An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

Liu, Dong; Glazebrook, K. D.

doi:10.1002/nav.20395

Cited by 26 publications

(12 citation statements)

References 23 publications

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“…Direct precursors to this study under operations literature include Glazebrook et al (2004), Li and Glazebrook (2010), and Jacobson et al (2012), which develop heuristic policies to the resource scheduling problem where all impatient jobs are present at the outset (i.e., under the assumption of no further arrivals). Essentially, two types of policies have been proposed: static and state-dependent.…”

Section: Introductionmentioning

confidence: 99%

When to Switch? Index Policies for Resource Scheduling in Emergency Response

Liu

Ding

Connor

2020

Production and Operations Management

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This study considers the scheduling of limited resources to a large number of jobs (e.g., medical treatment) with uncertain lifetimes and service times, in the aftermath of a mass casualty incident. Jobs are subject to triage at time zero, and placed into a number of classes. Our goal is to maximize the expected number of job completions. We propose an effective yet simple index policy based on Whittle’s restless bandits approach. The problem concerned features a finite and uncertain time horizon that is dependent upon the service policy, which also determines the decision epochs. Moreover, the number of job classes still competing for service diminishes over time. To the best of our knowledge, this is the first application of Whittle’s index policies to such problems. Two versions of Lagrangian relaxation are proposed in order to decompose the problem. The first is a direct extension of the standard Whittle’s restless bandits approach, while in the second the total number of job classes still competing for service is taken into account; the latter is shown to generalize the former. We prove the indexability of all job classes in the Markovian case, and develop closed‐form indices. Extensive numerical experiments show that the second proposal outperforms the first one (that fails to capture the dynamics in the number of surviving job classes, or bandits) and produces more robust and consistent results as compared to alternative heuristics suggested from the literature, even in non‐Markovian settings.

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Section: Introductionmentioning

confidence: 99%

When to Switch? Index Policies for Resource Scheduling in Emergency Response

Liu

Ding

Connor

2020

Production and Operations Management

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“…In patient triage applications, abandonments have been used to model medical emergency patients in danger of dying while awaiting treatment. See, for example, Argon et al (2008) and Li and Glazebrook (2010).…”

Section: Introductionmentioning

confidence: 99%

“…253 Glazebrook et al (2004), and Li and Glazebrook (2010), whereas API methods which utilize simulation are discussed in Powell (2011, §10.5) and Bertsekas (2012, Chap. 6 and 7).…”

Section: Introductionmentioning

confidence: 99%

Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement

James

Glazebrook

Lin

2016

INFORMS Journal on Computing

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Developing effective service policies for multiclass queues with abandonment: asymptotic optimality and approximate policy improvemen James, Terry Informs T. James, K. Glazebrook, K. Lin, "Developing effective service policies for multiclass queues with abandonment: asymptotic optimality and approximate policy improvement," INFORMS Journals on Computing, v.28, no.2 (Spring 2016) e study a single server queuing model with multiple classes and impatient customers. The goal is to determine a service policy to maximize the long-run reward rate earned from serving customers net of holding costs and penalties respectively due to customers waiting for and leaving before receiving service. We first show that it is without loss of generality to study a pure-reward model. Since standard methods can usually only compute the optimal policy for problems with up to three customer classes, our focus is to develop a suite of heuristic approaches, with a preference for operationally simple policies with good reward characteristics. One such heuristic is the Råà rule-a priority policy that ranks all customer classes based on the product of reward R, service rate å, and abandonment rate à. We show that the Råà rule is asymptotically optimal as customer abandonment rates approach zero and often performs well in cases where the simpler Rå rule performs poorly. The paper also develops an approximate policy improvement method that uses simulation and interpolation to estimate the bias function for use in a dynamic programming recursion. For systems with two or three customer classes, our numerical study indicates that the best of our simple priority policies is near optimal in most cases; when it is not, the approximate policy improvement method invariably tightens up the gap substantially. For systems with five customer classes, our heuristics typically achieve within 4% of an upper bound for the optimal value, which is computed via a linear program that relies on a relaxation of the original system. The computational requirement of the approximate policy improvement method grows rapidly when the number of customer classes or the traffic intensity increases.

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“…For this case, Glazebrook et al (2004) and Argon et al (2008) have proposed simple heuristics for job sequencing, neither of which have uniformly strong performance. The best solution approach to date for the perfect triage problem is due to Li and Glazebrook (2010) and utilises a fluid model of the system to underpin an approximate DP methodology. In Section 4 this approach is further developed so that it can yield effective solutions to our Bayesian model for the problem in which triage is subject to error.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach to the triage problem with imperfect classification

Liu¹,

Glazebrook

2011

European Journal of Operational Research

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A collection of jobs (or customers, or patients) wait impatiently for service. Each has a random lifetime during which it is available for service. Should this lifetime expire before its service starts then it leaves unserved. Limited resources mean that it is only possible to serve one job at a time. We wish to schedule the jobs for service to maximise the total number served. In support of this objective all jobs are subject to an initial triage, namely an assessment of both their urgency and of their service requirement. This assessment is subject to error. We take a Bayesian approach to the uncertainty generated by error prone triage and discuss the design of heuristic policies for scheduling jobs for service to maximise the Bayes' return (mean number of jobs served). We identify problem features for which a high price is paid in number of services lost for poor initial triage and for which improvements in initial job assessment yield significant improvements in service outcomes. An analytical upper bound for the cost of imperfect classification is developed for exponentially distributed lifetime cases.

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An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

Cited by 26 publications

References 23 publications

When to Switch? Index Policies for Resource Scheduling in Emergency Response

When to Switch? Index Policies for Resource Scheduling in Emergency Response

Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement

A Bayesian approach to the triage problem with imperfect classification

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