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**Harvard**

Almgren, T., Andréasson, N., Patriksson, M., Strömberg, A., Wojciechowski, A. och Önnheim, M. (2012) *The opportunistic replacement problem: theoretical analyses and numerical tests*.

** BibTeX **

@article{

Almgren2012,

author={Almgren, Torgny and Andréasson, Niclas and Patriksson, Michael and Strömberg, Ann-Brith and Wojciechowski, Adam and Önnheim, Magnus},

title={The opportunistic replacement problem: theoretical analyses and numerical tests},

journal={Mathematical Methods of Operations Research},

issn={1432-2994},

volume={76},

issue={3},

pages={289-319},

abstract={We consider a model for determining optimal opportunistic maintenance schedules with respect to a maximum replacement interval. This problem generalizes that of Dickman et al. (J Oper Res Soc India 28:165–175, 1991) and is a natural starting point for modelling replacement schedules of more complex systems. We show that this basic opportunistic replacement problem is NP-hard, that the convex hull of the set of feasible replacement schedules is full-dimensional, that all the inequalities of the model are facet-inducing, and present a new class of facets obtained through a {0,1/2}-Chvátal–Gomory rounding. For costs monotone with time, a class of elimination constraints is introduced to reduce the computation time; it allows maintenance only when the replacement of at least one component is necessary. For costs decreasing with time, these constraints eliminate non-optimal solutions. When maintenance occasions are fixed, the remaining problem is stated as a linear program and solved by a greedy procedure. Results from a case study on aircraft engine maintenance illustrate the advantage of the optimization model over simpler policies. We include the new class of facets in a branch-and-cut framework and note a decrease in the number of branch-and-bound nodes and simplex iterations for most instance classes with time dependent costs. For instance classes with time independent costs and few components the elimination constraints are used favorably. For fixed maintenance occasions the greedy procedure reduces the computation time as compared with linear programming techniques for all instances tested.},

year={2012},

keywords={Maintenance optimization, Mixed integer programming, Complexity analysis, Polyhedral analysis},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 162877

A1 Almgren, Torgny

A1 Andréasson, Niclas

A1 Patriksson, Michael

A1 Strömberg, Ann-Brith

A1 Wojciechowski, Adam

A1 Önnheim, Magnus

T1 The opportunistic replacement problem: theoretical analyses and numerical tests

YR 2012

JF Mathematical Methods of Operations Research

SN 1432-2994

VO 76

IS 3

SP 289

OP 319

AB We consider a model for determining optimal opportunistic maintenance schedules with respect to a maximum replacement interval. This problem generalizes that of Dickman et al. (J Oper Res Soc India 28:165–175, 1991) and is a natural starting point for modelling replacement schedules of more complex systems. We show that this basic opportunistic replacement problem is NP-hard, that the convex hull of the set of feasible replacement schedules is full-dimensional, that all the inequalities of the model are facet-inducing, and present a new class of facets obtained through a {0,1/2}-Chvátal–Gomory rounding. For costs monotone with time, a class of elimination constraints is introduced to reduce the computation time; it allows maintenance only when the replacement of at least one component is necessary. For costs decreasing with time, these constraints eliminate non-optimal solutions. When maintenance occasions are fixed, the remaining problem is stated as a linear program and solved by a greedy procedure. Results from a case study on aircraft engine maintenance illustrate the advantage of the optimization model over simpler policies. We include the new class of facets in a branch-and-cut framework and note a decrease in the number of branch-and-bound nodes and simplex iterations for most instance classes with time dependent costs. For instance classes with time independent costs and few components the elimination constraints are used favorably. For fixed maintenance occasions the greedy procedure reduces the computation time as compared with linear programming techniques for all instances tested.

LA eng

DO 10.1007/s00186-012-0400-y

LK http://dx.doi.org/10.1007/s00186-012-0400-y

OL 30