Lesson 5.3: FSSIM

Icône de l'outil pédagogique Authors

Kamel Louhichi, Sander Janssen, Argyris Kanellopoulos, Guillermo Flichman, Martin van Ittersum, Huib Hengsdijk, Peter Zander, Maria Blanco, Grete Stokstad

Icône de l'outil pédagogique FSSIM – Farming System Simulator

FSSIM is a bio-economic model, developed within the SEAMLESS-IP, to assess at the farm level the impact of agricultural and environmental policies on performance of farms and on sustainable development indicators. It consists of a data module for agricultural management (FSSIM-AM) and a mathematical programming model (FSSIM-MP) (Figure 1). FSSIM-AM aims to identify current and alternative activities and to quantify their input and output coefficients (both yields and environmental effects) using the biophysical field model APES (Agricultural Production and Externalities Simulator) and other data sources. FSSIM-MP seeks to describe farmer’s behaviour given a set of biophysical, socio-economic and policy constraints, and to predict his/her responses under new technologies, policy and market changes. The principal outputs generated from FSSIM for a specific policy are forecasts on land use, production, input use, farm income and environmental externalities (e.g. nitrogen surplus, nitrate leaching, pesticide use, etc.). These outputs can be used directly or translated into indicators to provide measures of the impact of policies.



Figure 1. An overview of FSSIM as a combination of Agricultural Management module (FSSI-AM) and Mathematical Programming module (FSSIM-MP).

Icône de l'outil pédagogique The mathematical formula

The mathematical structure of FSSIM can be formulated as follows:

Maximise: (1)

Subject to: ; (2)


Where U is the variable to be maximised (i.e. utility), Z is the expected income, x is a (n x 1) vector of agricultural activity levels, A is a (m x n) matrix of technical coefficients, B is a (m x 1) vector of levels of available resources, f is a scalar for the risk aversion coefficient and s is the standard deviation of income according to states of nature defined under two different sources of variation: yield (due to climatic conditions) and prices.

The expected income (Z) is a non-linear profit function. Using matrix notation, this gives:


Where: i indexes agricultural activities, j indexes crop products, l indexes quota types (e.g. for sugar beet these are A and B), t indexes number of years in a rotation, p is a vector of average product prices, q is a vector of sold production, pa is a vector of additional price that the farmer gets when selling within quota l, qa is a vector of sold production within quota l , s is a vector of subsidies per crop within agricultural activity i (depending on the Common Market Organisations (CMOs)), c is a vector of variable cost per crop within agricultural activity i, d is a vector representing the linear term used to calibrate the model (depending on the calibration approaches), Y is a symmetric, positive (semi-) definite matrix of quadratic term used to calibrate the model (depending on the calibration approaches), h is a vector representing the length of a rotation within each agricultural activity, v is a scalar for the labour cost and L is the number of hours rented labour

Icône de l'outil pédagogique A unique model

The general context and the variety of questions that FSSIM must be able to answer justify a number of choices that makes this model unique:

  • Comparative static model: FSSIM is a mono-periodic model which optimizes an objective function for one period (i.e. one year) over which decisions are taken. This implies that it does not explicitly take account of time. Nevertheless, to incorporate some temporal effects, agricultural activities are based on “crop rotations” and “dressed animal[1]” rather than individual crops and animals.
  • Primal based-approach: FSSIM follows a primal-based approach, where technology is explicitly represented (Louhichi et al., 1999). It uses engineering production functions generated from agronomic theory and biophysical models (Hengsdijk and Van Ittersum, 2003). These engineering functions constitute the essential linkage between the biophysical and economic models. This discrete mathematical programming approach can (better) capture the technological and policy constraints than a behaviour function in econometric models.
  • A positive model, where the main objective is to reproduce the observed production situation as precisely as possible by making use of the observed behaviour of economic agents (Janssen and Van Ittersum, 2007).
  • A risk programming model, taking into account the risk according to the Mean-Standard deviation method in which expected utility is defined under expected income and risk (Hazell and Norton, 1986).
  • Modular model: it has a modular setup to be re-usable, adaptable and easily extendable to achieve different modelling goals. Thanks to this modularity, FSSIM provides the capabilities to activate and deactivate modules according to regions and conditions. It allows also the subsequent incorporation of additional modules which might be needed to simulate activities not included in the existing version, such as perennial activities, and the replacement of modules with alternative versions.
  • Generic model: it was designed sufficiently generic and with a transparent syntaxes in order to be applied to many different farming systems across Europe and elsewhere, and to assess different policies under various conditions.
  • Automatic and integrated components: it includes several components, which have been linked and integrated. The communication between these different components is based on explicit definitions of spatial scales and software for model integration. It is foreseen that each component can be reused independently for other applications and modeling exercises. New components can also be added in later stages.

FSSIM exists both as stand-alone version and as a version integrated within SEAMLESS-IF. In order to make all FSSIM components easier to manipulate a Graphical User Interface (GUI) was developed. This GUI assists users in setting up scenarios, running the simulations and exploring model outputs in response to changing inputs.

[1] The concept of ‘dressed animal’ represents an adult animal and young stock taking into account the replacement rate.

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