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

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

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

## 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