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Capacitated Planned Maintenance pp 7–24Cite as

The Capacitated Planned Maintenance Problem

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 686))

Abstract

This chapter introduces the Capacitated Planned Maintenance Problem (CPMP) as a novel maintenance problem. The maintenance activities cover a set of periods before they must be executed again. The trade-off results from the available maintenance time per period. The CPMP is motivated by several practical applications and the assumptions are intensively discussed. A review of related well-known maintenance approaches is given. The mathematical formulation of the CPMP, model related assumptions, terminology and an efficient data structure are provided.

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Notes

  1. 1.

    Production and maintenance compete for the availability of the production system. Hence, a simultaneous optimization of both is very advantageous. Some approaches are discussed in Sect. 2.2. A combined approach of the Capacitated Lot-Sizing Problem (Bitran and Yanasse 1982) and the CPMP is presented in Appendix A.1.

  2. 2.

    An introduction to process industry and case studies are found in Neumann et al. (2002), Neumann and Schwindt (2000), and Reklaitis (1991).

  3. 3.

    On a short-time scale, the maintenance problem can also be related with a routing problem that optimizes the sequence in which the windmills are visited.

  4. 4.

    In the appendix, extensions of the CPMP are presented in Sect. A.1. Alternative formulations of the CPMP are provided in Sect. A.2.

  5. 5.

    In the discrete-time formulation of the Resource Constrained Project Scheduling Problem (Pritsker et al. 1969), the resource constraint is modeled with a sliding time window that is very similar to (P).

  6. 6.

    The constraint (C) is identical to the capacity constraint of the Generalized Bin Packing Problem (Hung and Brown 1978).

  7. 7.

    Some lower bounds presented in Chap. 6 are easily tightened via the Assumptions (2.3) and (2.4).

  8. 8.

    This assumption is commonly imposed on the KP (Martello and Toth 1990, p. 14) and it is also applicable here.

  9. 9.

    Immediate means that no third task is scheduled in between.

  10. 10.

    In the remainder of the thesis, singly linked and doubly linked lists are just referred to as list. Cf. Ottmann and Widmayer (2012, pp. 29–41) for the data structure list.

  11. 11.

    From the definitions follows First i  = left i0 and Last i  = right i, T+1.

  12. 12.

    Cf. Ottmann and Widmayer (2012, pp. 41–47 ) for the data structure stack. Implementation detail: In this context, it is noteworthy to introduce an efficient memory management (Bock 2004, pp. 241–242), which minimizes the number of memory allocation operations. Assume that memory for a specific data structure is required. Let a stack consist of pointers that reference several instances of the respective data structure. The stack is initialized in the initialization phase of the algorithm. Whenever a pointer to a new instance of the data structure is required, the memory is not allocated but the top element of the stack is returned and removed from the stack. If the instance is not needed anymore, the memory is not deallocated but the pointer is inserted in the stack.

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  1. WINFOR–Business Computing and Operations Research, University of Wuppertal, Wuppertal, Germany

    Torben Kuschel

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Kuschel, T. (2017). The Capacitated Planned Maintenance Problem. In: Capacitated Planned Maintenance. Lecture Notes in Economics and Mathematical Systems, vol 686. Springer, Cham. https://doi.org/10.1007/978-3-319-40289-5_2

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