Integrating Combinatorial Scheduling with Inventory Management and Queueing Theory
Keywords: scheduling
inventory management
queueing theory
dynamic scheduling
combinatorial scheduling
scheduling in supply chains
assembly scheduling
scheduling with inventory constraints
stability
stability of periodic scheduling
performance guarantees for scheduling algorithms
integration of queueing and scheduling
integration of scheduling and inventory management
short-run vs. long-run tradeoff
queueing/scheduling hybrid
polling system with flow-shop server
queueing/scheduling algorithm
characteristics of scheduling problems
real-world scheduling problems
polling system
makespan minimization
periodic scheduling
scheduling and related decision-making
dynamic flow shop
inventory availability
flow shop

The central thesis of this dissertation is that by combining classical scheduling methodologies with those of inventory management and queueing theory we can better model, understand and solve complex real-world scheduling problems. In part II of this dissertation, we provide models of a realistic supply chain scheduling problem that capture both its combinatorial nature and its dependence on inventory availability. We present an extensive empirical evaluation of how well implementations of these models in commercially available software solve the problem. We are therefore able to address, within a specific problem, the need for scheduling to take into account related decision-making processes. In order to simultaneously deal with combinatorial and dynamic properties of real scheduling problems, in part III we propose to integrate queueing theory and deterministic scheduling. Firstly, by reviewing the queueing theory literature that deals with dynamic resource allocation and sequencing and outlining numerous future work directions, we build a strong foundation for the investigation of the integration of queueing theory and scheduling. Subsequently, we demonstrate that integration can take place on three levels: conceptual, theoretical and algorithmic. At the conceptual level, we combine concepts, ideas and problem settings from the two areas, showing that such combinations provide insights into the trade-off between long-run and short-run objectives. Next, we show that theoretical integration of queueing and scheduling can lead to long-run performance guarantees for scheduling algorithms that have previously been proved only for queueing policies. In particular, we are the first to prove, in two flow shop environments, the stability of a scheduling method that is based on the traditional scheduling literature and utilizes processing time information to make sequencing decisions. Finally, to address the algorithmic level of integration, we present, in an extensive future work chapter, one general approach for creating hybrid queueing/scheduling algorithms. To our knowledge, this dissertation is the first work that builds a framework for integrating queueing theory and scheduling. Motivated by characteristics of real problems, this dissertation takes a step toward extending scheduling research beyond traditional assumptions and addressing more realistic scheduling problems.