Performance analysis and capacity planning for stochastic systems with cut-off service levels

更新提案中描述的研究项目旨在调查不同的截止服务水平定义对产能规划的影响，特别是对劳动力需求规划和轮班调度的影响。这些服务级别定义通常在工业中使用。它们定义了截止时间和截止日期，在截止时间之前收到的所有订单都必须完成处理。与传统服务水平相比，截断服务水平定义中的结构性差异阻碍了有关最佳能力的见解的转移。因此，必须开发新的容量规划方法。因此，整体目标是识别和解释系统参数（例如可用的处理能力）对可达到的截止服务水平的影响。这使我们能够深入了解切断服务水平对劳动力需求和轮班安排的影响。为此目的，将发展随机、时变、单阶段和多阶段系统的性能分析方法。离散时间排队网络将用于性能分析。对于适当的特殊情况，可以通过分析得出结构见解。它们是为确定性代理模型和单周期随机模型导出的。我们通过使用截止服务水平开发劳动力需求计划和轮班调度的新方法。之前获得的结构发现将作为解决方法的边界。然后，单阶段的结果将根据当前项目的结果扩展到多级系统。

The research project described in the renewal proposal is intended to investigate the influence of different cut-off service level definitions on capacity planning, in particular on workforce requirement planning and shift scheduling. These service level definitions are commonly used in industry. They define a cut-off time and a deadline by which all orders received by the cut-off time have to be completely processed. The structural differences in the definition of a cut-off service level compared to traditional service levels prevents the transfer of insights with regard to optimal capacities. Therefore, new methods for capacity planning have to be developed. The overall objective is therefore to identify and explain the influences of system parameters, e.g. the processing capacity available, on the achievable cut-off service level. This enables insights into the effects of cut-off service levels on workforce requirements and shift scheduling. For this purpose, performance analysis methods for stochastic, time-dependent, single-stage and multi-stage systems are to be developed. Discrete-time queueing networks will be used for the performance analysis. For appropriate special cases, structural insights are to be derived analytically. They are derived for deterministic surrogate models and single-period stochastic models. We develop new approaches for workforce requirement planning and shift scheduling by using a cut-off service level. The structural findings gained before will serve as bounds in the solution approaches. The single stage results will then be extended to multi-level systems, based on the results of the current project.