Moving Bins from Conveyor Belts onto Pallets Using FIFO Queues

Abstract

We study the combinatorial FIFO stack-up problem. In delivery industry, bins have to be stacked-up from conveyor belts onto pallets. Given $k$ 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 place becomes available for a pallet of bins of another label. The FIFO stack-up problem is NP-complete in general. In this paper we show that the problem can be solved in polynomial time, if the number $k$ of given sequences is fixed.