Further- more, they show that the solution obtained with the extra constraint is at most 1.5 revolutions more than the optimal without the extra constraint. The above research treats the carousel as a one-dimen- sional system, i.e., the travel perpendicular to the rotation of the carousel was not considered. Wen and Chang (1988) consider a two-dimensional car- ousel system and propose three heuristics that are extensions of Bartholdi and Platzman’s optimal algorithm. Han and McGinnis (1986), and Han et al. (1988) extend the nearest-neighbor heuristics discussed earlier for the dual-command AS/RS to carousels and rotary racks. (A rotary rack is similar to a carousel except that it has several layers, and each layer can be operated independently.)