
bin_packing(+Items, ++ItemSizes, +BinLoads)

   The one-dimensional bin packing constraint with loads: packing M items into N bins, each bin having a load

Arguments
   Items               A collection of M (domain) variables or integers (domain/value between 1 and N)
   ItemSizes           A collection of M non-negative integers
   BinLoads            A collection of N (domain) variables or non-negative integers

Type
   library(gfd)

Description
   This constraint is for one-dimensional bin-packing, that is, to pack M
   items with individual sizes into N bins, such that the sum of sizes of
   items in each bin equals the load of that bin, as specified in BinLoads.
   Each element of Items and its corresponding element in ItemSizes
   represents an item, such that the i'th element of ItemSizes is the size
   of the i'th item, and the i'th element of Item is the bin this item is
   packed into. BinLoads represent the load of each bin, i.e. the sum
   of the sizes of items assigned to that bin, with the j'th element 
   representing the load for bin j. An (integer finite domain) variable for 
   the load allows a constraint on the load to be specified, such as a
   minimum and/or maximum load for the bin.

    Note that the Gecode implementation of this constraint has index starting
    from 0, i.e. the numbering for the bins starts from 0. These native 
    indices are mapped to the  ECLiPSe indices starting from 1 with an 
    additional dummy zero'th bin that is assigned a dummy item 0. A version
    of this constraint that uses native Gecode indexing is available 
    as bin_packing_g/3.

   The global constraint catalog describes this constraint as a
   variation of their bin_packing constraint where the fixed capacity for
   every bin is replaced by the BinLoads variables. In addition, a more
   restricted version of this constraint is also described in the global 
   constraint catalog as bin_packing_capa, where instead of BinLoads,
   each bin is given its own integer capacity, the maximum load that
   bin can take, this is equivalent to giving the corresponding variable 
   for the bin in BinLoads the domain 0..Capacity. 

   This constraint is implemented using Gecode's binpacking() constraint.



Examples
   
[eclipse 7]: bin_packing([3,1,3], [4,3,1], [L1,L2,L3,L4]).

L1 = 3
L2 = 0
L3 = 5
L4 = 0



See Also
   bin_packing / 4, bin_packing_g / 3, fd_global : bin_packing / 3, ic_global : bin_packing / 3
