1 Introduction
2 Problem statement
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(i) Demand and arrival management: Decisions on the arrival rate are about releases into the queue, for example, in appointment scheduling, in order releases planning for manufacturing, or in acceptance of demand within revenue management.
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(ii) Queue configurations: Decisions on routing policies are affected by the time-dependent evolvement of parameters. The size of the waiting space may also be a time-dependent decision.
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(iii) Server capacities: The optimization of server capacities includes decisions on the number of servers and/or decisions on the server characteristics, for example, the skills or the processing rate.
3 Discussion
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Exact approaches: Optimization problems can be formulated as Markov decision problems under certain assumptions and can be used to prove insights on the structure of the solution, see, for example, [6]. However, they are often solved heuristically because of the state-space explosion. For example, approximate dynamic programming techniques or new methods like reinforcement learning are applied, see [4].
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Sequential approaches: Sequential approaches separate the queueing from the optimization part. For example, resource requirements per period are derived from a queueing model. They then serve as constraints in deterministic shift scheduling, see, for example, [2].
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Iterative approaches: In contrast to sequential approaches, such methods iterate between an evaluation part and an optimization part to get a new candidate solution, see, for example, [1]. Queueing approaches or simulation evaluates the candidate solution. Low-fidelity high-fidelity approaches may refine the evaluation part over the iterations to speed up the procedure. The optimization part uses the evaluated former solution(s) and often applies heuristic procedures.
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Integrated approaches: Integrated approaches transform analytical evaluations of queueing systems into optimization models. However, the resulting optimization problems can be linear or nonlinear mathematical models which are difficult to solve with exact methods, see, for example, [8].
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Stochastic programming: Stochastic programming replaces probability distributions by samples or scenarios and can handle time-dependent parameters or decisions, see, for example, [3]. However, it results in deterministic optimization problems which can be huge based on the number of considered samples.