On the optimal allocation of service to impatient tasks

Glazebrook, K. D.; Ansell, P. S.; Dunn, R. T.; Lumley, R. R.

doi:10.1017/s0021900200014030

Cited by 24 publications

(46 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall use an approximate DP approach, which has proved effective in other application domains. See, for example, Glazebrook et al (2004), Krishnan (1987), and Tijms (1994). This is a two-stage approach to policy development in which the problem's inaccessible value function is approximated by deployment of an assumption that all decisions beyond the current one are made according to a strongly performing static (state-independent) allocation policy.…”

Section: An Approximate Dp Approach To Heuristic Developmentmentioning

confidence: 99%

Allocation Models and Heuristics for the Outsourcing of Repairs for a Dynamic Warranty Population

2008

View full text Add to dashboard Cite

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-pro t 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. W e consider a scenario in which a large equipment manufacturer wishes to outsource the work involved in repairing purchased goods while under warranty. Several external service vendors are available for this work. We develop models and analyses to support decisions concerning how responsibility for the warranty population should be divided between them. These also allow the manufacturer to resolve related questions concerning, for example, whether the service capacities of the contracted vendors are sufficient to deliver an effective post-sales service. Static allocation models yield information concerning the proportions of the warranty population for which the vendors should be responsible overall. Dynamic allocation models enable consideration of how such overall workloads might be delivered to the vendors over time in a way which avoids excessive variability in the repair burden. We apply dynamic programming policy improvement to develop an effective dynamic allocation heuristic. This is evaluated numerically and is also used as a yardstick to assess two simple allocation heuristics suggested by static models. A dynamic greedy allocation heuristic is found to perform well. Dividing the workload equally among vendors with different service capacities can lead to serious losses.

show abstract

Section: An Approximate Dp Approach To Heuristic Developmentmentioning

confidence: 99%

Allocation Models and Heuristics for the Outsourcing of Repairs for a Dynamic Warranty Population

2008

View full text Add to dashboard Cite

show abstract

“…Our model has been studied in Glazebrook et al (2004), which develops a heuristic policy via a twostage process. The first stage analyzes a policy that allocates a fixed-service effort to each class at all time and computes the optimal allocation, and the second stage performs an exact policy improvement (PI).…”

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

View full text Add to dashboard Cite

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.

show abstract

“…We also refer to [19] for a recent survey on abandonments in a many-server system. More related to our present work are the papers that deal with optimal scheduling or control aspects of multi-class queueing systems in the presence of abandonments, see for instance [23,5,25,1,3,20,4,7].…”

Section: Introductionmentioning

confidence: 99%

“…As far as the authors are aware, the above two settings are the only ones for which structural optimality results have been obtained. State-dependent heuristics for the multi-class queue are proposed in [1] for two classes and no arrivals and in [23] for an arbitrary number of classes including new arrivals.…”

Section: Introductionmentioning

confidence: 99%

Dynamic fluid-based scheduling in a multi-class abandonment queue

Larrañaga

Ayesta

Verloop

2013

Performance Evaluation

View full text Add to dashboard Cite

We investigate how to share a common resource among multiple classes of customers in the presence of abandonments. We consider two different models: (1) customers can abandon both while waiting in the queue and while being served, (2) only customers that are in the queue can abandon. Given the complexity of the stochastic optimization problem we propose a fluid model as a deterministic approximation. For the overload case we directly obtain that thecµ/θ rule is optimal. For the underload case we use Pontryagin's Maximum Principle to obtain the optimal solution for two classes of customers; there exists a switching curve that splits the two-dimensional state-space into two regions such that when the number of customers in both classes is sufficiently small the optimal policy follows thecµ-rule and when the number of customers is sufficiently large the optimal policy follows thecµ/θ-rule. The same structure is observed numerically in the optimal policy of the stochastic model for an arbitrary number of classes. Based on this we develop a heuristic and by numerical experiments we evaluate its performance and compare it to several index policies. We observe that the suboptimality gap of our solution is small.

show abstract

On the optimal allocation of service to impatient tasks

Cited by 24 publications

References 16 publications

Allocation Models and Heuristics for the Outsourcing of Repairs for a Dynamic Warranty Population

Allocation Models and Heuristics for the Outsourcing of Repairs for a Dynamic Warranty Population

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

Dynamic fluid-based scheduling in a multi-class abandonment queue

Contact Info

Product

Resources

About