Justus Arne Schwarz

Storage technologies for wind power in the Columbia River Gorge

The transition from traditional energy sources to renewable has gained popularity and acceptance in recent years. This has been driven mainly by the current level of pollution, global warming, decommission of old nuclear power plants and the increasing cost of conventional energy sources. Nevertheless, one of the many steps to overcome is the seasonality or intermittency of renewable energy sources such as wind power. In recent years, new technologies have come up to address this problem, so the energy can be stored for future purposes. This paper analyses these energy storage alternatives for a specific case in the Columbia River Gorge for wind power. A hierarchical decision model is developed with criteria including political, social, environmental, technical and economical. The main conclusions highlight that the economical and technical criteria are among the most important ones for decision-makers.

Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times

This paper is motivated by the performance evaluation of circulating vertical conveyor systems (CVCSs). CVCSs are bulk queues of transportation type. These material handling systems feature generally distributed inter-arrival times, which can be longer than the bulk service time. This leads to interdependencies between the number of arrivals in consecutive service intervals and the number of loads in the queue. We propose a new discrete-time approach for the steady-state analysis of such bulk service queues of transportation type with general arrival and service processes and finite server and limited queue capacities. The approach is based on a finite Markov chain that generates complete probability distributions for the key performance measures, including the queue length, waiting time and departing batch size. The proposed approach is exact in the cases of discrete-time slots, e.g. as in communication systems. We investigate the discretisation error that arises if the approach is used as an approximation for the continuous time using a numerical comparison to a discrete-event simulation. Moreover, we examine the impact of arrival stream variability on the system performance and compare the positive effects of a higher frequency of server visits with the effects arising from larger pickup capacities.

The buffer allocation problem in production lines: Formulations, solution methods, and instances

Abstract Flow production lines with finite buffer capacities are used in practice for mass production, e.g., in the automotive and food industries. The decision regarding the allocation of buffer capacities to mitigate throughput losses from stochastic processing times and unreliable stations is known as the Buffer Allocation Problem (BAP).  This article classifies and reviews the literature on the BAP with respect to different versions of the optimization problem. It considers the detailed characteristics of the flow lines, the objective function, and the constraints. Moreover, a new classification scheme for solution methods is presented that differentiates between explicit solutions, integrated optimization methods, and iterative optimization methods. The characteristics of test instances derived from realistic cases and test instances used in multiple references are discussed.  The review reveals gaps in the literature regarding the considered optimization problems and solution methods, especially with a view on realistic lines. In addition, a library, FlowLineLib, of realistic and already used test instances is provided.

Approximations of time-dependent unreliable flow lines with finite buffers

Flow lines process discrete workpieces on consecutive machines, which are coupled by buffers. Their operating environment is often stochastic and time-dependent. For the flow line under consideration, the stochasticity is generated by random breakdowns and successive stochastic repair times, whereas the processing times are deterministic. However, the release rate of workpieces to the line is time-dependent, due to changes in demand. The buffers between the machines may be finite or infinite. We introduce two new sampling approaches for the performance evaluation of such flow lines: one method utilizes an approximation based on a mixed-integer program in discrete time with discrete material, while the other approximation is based on partial and ordinary differential equations in continuous time and with a continuous flow of material. In addition, we sketch a proof that these two approximations are equivalent under some linearity assumptions. A computational study demonstrates the accuracy of both approximations relative to a discrete-event simulation in continuous time. Furthermore, we reveal some effects occurring in unreliable flow lines with time-dependent processing rates.

A general model for batch building processes under the timeout and capacity rules

In manufacturing systems, batch building processes are very common, as goods are often transported or processed in batches and must therefore be collected before these transport or processing steps can occur. In this paper, we present a method for the performance analysis of general batch building processes in material flow systems under the timeout and capacity rules. The proposed model allows for stochastic collecting times and incorporates no restrictions with respect to the number of arriving units and their interarrival times. The accuracy of the discrete-time approach is demonstrated by comparing this approach with a discrete-event simulation model in continuous-time. Subsequently, the model is applied to two cases: a transportation case from the health care industry and the process of building a batch for a batch processor.

Warteschlangentheorie in der Betriebswirtschaftslehre

Warteschlangensysteme werden in zahlreichen Bereichen der Betriebswirtschaftslehre zur Analyse und Planung genutzt. Die Warteschlangentheorie hat zum Ziel den Vorgang des Wartens mit mathematischen Methoden zu beschreiben und mittels Leistungsanalysen Gestaltungsrichtlinien abzuleiten. Dieser Beitrag gibt eine Übersicht zu Anwendungsgebieten, Modellierungsansätzen und Zusammenhängen auf dem Gebiet der Warteschlangentheorie.