The Minimum Formwork Stock problem (MFS) consists in minimizing the quantity of shuttering materials needed for a construction site. This paper introduces this problem encountered in a French building company and presents two different solving approaches: a constraint programming model combined with a constructive heuristic and a Dantzig-Wolfe decomposition taking advantage of the size of real world instances. Then, a NP-hardness proof of the problem is established before providing results on real instances.
We describe algorithms to represent and compute groups of Hecke characters. We make use of an idèlic point of view and obtain the whole family of such characters, including transcendental ones. We also show how to isolate the algebraic characters, which are of particular interest in number theory. This work has been implemented in Pari/GP, and we illustrate our work with a variety of explicit examples using our implementation.
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