On the Mathematical Treatment of Pileproblems

Summary

Pileproblems are difficult discrete optimization problems. They deal with practical tasks like loading and unloading trains trucks or ships. We find problems of this kind also in civil engineering and in logistics of course. Even simpler definitions remain such problems hard to solve. We consider the following problem: A given pile — consisting of elementsv _i of a set V — should be moved step by step to a final pile with a possibly different structure. To reach the required final situation there are auxiliary places available. Calculating the number of necessary auxiliary piles is known to be NP-complete. We report on experiences with a branch-and-bound algorithm and a heuristic method.

Finally we introduce a more general problem that yields when using a mapping between the elements of the starting pile and the final pile that is not unique.

Finally we introduce a more general problem that yields when using a mapping between the elements of the starting pile and the final pile that is not unique.