The Weighted Uncapacitated Planned Maintenance Problem

Torben Kuschel
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Torben Kuschel: University of Wuppertal

Chapter Chapter 4 in Capacitated Planned Maintenance, 2017, pp 71-102 from Springer

Abstract: Abstract Industrial production systems consist of components that gradually wear off. This chapter introduces the Weighted Uncapacitated Planned Maintenance Problem (WUPMP). The maintenance activities cover a set of periods before they must be executed again. The trade-off results from the cost structure. The strongly $$\mathcal{N}\mathcal{P}$$ -hard WUPMP has the single-assignment property and the polytope is quasi-integral. A generalized period covering constraint has an integral polytope. The computational complexity of several problem variants is resolved. The WUPMP is solvable time O(n ⋅ T n+1 ⋅ 2 n ) and strongly polynomially solvable if the number of maintenance activities is a constant. Other optimal, strongly polynomial algorithms to different problem variants are provided. The WUPMP is a generalization of Uncapacitated Facility Location Problem but a special problem variant of the Uncapacitated Network Design Problem and of the Set Partitioning Problem. Structural insights for the Capacitated Planned Maintenance Problem (CPMP) are provided.

Keywords: Short Path; Dual Problem; Maintenance Activity; Optimal Objective Function; Uncapacitated Facility Location Problem (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-319-40289-5_4

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DOI: 10.1007/978-3-319-40289-5_4

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