Discrete Time Analysis of Consolidated Transport Processes

Diese Arbeit beschäftigt sich mit der Entwicklung zeitdiskreter Modelle zur Analyse von Transportbündelungen. Mit den entwickelten Modellen für Bestands- und Fahrzeugbündelungen, insbesondere Milkrun-Systeme, kann eine detaillierte Leistungsbewertung in kurzer Zeit durchgeführt werden. Darüber hinaus erlauben die Modelle die Analyse der Umschlagslagerbündelungen, beispielweise Hub-und-Spoke-Netzwerke, indem sie im Rahmen einer Netzwerkanalyse mit einander verknüpft werden

Lévy-driven polling systems and continuous-state branching processes

In this paper we consider a ring of N = 1 queues served by a single server in a cyclic order. After having served a queue (according to a service discipline that may vary from queue to queue), there is a switch-over period and then the server serves the next queue and so forth. This model is known in the literature as a polling model. Each of the queues is fed by a non-decreasing Lévy process, which can be different during each of the consecutive periods within the server's cycle. The N-dimensional Lévy processes obtained in this fashion are described by their (joint) Laplace exponent, thus allowing for non-independent input streams. For such a system we derive the steady-state distribution of the joint workload at embedded epochs, i.e. polling and switching instants. Using the Kella-Whitt martingale, we also derive the steady-state distribution at an arbitrary epoch. Our analysis heavily relies on establishing a link between fluid (Lévy input) polling systems and multi-type Jirina processes (continuous-state discrete-time branching processes). This is done by properly defining the notion of the branching property for a discipline, which can be traced back to Fuhrmann and Resing. This definition is broad enough to contain the most important service disciplines, like exhaustive and gated

Stochastic Modelling and Analysis of Warehouse Operations

This thesis has studied stochastic models and analysis of warehouse operations. After an overview of stochastic research in warehouse operations, we explore the following topics. Firstly, we search optimal batch sizes in a parallel-aisle warehouse with online order arrivals. We employ a sample path optimization and perturbation analysis algorithm to search the optimal batch size for a warehousing service provider, and a central finite difference algorithm to search the optimal batch sizes from the perspectives of customers and total systems. Secondly, we research a polling-based dynamic order picking system for online retailers. We build models to describe and analyze such systems via stochastic polling theory, find closed-form expressions for the order line waiting times, and apply polling-based picking to online retailers. We then present closed-form analytic expressions for pick rates of order picking bucket brigades systems in differe