| 1. |
- Almgren, Torgny, 1962, et al.
(författare)
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Optimization models for improving periodic maintenance schedules by utilizing opportunities
- 2012
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Ingår i: Proceedings of 4th Production and Operations Management World Conference, July 2012.
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Konferensbidrag (refereegranskat)abstract
- We present mathematical models for finding optimal opportunistic maintenance schedules for systems, in which components are assigned maximum replacement intervals. Our mod- els are applied to safety-critical components in an aircraft engine, for which maintenance opportunities naturally arise since entire modules are sent to the workshop when mainte- nance is required on one or more components. Case study results illustrate the advantage of the mathematical models over simpler policies, the benefit of coordinating the maintenance in economically dependent systems, and that our models can be utilized also for strategic investment decision support.
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| 2. |
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| 3. |
- Almgren, Torgny, 1962, et al.
(författare)
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The opportunistic replacement problem: analysis and case studies
- 2011
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We consider an optimization model for determining optimal opportunistic maintenance (that is, component replacement) schedules when data is deterministic. This problem generalizes that of Dickman, Epstein, and Wilamowsky [21] and is a natural starting point for the modelling of replacement schedules when component lives are non-deterministic. We show that this basic opportunistic replacement problem is NP-hard. We show that the convex hull of the set of feasible replacement schedules is full-dimensional, and that all the necessary inequalities also are facet-inducing. We show that when maintenance occasions are fixed, the remaining problem can be stated as a linear program; when maintenance costs are monotone with time, the latter is solvable through a greedy procedure. Results from a series of case studies performed in the areas of aircraft engine and wind turbine maintenance are also reported. These illustrate the advantages of utilizing opportunistic maintenance activities based on a complete optimization model, as compared to simpler policies.
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| 4. |
- Almgren, Torgny, 1962, et al.
(författare)
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The opportunistic replacement problem: theoretical analyses and numerical tests
- 2012
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Ingår i: Mathematical Methods of Operations Research. - : Springer Science and Business Media LLC. - 1432-2994 .- 1432-5217. ; 76:3, s. 289-319
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Tidskriftsartikel (refereegranskat)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.
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| 5. |
- Almgren, Torgny, 1962, et al.
(författare)
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The replacement problem: A polyhedral and complexity analysis. The complete version
- 2009
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We consider an optimization model for determining optimal opportunistic maintenance (that is, component replacement) schedules when data is deterministic. This problem, which generalizes that of Dickman et al., is a natural starting point for the modelling of replacement schedules when component lives are non-deterministic, whence a mathematical study of the model is of large interest. We show that the convex hull of the set of feasible replacement schedules is full-dimensional, and that all the necessary inequalities are facet-inducing. Additional facets are then provided through Chvatal-Gomory rounding. We show that when maintenance occasions are fixed, the remaining problem reduces to a linear program; in some cases the latter is solvable through a greedy procedure. We further show that this basic replacement problem is NP-hard.
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| 6. |
- Andréasson, Niclas, 1976, et al.
(författare)
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An Introduction to Continuous Optimization, 3rd edition
- 2016
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This is the third edition of a book that was originally published in 2005. The book is used primarily in the teaching of the Chalmers course TMA947 Nonlinear Optimization.
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| 7. |
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| 8. |
- Patriksson, Michael, 1964, et al.
(författare)
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Introduction to Continuous Optimization
- 2013
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This second edition introduces several areas and items that were not included in the first edition, as well as several corrections. A brief summary of these changes are given next. Chapter 1 includes a discussion on the diet problem, in addition to that on the staff planning problem, in order to very early on introduce linear programming. Figure 1.1 now has the terminating box ``Implementation'', whereas the original one had an infinite loop! Chapter 3 has been enriched by several new results on separating and supporting hyperplanes, and the associated theory of convex cones and their polar sets. Thanks to this study of separating hyperplanes,Theorem 5.17 on the necessity of the Fritz John conditions now has a complete proof. The end of Chapter 5 also includes a summary of the fascinating story of the development of the Karush--Kuhn--Tucker conditions. The sensitivity analysis in linear programming has been expanded with a discussion in Section 10.5.3 on the addition of a variable or a constraint, as well as an introduction to column generation based on the example of the minimum cost multi-commodity network flow problem (Section 10.6). Chapter 11 includes a brief discussion on Gauss--Newton methods for least-squares problems. Chapter 12 has changed its name from ``Optimization over convex sets'' to ``Feasible-direction methods,'' in order to reflect the fact that the scope is now wider---from essentially polyhedral sets to general closed sets (which, however, most often will be assumed to be convex). In particular, we have added new sections on algorithms defined by closed descent maps---an algorithm principle which was devised and analyzed mainly in the 1960s, and which is a quite elegant means to describe iterative methods. We also utilize this principle to contrast established convergent methods (such as the Frank--Wolfe method) and failed attempts (such as the algorithm of Zoutendijk). We have also added a brief discussion on reduced gradient methods, which are relatives to the simplex method; they are---in their original statement---not convergent, but a small adjustment results in a closed descent map and hence a convergent method. Exercises and their solutions are now placed at the end of the book, rather than at the end of each chapter. The first edition from 2005 has been used in teaching of several courses at Chalmers University of Technology and the University of Gothenburg. We wish to thank all the students who have given us remarks on the book. We would also like to thank Dr. Kin Cheong Sou for remarks and corrections on the first edition.
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