Workshop
Mathematical modeling of transport and production logistics
Mathematical modeling of transport and production logistics
Dieter Armbruster, Arizona State University, USA
Production systems in Biology: Simulating molecular pathways
Abstract:
We are using production systems methods for the analysis of molecular biological pathways. Such pathways typically comprise a sequence of enzymes that act as machines, each converting a stream of input molecules into a stream of output molecules. Such systems have many common features with factories, and networks of molecular pathways have common functions with supply chains. We will illustrate our approach for Glycolysis and a signalling pathway.
Reik Donner, Technische Universität Dresden, Germany
Local and Global Dynamics of Production and Supply Networks under Mixed Production Strategies
Reik Donner1, Johannes Höfener1,2, Kathrin Padberg1, Stefan Lämmer1, Dirk Helbing3
1 TU Dresden, Andreas-Schubert-Str. 23, 01062 Dresden, Germany
2 MPI for Dynamics of Complex Systems, Nötznitzer Str. 38, 01187 Dresden, Germany
3 ETH Zürich, Universitätstr. 41, 8092 Zürich, Switzerland
Abstract:
The analysis and control of dynamic material flows in traffic, production, and logistics is a subject of contemporary interest. In this contribution, we introduce a generalised input-output model of commodity flows that allows to study the dynamics of production and supply networks under different production strategies. It is demonstrated that production units subjected to a temporally varying demand and/or supply show an amplification of these variations for both push and pull strategies. Using an extended linear stability analysis, we identify under which conditions a consideration of mixed push-pull strategies leads to a suppression of these effects. Our corresponding results have important implications for the strategic planning and control of manufacturing networks.
Simone Goetlich, Technische Universität Kaiserslautern, Germany
Optimization Techniques For Supply Network Models
Abstract:
In this talk, we introduce an optimization problem based on recently established continuous equations for supply networks. We show that for particular discretizations the resulting problem is in fact a MIP. We present presolve techniques inspired by the continuous dynamics to reduce the computational effort. Furthermore, we show that under certain conditions on the objective functional the MIP is in fact equivalent to a linear programming problem.
Marco Laumanns, ETH Zurich, Switzerland
Computing the value of transshipment flexibility in distribution networks
Abstract:
Lateral stock transshipments might lead to cost savings by effectively sharing inventory on the same echelon level. We present an approach to quantify the value of this additional flexibility by determining the optimal control policies, and the resulting cost, in supply networks with transshipments under uncertain demand. The minimum guaranteed cost reduction compared to the base case without transshipment can then be used as a lower bound for the value of this flexibility option.
This is joint work with F. Cassim, J. Chastenet and J. Uffer (EPF Lausanne) and M. Reimann (Warwick Business School)
Erjen Lefeber, Technische Universiteit Eindhoven, Netherlands
Controller design for flow networks of switched servers with setup times: the Kumar-Seidman case as an illustrative example
Abstract:
In this talk we consider the control of a reentrant manufacturing system with setup times, as introduced by Kumar and Seidman. In most literature on control of a network of servers with setup times, first a policy is introduced and then the resulting network behavior is analyzed. In manufacturing systems the network typically is fixed and given a priori. Furthermore, optimal steady state behavior is desired. Therefore, this talk follows a different approach. First optimal steady state network behavior is determined, then a feedback controller is presented which makes the network converge towards this desired steady state behavior. The resulting controller is a non-distributed controller: each server needs global state information. For a manufacturing system this is not a problem, since global information typically is available. Finally it is shown that also a distributed controller (each server needs only local state information) can be used to achieve the same result.
Karsten Peters, Technische Universität Dresden, Germany
Dynamics in Logistics Networks - Stochastic vs. Deterministic Approaches
Abstract:
Logistics networks are complex networks of nonlinear dynamical elements, designed to fulfill certain functional requirements. Due to intrinsic rules and external disturbances these material flow networks show a rich variety of dynamical behaviour. In particular for delivery or supply networks phenomena like the bullwhip effect have been described. For analysis stochastic as well as different deterministic models are used. We investigate the dynamical phenomena in different networks and give some new results on the influence of topological features on the dynamics. Furthermore we adress the question how the theoretical models can be linked to practical requirements in the organization of logistics processes. The results can be used to optimize the structure of the material and information flow networks in order to obtain more reliable, stable and robust supply networks.
Alexander Pogromsky,Technische Universiteit Eindhoven, Netherlands
An anti-windup control of manufacturing lines: performance analysis
Abstract:
The talk focuses on a tracking control problem for manufacturing lines. The control problem is to change the production speed for each workstation so that the cumulative output of the line follows the fluctuating market demand with an acceptable accuracy. It turns out that one of the main obstacles to achieve this control goal is the saturation-like nonlinearity in the model, that reflects the fact that the production speed is nonnegative and cannot exceed some threshold value. To overcome this difficulty an anti-windup controller is proposed. It can be proven that for a certain class of the market fluctuations this controller guarantee that the closed loop system is convergent, i.e. after some transient time all solutions converge to a unique limit solution that depends only on the input of the system. This property allows to analyse the performance of the system. Due to marginal stability of the open loop system and saturation nonlinearity in the feedback, classical approaches to characterize the system performance in terms of L2 (Lp) gain based on either quadratic or Popov Lyapunov functions cannot be applied. It is proposed to analyse the performance of the closed loop system under harmonic market fluctuation via the describing function approach (harmonic linearization). To make this approach rigorous conditions that allow to estimate the accuracy of the describing functions method were derived. To apply the derived controller for a line with several workstations one has to guarantee that a cascade of the convergent system is convergent. The corresponding theorem is proven and the theoretical results are demonstrated via computer simulation for a discretized in time discrete-event model.
Mykhaylo Postan, Odessa National Maritime University, Ukraine
Optimal Preemptive Resume Priorities for Repair of Unreliable Machines in Two-Phase Production System
Abstract:
Two-phase production system with unreliable and renewable machines in parallel at both phases is considered. The Poisson flow of parts arrives at first phase, and total number of parts at both phases is restricted by number N. Processing times of parts at i-th phase is exponentially distributed random variable with mean 1/mu_i , i=1,2. The life-time of any machine at i-th phase and its repair-time at repair shop are mutually independent and exponentially distributed random variables with the means 1/ai and 1/bi correspondingly. It is assumed that only one machine may be under repair at arbitrary moment of time. The problem of optimal preemptive resume priority rule finding is studied for process of failured machines renewal at repair shop. For calculation of the state-probabilities of corresponding Markov process the combination of asymptotic expansion in a power series and matrix algorithm is proposed.
This is a joint work with Sergey Dashkovskiy (University of Bremen)
Oliver Rose, Technische Universität Dresden, Germany
Improving the accuracy of simple simulation models for complex production systems
Abstract:
Semiconductor wafer fabrication facilities (wafer fabs) are among the most complex production facilities. A large product variety, hundreds of processing steps per product, hundreds of machines of different types, and automated transport lead to a system complexity which is hard to understand and hard to handle. For educating planners and developing adequate material flow control mechanisms, simple models for this complex environment are required. We present new modeling approaches which lead to rather accurate cycletime-over-utilization curves and provide good cycle time distribution estimates for semiconductor fabs.
Evgeny Spodarev, Universität Ulm, Germany
Modelling, simulation and prediction of city road traffic
Abstract:
In this talk, the problem of the prediction of traffic velocities and travel times in large urban regions is considered. The data is given by the GPS positions of test vehicles (taxis in Berlin) observed over a large period of time (two years). It is shown how the methods of stochastic geometry and spatial statistics can be applied to asses, model and simulate the traffic trajectories of the test vehicles. From these trajectories, the mean, actual and future velocity maps of the downtown of Berlin are constructed. This enables the calculation of the shortest or fastest travel routes by means of ant algorithms as well as the prediction of the traffic state up to 20 min. into the future. This research project was supported by and carried out in cooperation with the Institute of Transport Research, German Aerospace Center, Berlin.
This is joint work with Hans Braxmeier and Volker Schmidt from Ulm University