Tight absolute bound for First Fit Decreasing bin-packing: FFD(L)⩽11/9FFD(L)⩽11/9OPT(L)+6/9OPT(L)+6/9

First Fit Decreasing is a classical bin-packing algorithm: the items are ordered by non-increasing size, and then in this order the next item is always packed into the first bin where it fits. For an instance L   let FFD(L)FFD(L) and OPT(L)OPT(L) denote the number of bins used by algorithm FFD and by an optimal algorithm, respectively. In this paper we give the first complete proof of the inequalityFFD(L)⩽11/9⋅OPT(L)+6/9.FFD(L)⩽11/9⋅OPT(L)+6/9. This result is best possible, as was shown earlier by Dósa (2007) [3]. The asymptotic coefficient 11/9 was proved already in 1973 by Johnson, but the tight bound of the additive constant was an open question for four decades.