| 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. |
- 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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| 3. |
- 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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| 4. |
- Thörnblad, Karin, 1971, et al.
(författare)
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A competitive iterative procedure using a time-indexed model for solving flexible job shop scheduling problems
- 2013
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We investigate the efficiency of a discretization procedure utilizing a time-indexed mathematical optimization model for finding accurate solutions to flexible job shop scheduling problems considering objectives comprising the makespan and the tardiness of jobs, respectively. The time-indexed model is used to find solutions to these problems by iteratively employing time steps of decreasing length. The solutions and computation times are compared with results from a known benchmark formulation and an alternative, slightly enhanced version of the same. For the largest instances---considering both objectives---the proposed method finds significantly better solutions than the other models within the same time frame, although there is a large difference in the performance of the models depending on which objective is considered. This implies that the evaluation of scheduling algorithms must be performed with respect to an objective that is suitable for the real application for which they are intended. The minimization of the makespan is no such objective, although it is the most widely used objective in research. We propose an objective incorporating tardiness. The iterative procedure for solving the time-indexed model outperforms the other models regarding the time to find the best feasible solution. We conclude that our iterative procedure with the time-indexed model is competitive with state-of-the-art mathematical optimization models. Since the proposed procedure quickly finds solutions of good quality to large instances, our findings imply that the new procedure is beneficially utilized for scheduling real flexible job shops.
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| 5. |
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| 6. |
- Thörnblad, Karin, 1971, et al.
(författare)
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An efficient algorithm for solving the flexible job shop scheduling problem
- 2013
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Ingår i: 25th NOFOMA conference proceedings, June 3-5 2013, Göteborg, Sweden.
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Konferensbidrag (refereegranskat)abstract
- Purpose: To investigate the efficiency of a discretization procedure utilizing a time-indexed mathe-matical optimization model for finding accurate solutions to flexible job shop scheduling problems considering objectives comprising makespan and tardiness, respectively. Design/methodology/approach: A time-indexed mixed integer programming model is used to find solutions by iteratively employing time steps of decreasing length. The solutions and computation times are compared with results from a known benchmark formulation and an alternative model. Findings: The proposed method finds significantly better solutions for the largest instances within the same time frame. Both the other models are better choices for some smaller instances, which is expected since the new method is designed for larger problems. Only our alter-native model is able to solve two of the largest instances when minimizing the tardiness. Research limitations/implications: Interesting future research topics include the introduction of constraints representing other relevant entities such as the availability of tools and fixtures, and the scheduling of maintenance activities and personnel. Practical implications: Real cases of flexible job shop problems typically yield very large models. Since the new procedure quickly finds solutions of good quality to such instances, our findings imply that the new procedure is beneficially utilized for scheduling real flexible job shops. Original/value: We show that real flexible job shop problems can be solved through the solution of a series of carefully formulated discretized mathematical optimization models.
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| 7. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Mathematical modelling of a real flexible job shop in aero engine component manufacturing
- 2011
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Ingår i: Proceedings of 10th Workshop on Models and Algorithms for Planning and Scheduling Problems, June 2011, Nymburk, Czech Republic.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We formulate two mixed integer programming models stemming from a real flexible job shop problem with a total of ten resources and five main processing multipurpose machines. The models are compared w.r.t. memory usage, computation times, and accuracy.
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| 8. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Mathematical optimization of a flexible job shop problem including preventive maintenance and availability of fixtures
- 2012
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Ingår i: Proceedings of the 4th World P&OM Conference / 19th International Annual EurOMA Conference, Amsterdam, Netherlands, July 2012.
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Konferensbidrag (refereegranskat)abstract
- The multitask cell at Volvo Aero Corporation is a flexible job shop containing ten resources aimed at being flexible with regard to product mix and processing types. Computing schedules for this type of job shop is an NP-hard problem. The computation times will therefore always be an issue, especially as the scheduling problem includes limited availability of fixtures and preventive maintenance planning. Computational results show that with the method developed we are able to produce optimal, or near-optimal, schedules for real data instances within an acceptable time frame. The scheduling principle proposed shortens lead times and minimizes tardiness.
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| 9. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Optimering av scheman för en verklig produktionscell: tidsdiskretisering reducerar lösningstiden utan att lösningarnas kvalitet försämras
- 2011
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Ingår i: PLANs forsknings- och tillämpningskonferens, 31 aug-1 sep 2011, Norrköping, Sverige.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Vid optimering av industriella schemaläggningsproblem är kompromissen mellan beräkningstid och resultatnivå ofta kritisk, med risken att en optimeringsmodell förenklas så mycket att dess resultat inte är praktiskt relevant. I artikeln jämförs två matematiska optimeringsmodeller för optimal schemaläggning av en verklig produktionscell på Volvo Aero. I den ena modellen beskrivs bl. a. operationers starttider m.h.a. kontinuerliga variabler, medan tiden har diskretiserats i den andra modellen. Diskretiseringen innebär att planeringshorisonten indelas i ett antal tidssteg, här kallade diskreta tidsperioder. Det är en förenkling eftersom all indata då måste uttryckas i helt antal diskreta tidsperioder och varje operation endast kan schemaläggas vid början av en tidsperiod. Den senare modellen visade sig överlägsen vad gäller beräkningstider och bedömdes därför ha mycket stor potential, trots risken för approximeringsfel p.g.a. tidsdiskretiseringen. 2 I artikeln presenteras tester med verkliga indata, vilka visar att approximeringsfelen blir mycket små när den diskreta tidsperiodens längd är en timma eller mindre, trots att några operationstider är kortare än så. Det optimala schemat från den tidsdiskreta modellen har före jämförelsen justerats så att alla operationstider är de ursprungliga, detta utan att förändra vare sig maskinval eller valda sekvenser på maskinerna. Denna modell har goda förutsättningar att fungera praktiskt, eftersom den både är snabb och ger goda resultat.
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| 10. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Optimization of schedules for a multitask production cell
- 2010
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Ingår i: Proceedings of The 22nd NOFOMA Conference in Kolding, Denmark, 10-11th of June 2010.
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Konferensbidrag (refereegranskat)abstract
- Purpose of this paper; To optimize production schedules of a real production cell containing multi-purpose machines working as a job-shop in a complex logistic environment producing aircraft engine components. The planning and control of the production in the so called multitask cell results in a complex combinatorial problem. Design/methodology/approach; A mathematical optimization model of the multitask cell has been developed and tested on real data instances. The current production planning prerequisites have been studied in order to choose an appropriate objective function. Findings; Production plans resulting from the optimization model, are compared with schedules formed by the First in First Out (FIFO) and Earliest Due Date (EDD) priority rules, which are similar to the current manual planning of the multitask cell. Practical implications; The proposed scheduling principle will shorten lead times, and provide a more efficient use of the resources of the multitask cell. The effects are most significant at times with high utilization of the cell. What is original/value of paper; The development of theory and practice of optimization, together with the development of computer hardware during the past decades, enable the utilization of optimization as a tool for computing efficient production schedules in a complex logistic environment.
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