Index policies for the maintenance of a collection of machines by a set of repairmen

Glazebrook, K. D.; Mitchell, H. M.; Ansell, P. S.

doi:10.1016/j.ejor.2004.01.036

Cited by 57 publications

(54 citation statements)

References 11 publications

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“…In Section 3 we establish the indexability of a class of restless bandits designed to model machine maintenance problems in which maintenance interventions (the active action) have to be scheduled to mitigate escalating costs as machines deteriorate (when passive). Whittle (1996, p. 221, p. 280) and Glazebrook et al (2005) have previously given index-based analyses of particular models, but we show here that indexability is guaranteed in general. Identification of the Whittle indices concerned is followed by a numerical investigation which demonstrates the very strong performance of Whittle's index heuristic in 8000 problems.…”

Section: Introductionmentioning

confidence: 86%

“…The indices identified by this route generalise those of Gittins, and Whittle proposed their use in the construction of heuristics for restless bandit problems. The importance of Whittle's contribution was underscored by Weber and Weiss (1990) who established a form of asymptotic optimality for the index heuristic and, more recently, in a range of empirical studies which have demonstrated its outstandingly strong performance in a range of application domains; see, for example, Ansell et al (2003) and Glazebrook et al (2005). Furthermore, Glazebrook et al (2002) have discussed the development of bounds on the degree of reward suboptimality of Whittle's index policy.…”

Section: Introductionmentioning

confidence: 99%

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Some indexable families of restless bandit problems

2006

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In 1988 Whittle introduced an important but intractable class of restless bandit problems which generalise the multiarmed bandit problems of Gittins by allowing state evolution for passive projects. Whittle's account deployed a Lagrangian relaxation of the optimisation problem to develop an index heuristic. Despite a developing body of evidence (both theoretical and empirical) which underscores the strong performance of Whittle's index policy, a continuing challenge to implementation is the need to establish that the competing projects all pass an indexability test. In this paper we employ Gittins' index theory to establish the indexability of (inter alia) general families of restless bandits which arise in problems of machine maintenance and stochastic scheduling problems with switching penalties. We also give formulae for the resulting Whittle indices. Numerical investigations testify to the outstandingly strong performance of the index heuristics concerned.

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Some indexable families of restless bandit problems

2006

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“…While this property appears natural, it is little understood and is often extremely difficult to prove. There is a developing literature centered around this very issue in a range of application areas of which routing is but one (see, e.g., Glazebrook, Niño-Mora, and Ansell [17], Ansell, Glazebrook, Niño-Mora, and O'Keeffe [2], Glazebrook, Mitchell, and Ansell [16], and Glazebrook, Kirkbride, and Ouenniche [15]). …”

Section: Introductionmentioning

confidence: 99%

Dynamic Routing of Customers With General Delay Costs in a Multiserver Queuing System

Argon¹,

Ding²,

Glazebrook³

et al. 2009

Prob. Eng. Inf. Sci.

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We consider a network of parallel service stations each modeled as a single-server queue. Each station serves its own dedicated customers as well as generic customers who are routed from a central controller. We suppose that the cost incurred by a customer is an increasing function of her time spent in the system. In a significant advance on most previous work, we do not require waiting costs to be convex, still less linear. With the objective of minimizing the long-run average waiting cost, we develop two heuristic routing policies, one of which is based on dynamic programming policy improvement and the other on Lagrangian relaxation. In developing the latter policy, we show that each station is "indexable" under mild conditions for customers' waiting costs and also prove some structural results on the admission control problem that naturally arises as a result of the Lagrangian relaxation. We then test the performance of our heuristics in an extensive numerical study and show that the Lagrangian heuristic demonstrates a strong level of performance in a range of traffic conditions. In particular, it clearly outperforms both a greedy heuristic, which is a standard proposal in complex routing problems, and a recent proposal from the heavy traffic literature.

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“…al. [14] 2007 VIA Singh et al [25] 2007 VIA Ko et al [48] 2007 VIA Glazebrook et al [23] 2005 VIA Zobel et al [50] 2005 VIA main architect of the CPLEX linear programming software, has performed careful studies that conclusively demonstrate that for many large-scale and sparse problems (like those LPs arising from solving MDPs), LP algorithms often run thousands of times faster than a decade ago [10]. This multiple order of magnitude difference is solely from improved algorithms, as Bixby compared different versions of the CPLEX code on the same (modern) computing hardward.…”

Section: Introductionmentioning

confidence: 99%