The Objectives and Priorities for the Azorean Dairy Farmers’ Decisions - The Agricultural Economics of the 21st Century - page 144

agriculture researches and the results obtained using alternative methods are simi-
lar. That means that any method can explain the preferences revealed by farmers.
This criterion intends to minimize the distance of any point to its ideal, so the sum
of negative and positive deviational variables is minimized and it underlines the use
of metric 1. This problem can be formulated in terms of goal programming, as
following:

Min X

q

n i þ p i

W i

f i

i¼ 1

subject to
X

q

w j f ij þ n i p i ¼ f i i ¼ 1, 2, ... , q

j¼ 1

X

q

W j ¼ 1

j¼ 1

where p i and n i are the positive (over-achievement) and negative deviational
variables respectively for each objective. From a preferential point of view, an L 1
criterion is consistent with an additive and separable utility function, and permits
the estimation of a standard function (Amador et al. 1998 ). That means weights
obtained from the last equation lead to the following function:

Max X

n

w i f i x

ðÞ
K i

μ ¼

i¼ 1

subject to
X F

K i ¼

∈

f i

f i

where K i is a normalized factor obtained by the difference between the maxi-
mum value— f i * (ideal)—and the minimal— f i * (anti-ideal)—of objective i of the
payoff matrix. This allows estimating the weights which indicate the ranking of the
objectives followed by a farmer elicited.

4.1 Multi-criteria Model Definition

The farmers optimize their personal utility function which comprises the objectives
taken into account by the decision maker. The optimization of these objectives is
limited by certain constraints that need to be met.
Decision variables, objectives, and constraints are the main elements of the
model described for Azorean dairy farmers in different systems grazing. In the
multi-criteria model, the decision variables can assume any value of the feasible set,