Optimal management of cross-trained workers in services with negligible switching costs

Berman, Oded; Wang, Jiamin; Isotupa, K. P. Sapna

doi:10.1016/j.ejor.2004.03.024

Cited by 24 publications

(29 citation statements)

References 8 publications

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“…B ≥ B l S j=k 0 P (j) = 1 equations (1), (6), (7), (8), (9). Berman et al (2005) refer to this problem as problem P 1 . It is important to note that B, F and L are expected values and can be real-valued.…”

Section: Berman Et Al Modelmentioning

confidence: 99%

“…However, the goal of the current work is to demonstrate the applicability of constraint programming to computing the optimal values for the given policy type and not to address theoretical optimality questions. Therefore, the term optimal policy is used throughout the paper to refer to the optimal numerical parameters for the policy type proposed by Berman et al (2005).…”

Section: Policy Definitionmentioning

confidence: 99%

“…The policy type adopted here is the one proposed by Berman et al (2005). A policy is defined in terms of quantities k i , for i = 0, .…”

Section: Policy Definitionmentioning

confidence: 99%

“…These managers are thus interested in finding a switching policy that minimizes the expected customer waiting time in the front room, subject to the constraint that the expected number of workers in the back room is sufficient to complete all required work. This queueing control problem has been studied in detail by Berman, Wang and Sapna (2005), who propose a heuristic for solving it.…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 presents a description of the problem and the work done by Berman et al (2005). In the next section, three CP models for this problem are proposed.…”

Section: Introductionmentioning

confidence: 99%

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A Constraint Programming Approach for Solving a Queueing Design and Control Problem

Terekhov

Beck

Brown

2009

INFORMS Journal on Computing

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In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is minimized while the expected back room staffing is sufficient to perform all work. Three novel constraint programming models and several shaving procedures for these models are presented. Experimental results show that a model based on closed-form expressions together with a combination of shaving procedures is the most efficient. This model is able to find and prove optimal solutions for many problem instances within a reasonable run-time. Previously, the only available approach was a heuristic algorithm. Furthermore, a hybrid method combining the heuristic and the best constraint programming method is shown to perform as well as the heuristic in terms of solution quality over time, while achieving the same performance in terms of proving optimality as the pure constraint programming model. This is the first work of which we are aware that solves such queueing-based problems with constraint programming.

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Section: Berman Et Al Modelmentioning

confidence: 99%

Section: Policy Definitionmentioning

confidence: 99%

“…The policy type adopted here is the one proposed by Berman et al (2005). A policy is defined in terms of quantities k i , for i = 0, .…”

Section: Policy Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Section 2 presents a description of the problem and the work done by Berman et al (2005). In the next section, three CP models for this problem are proposed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Constraint Programming Approach for Solving a Queueing Design and Control Problem

Terekhov

Beck

Brown

2009

INFORMS Journal on Computing

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Two‐class constrained optimization with applications to queueing control

Girard

Green

Lewis

et al. 2020

Naval Research Logistics

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Constrained Markov decision process (CMDP) is a methodology that has not seen wide applications in the literature, but is a more natural specification for modeling preferences in modern service systems. In this paper we present a general framework for solving two‐class CMDPs. In particular, we show that CMDPs can be solved by using the Lagrangian dual to specify a particular unconstrained problem. If an appropriate Lagrange multiplier can be discerned, structural results can be exploited to solve the original CMDP with the appropriate structure. We show that for two queues in parallel or two queues in series, the framework leads to simple threshold‐like optimal policies. The results in each case are used to develop heuristics for analogous problems with abandonments with applications to health care, call centers, and manufacturing systems. The efficacy of the heuristics is verified in each case via a detailed numerical study.

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