Two-dimensional strip packing with unloading constraints

Abstract

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 $a_i$ with height $h\left(a_i\right)$, width $w\left(a_i\right)$ and class $c\left(a_i\right)$. As in the strip packing problem, we have to pack all items, minimizing the height used, but now we have the additional constraint that items of higher classes cannot block the way out of items of lower classes. For the case in which horizontal and vertical movements for removing 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 an 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 in dealing with routing problems with loading/unloading constraints.