COST FUNCTION

Crop allocation is a spatio-temporal planning problem in which crops are

assigned to landunits x_{b,i} over a fixed horizon H of time. A Landunit
is defined as a piece of indivisible and homogeneous land whose historic
and biophysical properties are identical. The landunits are spatial
sampling of the farmland where x_{b,i} denotes the landunit $i$ of block
$b$. Blocks are characterized by one cropping system defined by the same
sequence of crops and by the use of a coherent set of production
techniques applied to these crops (e.g. fertilizer, irrigation water).
The delimitation of blocks are not reshaped in the CAP considered in
this work.

More formally, the Crop allocation problem is defined by a tuple
 where
  - X a set of variables x_{b,i}^{t} that define the landunits
   i in block b (i \in [1, N_b, b \in [1, B]. Each landunit is described by H variables that
   represent the landunit occupation at each date. 
  - D the domains D_{b,i} of variables x_{b,i}^{t} is the set of
  possible  crop over the block b. 
  -W the cost functions W_i that define the hard and soft constraints. W_i can be (1) simple cost functions, 
  (2) same constraints,  (3) global constraints regular, (4) global cardinality constraints, 
  (5) soft global cardinality constraints. These constraints are precisely define according the the CAP. 
  
  
CAP instances
-------------
The CAP described in this benchmark we consider a 4 blocks sampled into
N landunits Four crops are produced over the all blocks : winter wheat
(BH), spring barley (OP), maize (MA) and winter rape (CH). Each block
has a fixed area (areablock(1) = 48ha, areablock(2) = 24ha, areablock(3)
= 48ha, areablock(4) = 60ha). The blocks 1 and 3 have an access to
irrigation equipments r_1 and r_2. The annual quota of irrigation water
over the blocks is 6000 m^{3} (respectively 4000 m^3) for r_1
(respectively r_2). Only the maize (MA) can be irrigated. There are two
different types of soil : A (block 1, 3) and B (block 2, 4).

The number of landunits N is increased from 15 to 120. For the CAP
instance with 15 landunits N_1=N_3=4, N_2=2 and N_4=5 where N_i is the
number of landunits in the block i. Note that in this instance the
area of each landunit is 12ha. These landunits are gradually refined
by splitting them into 2, 4 and 8 smaller ones, to respectively build
the instances with 30, 60 and 120 landunits. These sampling are chosen
to be representative of different farm size. The planning horizon H=9.
According to the minimum return time (winter wheat rt(BH)=2, spring
barley rt(OP)=3, maize rt(MA)=2 and winter rape rt(CH)=3) the four
last years are dedicated to the future variable while the five first
are the historic.


benchmark organization: ./Bi-LUj.wcsp ==> 16 instances in toulbar2
format associated to the block i (where j denote the number of landunit
in the block) ./B1234-LU*.wcsp ==> 8 instances in toulbar2 format
associated to the the all block 1 2 3 4 *.ub ==> optimal solution
obtained by DFBB using the default option. *.sol ==> a complete
assignment

question : makploga@toulouse.inra.fr