Minimizing the Maximum Number of Open Stacks by Customer Search

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We describe a new exact solver for the minimization of open stacks problem (MOSP). By combining nogood recording with a branch and bound strategy based on choosing which customer stack to close next, our solver is able to solve hard instances of MOSP some 5-6 orders of magnitude faster than the previous state of the art. We also derive several pruning schemes based on dominance relations which provide another 1-2 orders of magnitude improvement. One of these pruning schemes largely subsumes the effect of the nogood recording. This allows us to reduce the memory usage from an potentially exponential amount to a constant ~2Mb for even the largest solvable instances. We also show how relaxation techniques can be used to speed up the proof of optimality by up to another 3-4 orders of magnitude on the hardest instances.