The CLP Procedure

where bin_packing_constraint is specified in the following form:

( ( <… >) ( <… >) ( <… > ) )

The PACK constraint is used to assign items to bins, subject to the sizes of the items and the capacities of the bins. The item variable assigns a bin to the th item. The variable holds the size or weight of the th item. The domain of the load variable constrains the capacity of bin .

For example, suppose there are three bins with capacities 3, 4, and 5. There are five items with sizes 4, 3, 2, 2, and 1 to be assigned to these three bins. The following statements formulate the problem and find a solution:

proc clp out=out;
   var bin1 = [0,3];
   var bin2 = [0,4];
   var bin3 = [0,5];
   var (item1-item5) = [1,3];
   pack ((item1-item5) (4,3,2,2,1) (bin1-bin3));
run;   

Each row of Table 3.2 represents a solution to the problem. The number in each item column is the number of the bin to which the corresponding item is assigned.

Note: In specifying a PACK constraint, it can be more efficient to list the item variables in order by nonincreasing size and to specify VARSELECT=FIFO in the PROC CLP statement.