A set of items has to be assigned to a set of bins with size one. If n
ecessary, the size of the bins can be extended. The objective is to mi
nimize the total size, i.e., the sum of the sizes of the bins. The Lon
gest Processing Time heuristic is applied to this NP-hard problem. For
this approximation algorithm we prove a worst-case bound of 13/12 whi
ch is shown to be tight when the number of bins is even. (C) 1998 Else
vier Science B.V.