Two Dimensional Strip Packing with Unloading Constraints

In this paper we present approximation algorithms for the two dimensional strip packing problem with unloading constraints. In this problem, we are given a strip S of width 1 and unbounded height, and n items of C different classes, each item ai with height h(ai), width w(ai) and class c(ai). As in the strip packing problem, we have to pack all items minimizing the used height, but now we have the additional constraint that items of higher classes cannot block the way out of lower classes items. In all problems but one we assume that orthogonal rotation of the items is allowed. For the case in which horizontal and vertical movements to remove the items are allowed, we design an algorithm whose asymptotic performance bound is 3. For the case in which only vertical movements are allowed, we design a bin packing based algorithm with asymptotic approximation ratio of 5.745. Moreover, we also design approximation algorithms for restricted cases of both versions of the problem. These problems have practical applications on routing problems with loading/unloading constraints.