backtracking

int bp (…) {
	if all items have been placed in bins
		return the total number of bins used
	for each bin that we can place the next item in
		place the item in that bin
		call bp() recursively to find the minimum number of bins used to store all of the items given that the items already stored cannot be moved
		remove the item from the bin
	return the minimum number of bins needed
}

To reduce the amount of backtracking required to find the optimal solution, the following heuristics are used:

a. Presort the sizes in decreasing order.

b. Compute a lower bound on the number of bins by adding the sizes together,
  dividing by the capacity, and rounding up to the nearest integer; and
  quit when an assignment requiring that number of bins is found.

c. Keep track of the smallest number of bins found previously (initially
  this is just the number of items) and do not consider any (partial)
  assignment that would require at least that many bins.

 d. When the current item has the same size as an item stored in the partial 
  assignment, never place it in a bin to the left of the bin in which that 
  item was stored.                                         

 e. Never place an item in a bin that has the same amount of room remaining
  as one that was tried previously for this item.

 f. When looping over bins in which to place an item, try them in decreasing
  order of capacity *remaining*.