Stack-up algorithms for palletizing at delivery industry

Abstract

We study the following multi-objective combinatorial stack-up problem from delivery industry. Given a sequence q of labeled bins and two positive integers s and p. The aim is to stack-up the bins by iteratively removing one of the first s bins of the sequence and put it to one of p stack-up places. Each of these places has to contain bins of only one label, bins of different labels have to be placed on different places. If all bins of a label are removed from q, the corresponding place becomes available for bins of another label. We analyze the worst-case performance of simple algorithms for the stack-up problem that are very interesting from a practical point of view. In particular, we show that the so-called Most-Frequently on-line algorithm is (2,2)-competitive and has optimal worst-case on-line performance.