The multidimensional vector bin packing problem consists in packing m-dimensional items into a minimum number of m-dimensional bins with unit capacity in each of the m dimensions in such a way that the sum of each coordinate of the items received by any bin is not larger than one. We improve the lower bound of the First-Fit-Decreasing heuristic when m≥5 and odd, and prove that this heuristic is optimal when m = 2 if each item has at least one coordinate larger than 1/2. Finally, if this last condition holds and m≥3, we show that the problem remains NP-hard.
|Original language||English (US)|
|Number of pages||9|
|State||Published - Dec 1 1990|