Dynamic Scheduling with Queueing Methods to Control Nervousness of a Batch Scheduling System

This thesis is inspired by scheduling problems arising in the manufacturing industry. Due to uncertainty regarding the future, existing schedules have to be adjusted to new information from time to time. On the one hand, each so-called rescheduling aims to optimise the resource utilisation as well as the flow time of jobs (efficiency-oriented point of view). On the other hand, deviations from the original schedule should be minimised (stability-oriented point of view) because frequent and severe schedule alterations can entail serious procedural as well as economic consequences, known as schedule nervousness in the literature. The relevance of the resulting goal conflict for real-world applications constitutes the main motivation for this research. Mathematically, we model and analyse a stochastic, multicriteria scheduling problem with the help of discrete-time queueing theory. Our focus lies on a probabilistic equilibrium analysis based on an embedded Markov chain combined with suitable transformations regarding probability generating functions. Besides giving model-specific results, the thesis at hand establishes a novel approach to combine dynamic scheduling and queueing theory.