Optimal Balanced Control for Call Centers

Bhulai, Sandjai; Farenhorst-Yuan, Taoying; Heidergott, Bernd; Laan, Dinard van der

doi:10.2139/ssrn.1539385

Cited by 3 publications

(5 citation statements)

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“…For the computation of the performance measures, it means that we employ the equivalent continued functions in

n

for the stationary probabilities (Jagers & Van Doorn, 1986). In practice, a noninteger value for the threshold

n

can be obtained by randomizing in between two adjacent integer threshold policies as explained in Bhulai et al (2012).…”

Section: Numerical Analysismentioning

confidence: 99%

Dynamic policy for idling time preservation

Legros¹

2022

Naval Research Logistics

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This study aims to determine and evaluate dynamic idling policies where an agent can idle while some customers remain waiting. This type of policies can be employed in situations where the flow of urgent customers does not allow the agent to spend sufficient time on back‐office tasks. We model the system as a single‐agent exponential queue with abandonment. The objective is to minimize the system's congestion while ensuring a certain proportion of idling time for the agent. Using a Markov decision process approach, we prove that the optimal policy is a threshold policy according to which the agent should idle above (below) a certain threshold on the queue length if the congestion‐related performance measure is concave (convex) with respect to the number of customers present. We subsequently obtain the stationary probabilities, performance measures, and idling time duration, expressed using complex integrals. We show how these integrals can be numerically computed and provide simpler expressions for fast‐agent and heavy‐traffic asymptotic cases. In practice, the most common way to regulate congestion is to control access to the service by rejecting some customers upon arrival. Our analysis reveals that idling policies allow high levels of idling probability that such rejection policies cannot reach. Furthermore, the greatest benefit of implementing an optimal idling policy occurs when the objective occupation rate is close to 50% in highly congested situations.

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“…For the computation of the performance measures, it means that we employ the equivalent continued functions in

n

for the stationary probabilities (Jagers & Van Doorn, 1986). In practice, a noninteger value for the threshold

n

can be obtained by randomizing in between two adjacent integer threshold policies as explained in Bhulai et al (2012).…”

Section: Numerical Analysismentioning

confidence: 99%

Dynamic policy for idling time preservation

Legros¹

2022

Naval Research Logistics

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“…It is hard to obtain the optimal value of θ more precisely because then considerably lower values of ε would be necessary and the simulation would then take a very long time. Methods like gradient estimation by simulation (see for example Heidergott et al 2010;Bhulai et al 2012) could speed up the optimization of θ , but in regions where the function is almost flat it remains difficult. Therefore we focus on the relative size of performance improvements which has more practical value than obtaining the optimal value of θ with high precision.…”

Section: Instancementioning

confidence: 99%

Assigning multiple job types to parallel specialized servers

Laan

2018

Discrete Event Dyn Syst

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In this paper methods of mixing decision rules are investigated and applied to the so-called multiple job type assignment problem with specialized servers. This problem is modeled as continuous time Markov decision process. For this assignment problem performance optimization is in general considered to be difficult. Moreover, for optimal dynamic Markov decision policies the corresponding decision rules have in general a complicated structure not facilitating a smooth implementation. On the other hand optimization over the subclass of so-called static policies is known to be tractable. In the current paper a suitable static decision rule is mixed with dynamic decision rules which are selected such that these rules are relatively easy to describe and implement. Some mixing methods are discussed and optimization is performed over corresponding classes of so-called mixing policies. These mixing policies maintain the property that they are easy to describe and implement compared to overall optimal dynamic Markov decision policies. Besides for all investigated instances the optimized mixing policies perform substantially better than optimal static policies.

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“…Optimizing the expected performance g(θ ) of Bernoulli policies over θ ∈ [0, 1] is relatively easy if g(θ ) is a smooth function of θ ∈ [0, 1]. Indeed (see, e.g., [7] or [12]), it follows for a family of Bernoulli policies as given by (6) and any θ…”

Section: Bernoulli Policiesmentioning

confidence: 99%

“…Alternatively, gradient estimation by measurevalued differentiation could be applied to approximate some (optimal) value θ * ∈ [0, 1] for which g (θ * ) = 0. In [6] this simulation technique is applied to a call center operation problem with two types of jobs having different service requirements for which in various ways, two reasonable applicable decision rules are obtained that are mixed to improve the system performance. The technique is relatively fast to approximate an optimal value for θ .…”

Section: Bernoulli Policiesmentioning

confidence: 99%

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Optimal Mixing of Markov Decision Rules for MDP Control

Laan¹

2011

Prob. Eng. Inf. Sci.

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In this article we study Markov decision process (MDP) problems with the restriction that at decision epochs, only a finite number of given Markov decision rules are admissible. For example, the set of admissible Markov decision rules ${\cal D}$ could consist of some easy-implementable decision rules. Additionally, many open-loop control problems can be modeled as an MDP with such a restriction on the admissible decision rules. Within the class of available policies, optimal policies are generally nonstationary and it is difficult to prove that some policy is optimal. We give an example with two admissible decision rules—${\cal D}$={d1, d2} —for which we conjecture that the nonstationary periodic Markov policy determined by its period cycle (d1, d1, d2, d1, d2, d1, d2, d1, d2) is optimal. This conjecture is supported by results that we obtain on the structure of optimal ${\cal D}$ Markov policies in general. We also present some numerical results that give additional confirmation for the conjecture for the particular example we consider.

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Optimal Balanced Control for Call Centers

Cited by 3 publications

References 0 publications

Dynamic policy for idling time preservation

Dynamic policy for idling time preservation

Assigning multiple job types to parallel specialized servers

Optimal Mixing of Markov Decision Rules for MDP Control

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