# An approximation algorithm for stacking up bins from a conveyer onto pallets

## Abstract

Given sequence of bins *q* = (*b*_{1},. . . , *b*_{n}) and a positive integer *p*. Each bin is destined for. We consider the problem to remove step by step all bins from *q* such the positions of the bins removed from *q* are as less as possible and after each removal there are at most *p* open (A pallet *t* is called open if the first bin for *t* is already removed from *q* but the last bin for *t* is still contained in *q*. If a bin *b* is removed from *q* then all bins to the right of *b* are shifted one position to the left.)

The maximal position of the removed bins and the maximal number of open pallets are called the storage capacity and the number of stack-up places, respectively. We introduce an O(n · log(p)) time approximation algorithm that processes each sequence q with a storage capacity of at most *s*_{min}(*q*, *p*) · [log_{2}(*p* + 1)] bins and *p* + 1 stack-up places, where *s*_{min}(*q*,*p*) is the minimum storage capacity necessary to process *q* with *p* stack-up places.

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