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Feasibility recovery for the Unit-capacity Constrained Permutation Problem

Pascale Bendotti 1 Pierre Fouilhoux 2
2 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : The Unit-capacity Constrained Permutation Problem with Feasibility Recovery (UCPPFR) is to find a sequence of moves for pieces over a set of locations. From a given location, a piece can be moved to a unit capacity location, i.e. the latter location must be free of its original piece. Each piece has a specific type, and in the end every location must contain a piece of a required type. A piece must be handled using a specific tool, thus incurring a setup cost whenever a tool changeover is required. It could be necessary to use some Steiner locations to find a solution, thus incurring a Steiner cost. The aim of the UCPPFR is to find a sequence of moves with a minimum total setup and Steiner cost. We give a necessary and sufficient condition to check whether an instance admits a solution with no Steiner location. We show that the UCPPFR reduces to finding simultaneously a vertex-disjoint path cover and a shortest common supersequence. Finally, using a compact encoding for solutions and integer linear programming tools, we solve real instances coming from the nuclear power plant fuel renewal problem.
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Submitted on : Thursday, June 22, 2017 - 5:27:58 PM
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Pascale Bendotti, Pierre Fouilhoux. Feasibility recovery for the Unit-capacity Constrained Permutation Problem. Discrete Optimization, Elsevier, 2016, Volume 22, Part A, pp.66-86. ⟨10.1016/j.disopt.2015.09.004⟩. ⟨hal-01545594⟩



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