On-Line Algorithms for Controlling Palletizers

We consider the FIFO Stack-Up problem which arises in delivery industry, where bins have to be stacked-up from conveyor belts onto pallets. Given are k sequences $$q_1, \ldots , q_k$$ of labeled bins and a positive integer p. The goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. Each of these pallets has to contain bins of only one label, bins of different labels have to be placed on different pallets. After all bins of one label have been removed from the given sequences, the corresponding stack-up place becomes available for a pallet of bins of another label. In this paper we consider on-line algorithms for instances where we only know the next c bins of every sequence instead of the complete sequences. We implemented our algorithms and could show that for realistic, but randomly generated instances our best approach leads only 12% more stack-up places than an optimal off-line solution. On the other hand we could show worst-case examples which show an arbitrary large competitive factor when comparing our on-line solutions with optimal off-line solutions.