Permanent grassland | |
| QUO | quota in litre | |
| REF | Culling rate | |
| PROL | prolificity per DC [Dairy Cow ?] | |
| pxLait | Price of milk in € per litre | |
| TxVendu | Rate of calves sold | |
| PARAMETER | prixc(C) | Price of sales crops in € per tonne |
| cout(C) | Costs per crop in € per ha | |
| rdtg(C) | Yield of sales crops in tonnes per ha | |
| coutco(CO) | cost of concentrates in € per tonne | |
| mbc(C) | Gross margin of crops | |
| prixa(A) | Selling price in € per animal | |
| pl(A,R) | productivity in litre per animal | |
| charges(A) | Fixed and operating costs in € per animal | |
| TABLE | besco(A,R,CO) | Animal soya needs in t per animal |
| rdtf(C,F) | Fodder yield in tonne per ha | |
| besf(A,R,F) | Animal fodder needs in t per animal | |
| VARIABLE | Z | Total gross margin |
| X(C) | Crop area | |
| N(A,R) | Number of animals |
If you have difficulties working with these indications only, you may download the data in .gms format : modelEco_dairyFarm_data.zip
