Discrete Time Analysis of Batch Processes in Material Flow Systems
Date: April 30, 2007
Time: 3:00 pm
Place: Dunstan 202
Marc Schleyer
Institute for Conveying Technology and Logistics
University of Karlsruhe, Germany
Abstract
Discrete Time Analysis of Batch Processes in Material Flow Systems
Information flow and physical processes in material flow systems can be modeled and evaluated by either simulation or analytical methods. It is crucial for the modeled real world application that stochastic events as demand, processing times, machine failures, scrap etc. are considered in an appropriate manner. Thus, queueing theory is the most suitable analytical tool in the literature for stochastic modeling of material flow systems. On this level, average performance measures can be derived if some basic parameters have been determined from past observations of the system. However, performance measures based on system averages are not sufficient to verify whether the requested shipping times can be met with an acceptable probability, which usually lies between 95% and 99%, possibly depending on order types.
Therefore, for the evaluation of design alternatives in respect to their ability to reach the requested sojourn time from order entry to exit, discrete time queueing models are proposed. Hence, we use models primarily developed for the evaluation of ATM (Asynchronous Transfer Mode) networks. Since there is still a lack of appropriate discrete time models for the analysis of material flow processes on the basis of general distributions, we are motivated to find new solutions for problems in this field. Especially, models for the description of batch processes are missing. Therefore, we have developed a variety of batch queueing models in the discrete time domain. The proposed models for the analysis of batch processes are: Batch building under the capacity rule, batch building under the timeout rule, batch building under the minimum batch size rule, G/G/1-queue with batch arrivals, G/G [K,K]/1-queue, G/G [L,K]/1-queue, and batch split. For each queueing system we provide methods for a detailed analysis of the waiting and departure process on the basis of discrete distributions.
In the context of our research we developed a software-solution called the "Logistic Analyzer" which is well-suited for the application to practical problems. This seminar contribution is concluded discussing advantages and disadvantages of the proposed analytical methods compared to simulation.
