Activity 15C : « Paris Basin » model

Length : around 50 minutes

You are going to enrich the model that you wrote in the exercise in Lesson 11. You can use your model or the corrected version : modelEco_ParisBasin_technic.gms.

« A farmer in the Paris basin has a 100 ha arable crop farm. He can grow soft wheat (bleT), rapeseed, spring barley (orgeP) and winter barley (orgeH) and hemp (chan) in “Integrated pest management” only. For each crop, he can choose between three management systems :

Intensive (written « intens ») : it is the most intensive system in terms of chemical inputs. The farmer often has a “preventive” use of phytosanitary products. In other words, he does not wait for the appearance of diseases or pests in order to spray the crops.
Sustainable (written « rais ») : it involves “sustainable” practices. ». The interventions of the farmer are determined following the observation of diseases or pests in the plot. The quantities used are adapted to the situation.
Integrated pest management ( written « protI ») : such practices integrate prophylactic agronomic measures which contribute to a decrease in the pressure caused by pests. They can involve considerations concerning sowing dates, variety choices, crop successions in a plot, etc…
Integrated pest management at cropping system level (written « SystCI ») : this practice was developed in order to fight against pests and offers agronomic levers at cropping system level, notably with a change in cropping patterns.

The details of the variable costs are known for each management system and each crop : expenses in phytosanitary products (op_phyto), in fertilizer (op_engrais), in seeds (op_sem) and in mechanization (meca_MO) (fuel and depreciation).

Total costs per crop (€/ha) and management system
Crops	Cost types	Management system
Crops	Cost types	Intensive	Sustainable	Integrated pest management	Cropping system
bleT	op_phyto	142	112	73	59
bleT	op_engr	192	187	168	168
bleT	op_sem	50	50	30	30
bleT	meca_MO	268	262	263	263
colza	op_phyto	203	153	101	57
colza	op_engr	170	157	139	131
colza	op_sem	37	37	37	37
colza	meca_MO	314	288	299	304
orgeP	op_phyto	192	201	120	103
orgeP	op_engr	149	147	133	133
orgeP	op_sem	65	65	65	65
orgeP	meca_MO	262	263	276	287
orgeH	op_phyto	234	192	117	110
orgeH	op_engr	166	164	147	147
orgeH	op_sem	65	65	65	65
orgeH	meca_MO	278	259	258	265
chan	op_phyto	–	–	–	0
chan	op_engr	–	–	–	162
chan	op_sem	–	–	–	90
chan	meca_MO	–	–	–	124

The farmer knows the expected yields and working time requirements for each management system and each crop.
The farmer can work 2000 hours a year.

Yields (q/ha) per crop and management system
Crop	Management system
	Intensive			Sustainable		Integrated pest management	Cropping system
bleT	72,8			71		65	66
rapeseed	31			29		26,3	26
orgeP	62,6			62		56	57
orgeH	71			70		64	65
chan	–			–		–	10,5
Working time (hours per ha) per crop and management system
Crop		Management system
		Intensive	Sustainable		Integrated pest management		Cropping system
bleT		3,2	3,1		3,1		3,1
rapeseed		4	3,6		4		4,1
orgeP		3,1	3,1		3,3		3,4
orgeH		3,3	3		3		3,1
chan		–	–		–		1,8

The selling prices of the different crop types are as follows : 180€/t for soft wheat, 365€/t for rapeseed, 170€/t for spring barley, 155€/t for winter barley and 320€/t for hemp.

It was observed that farmers used a cropping pattern for organisational reasons, by alternating summer crops and winter crops, and for agronomic reasons notably due to the positive effects of a crop on the next one : soil structure and fertility, pest control, etc. But rotations are currently often short (one crop can sometimes be used twice in a row), which leads to the need to increase the inputs in fertilizer and phytosanitary products.

You are going to integrate the rotations into the model.

In the « intensive » « sustainable » and « integrated pest management » management systems, the rotation must respect the following agronomic rules :
– Oilseed crops cannot be cultivated more than once every three years on the same plot,
– cereal crops cannot be grown two years in a row
– each cereal crop can be cultivated on half the cultivated area dedicated to cereal crops at the most

The final rotation, that of « integrated cropping system » introduces hemp in order to extend the rotation. Longer rotations, which imply that a crop is grown less frequently in the rotation, make it possible to control pests more efficiently. It follows the following rules :
– oilseed crops cannot be cultivated more than once every three years on the same plot,
– cereal crops cannot be grown more than one year on the same plot
– each cereal crop can be cultivated on half the cultivated area dedicated to cereal crops at the most
– hemp is grown once every six years

The objective of the farmer is to maximize his income. »

Writing the model

Introduce these rotation constraints into the model

Suggestions :
– make intermediary calculations such as total costs and gross margin
– use the abbreviations
– present all the rotations in the form of proportions with a common divisor (for example 12) in order to facilitate the writing of more generic constraints

Watch out for divisions by zero !

Check the answers and the writing of the model

Analysing price changes

You will carry out several simulations in order to analyse the influence of an increase in cereal prices on cropping pattern choices. For that purpose, you will modify the price parameter in the model. The new prices are as follows :

Decrease in prices (Simulation 1) : 110€/t of wheat, 210€/t of rapeseed, 85€/t of spring barley and 70€/ha for winter barley.

Increase in prices (Simulation 2) : 230€/t wheat, 400€/t of rapeseed, 195€/t of spring barley and 160€/ha for winter barley.

Answer the following questions :

What are the new gross margins following the price changes ?
Do prices have an impact on rotations ? What impact is that ?
What are the new cropping pattern approaches ? Comment the solution.

Check the answers and the writing of the model.