5.2.2. Sequencing and routing for man-on-board AS/RS
The routing problem for man-on-board AS/RS is a TSP with a Chebyshev distance metric. The literature on this problem has been focused primarily on efficient heuristics. Gudehus (1973) describes the band heuristic, which divides the rack into two equal height horizontal bands; the points in the lower band are visited in the increasing x-coordinate direction, while the points in the upper band are visited in the opposite direction. If the tour must visit many points, the rack may be divided into several
pairs of horizontal bands. Goetschalckx and Ratliff(1988c) propose a convex hull algorithm based on the property of Chebyshev metric that some points not on the convex hull can be inserted into it without incurring additional travel distance. The algorithm
constructs the convex hull of all the picking locations, then those free insertion locations for each segment of the convex hull are identified and inserted into the convex hull, and then the remaining points are sequentially inserted into the tour in
a way that minimizes the increase in tour length
for each insertion. The band algorithm is easy toimplement and computationally efficient, but might give inferior solutions in some cases. On the other
hand, the convex hull algorithm is effective in findingshort tours, but is difficult to implement (to findwith the assumptions they made and followed by the
other results that relax some of the restrictive
assumptions (see the problem setting column in
Table 7).