Activité 23 : Modèle “Lauragais” – Espérance / écart type

Length : around 30 minutes

Risk must be introduced as expectation-standard deviation. Based on the modelEco_lauragais1.gms solution model, or on the one you wrote in activity 20, add risk as expectation/standard deviation. The risk aversion coefficient is 1.

Reminder of the model statement :

“A farm in the Lauragais, a region in south-western France, has 200 ha of farmland, 100 ha of which are irrigated. A farmer and her husband work on this farm, both are skilled workers.

The farmer sells her production via a local agricultural cooperative which is very involved in the production and marketing of seeds. It thus has the choice between two types of production : arable crops for the human or animal feed market and seed crops produced under contract with the cooperative. She can grow the following arable crops (for the human or animal feed market) : soft wheat, durum wheat, soya-bean and sunflower. As for seed crops, she can grow maize and vegetable crops : cucumber, cabbage, sugar beet, carrot, onion and parsley. Seed crops are much more profitable, but the quality requirements of the cooperative are very strict and certain years, climatic conditions do not make it possible to meet the quality required by the specifications. The price, which depends on quality, suffers the consequences. In some cases, the cooperative can turn down the entire harvest. The gross margin of this production is therefore equal to zero.

Seed crops require unskilled labour for the harvest. This work is entirely carried out by hired labour and must be supervised by a skilled worker (family-based or also hired). One skilled worker is needed to supervise 20 unskilled workers. A hired worker costs 11.1€/hour and a skilled worker 73.3€/hour. The fixed costs of the farm are 93293€. The farmer can rent land to her neighbours at a rate of 519€. Costs for each crop are divided into three types : operating costs excluding labour-force, specific costs, and the costs of hired labour. They are distributed as follows :

*This concerns the sum of the multiplications of unskilled labour needs (see following table) by the hourly rate of labour.

Crops do not require the same amount of labour every month of the year. Only arable crops call for skilled labour for mechanised tasks. Seed crops require significant amounts of unskilled labour during the harvest period. Labour needs are divided into skilled labour and non-skilled labour as follows :

The table below shows the yields in quintals per hectare for food crops and the gross proceeds in euros per hectare for seed crops over the last ten years. The yields vary over the years, and the gross proceeds of seed crops even more so.

Selling prices are as follows : 25€ for durum wheat, 14€ for soft wheat, 35€ for sunflower and 36€ for soya-bean.

The objective of the farmer is to maximize her income.”

Add the constraints to the model in order to maximize the gross margin. Add an equation so as to calculate the random income for each state of nature and standard deviation. The list of potentially useful equation is as follows :

objective    objective function
income      income
land       land constraint
labour(m)  skilled labour constraint
irrigation  irrigable land availability constraint
incomeal(E) random income calculation equation
standard deviationR   income standard deviation

Check that the equations and solutions of your model are accurate modelEco_lauragaisStandardDeviation.gms.