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The Weighted Uncapacitated Planned Maintenance Problem

In: Capacitated Planned Maintenance

Author

Listed:
  • Torben Kuschel

    (University of Wuppertal)

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.

Suggested Citation

  • Torben Kuschel, 2017. "The Weighted Uncapacitated Planned Maintenance Problem," Lecture Notes in Economics and Mathematical Systems, in: Capacitated Planned Maintenance, chapter 0, pages 71-102, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-40289-5_4
    DOI: 10.1007/978-3-319-40289-5_4
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