Optimized appointment scheduling
Optimized appointment scheduling
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DOI：
10.1016/j.ejor.2014.05.027
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
B. Kemper;C. Klaassen;M. Mandjes
中科院分区：
文献类型：
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作者：
B. Kemper;C. Klaassen;M. Mandjes
在服务系统中，为了平衡服务器的空闲时间和客户的等待时间，可以在预约调度中预先确定客户的到达时间。我们提出了在D/G/1型系统中确定预约时间表的程序，通过顺序地最小化每个客户的预期损失。我们的方法提供了任何凸损失函数的调度；对于二次损失函数和绝对值损失函数的实际相关情况，得到了吸引人的闭形式结果。重要的是，我们的方法没有对服务时间分布施加任何条件；甚至允许客户的服务时间有不同的分布。我们要解决的下一个问题与客户的理论有关。我们开发了一个准则，当服务时间分布属于一个尺度族，如指数族时，产生最优顺序。客户应按其规模参数的非降序排列。在一般情况下，最优调度可以用数值方法计算，而在稳态情况下，在二次损失函数和绝对值损失函数下，对于服务时间呈指数分布的情况，最优调度可以用封闭形式计算。我们的发现用一些数值例子来说明；这些还解决了瞬态调度收敛到相应的稳态调度的速度。
In service systems, in order to balance the server’s idle times and the customers’ waiting times, one may fix the arrival times of the customers beforehand in an appointment schedule. We propose a procedure for determining appointment schedules in such a D/G/1-type of system by sequentially minimizing the per-customer expected loss. Our approach provides schedules for any convex loss function; for the practically relevant cases of the quadratic and absolute value loss functions appealing closed-form results are derived. Importantly, our approach does not impose any conditions on the service time distribution; it is even allowed that the customers’ service times have different distributions.A next question that we address concerns theorderof the customers. We develop a criterion that yields the optimal order in case the service time distributions belong to a scale family, such as the exponential family. The customers should be scheduled then in non-decreasing order of their scale parameter.While the optimal schedule can be computed numerically under quite general circumstances, in steady-state it can be computed in closed form for exponentially distributed service times under the quadratic and absolute value loss function. Our findings are illustrated by a number of numerical examples; these also address how fast the transient schedule converges to the corresponding steady-state schedule.