55,542 research outputs found
Manufacturing Systems Line Balancing using Max-Plus Algebra
In today\u27s dynamic environment, particularly the manufacturing sector, the necessity of being agile, and flexible is far greater than before. Decision makers should be equipped with effective tools, methods, and information to respond to the market\u27s rapid changes. Modelling a manufacturing system provides unique insight into its behavior and allows simulating all crucial elements that have a role in the system performance. Max-Plus Algebra is a mathematical tool that can model a Discrete Event Dynamic System in the form of linear equations. Whereas Max-Plus Algebra was introduced after the 1980s, the number of studies regarding this tool and its applications is fewer than regarding Petri Nets, Automata, Markov process, Discrete Even Simulation and Queuing models. Consequently, Max-Plus Algebra needs to be applied and tested in many systems in order to explore hidden aspects of its function and capabilities. To work effectively; the production/assembly line should be balanced. Line balancing is one of the manufacturing functions that tries to divide work equally across the production flow. Car Headlight Manufacturing Line as a Discrete Manufacturing System is considered which is a combination of manufacturing and assembly lines composed of different stations. Seven system scenarios were modeled and analyzed using Max-Plus to balance the car headlights production line. Key Performance Indicators (KPIs) are used to compare the various scenarios including Cycle Time, Average Deliver Rate, Total Processing Lead Time, Stations\u27 Utilization Rate, Idle Time, Efficiency, and Financial Analysis. FlexSim simulation software is used to validate the Max-Plus models results and its advantages and drawbacks compared with Max-Plus Algebra. This study is a unique application of Max-Plus Algebra in line balancing of a manufacturing system. Moreover, the problem size of the considered model is at least twice (12 stations) that of previous studies. In the matter of complexity, seven different scenarios are developed through the combination of parallel stations and buffers. Due to that the last scenario is included four parallel stations plus two buffers Based on the findings, the superiority of scenario 7 compared to other scenarios is proved due to its lowest system delivering first output time (14 seconds), best average delivery rate (24.5 seconds), shortest cycle time (736 seconds), shortest total processing lead time (11,534 seconds), least percentage of idle time (12%), lowest unit cost ($6.9), and highest efficiency (88%). However, Scenario 4 has the best utilization rate at 75%
Perspectives on Multi-Level Dynamics
As Physics did in previous centuries, there is currently a common dream of
extracting generic laws of nature in economics, sociology, neuroscience, by
focalising the description of phenomena to a minimal set of variables and
parameters, linked together by causal equations of evolution whose structure
may reveal hidden principles. This requires a huge reduction of dimensionality
(number of degrees of freedom) and a change in the level of description. Beyond
the mere necessity of developing accurate techniques affording this reduction,
there is the question of the correspondence between the initial system and the
reduced one. In this paper, we offer a perspective towards a common framework
for discussing and understanding multi-level systems exhibiting structures at
various spatial and temporal levels. We propose a common foundation and
illustrate it with examples from different fields. We also point out the
difficulties in constructing such a general setting and its limitations
Algebras, Hawking Radiation and Information Retention by Stringy Black Holes
We have argued previously, based on the analysis of two-dimensional stringy
black holes, that information in stringy versions of four-dimensional
Schwarzschild black holes (whose singular regions are represented by
appropriate Wess-Zumino-Witten models) is retained by quantum -symmetries
when the horizon area is not preserved due to Hawking radiation. It is key that
the exactly-marginal conformal world-sheet operator representing a massless
stringy particle interacting with the black hole requires a contribution from
generators in its vertex function. The latter correspond to
delocalised, non-propagating, string excitations that guarantee the transfer of
information between the string black hole and external particles. When
infalling matter crosses the horizon, these topological states are excited via
a process: (Stringy black hole) + infalling matter (Stringy
black hole), where the black hole is viewed as a stringy state with a
specific configuration of charges that are conserved. Hawking
radiation is then the reverse process, with conservation of the
charges retaining information. The Hawking radiation spectrum near the horizon
of a Schwarzschild or Kerr black hole is specified by matrix elements of
higher-order currents that form a phase-space algebra. We show
that an appropriate gauging of this algebra preserves the horizon
two-dimensional area classically, as expected because the latter is a conserved
Noether charge.Comment: 21 pages, no figure
Patch-based Hybrid Modelling of Spatially Distributed Systems by Using Stochastic HYPE - ZebraNet as an Example
Individual-based hybrid modelling of spatially distributed systems is usually
expensive. Here, we consider a hybrid system in which mobile agents spread over
the space and interact with each other when in close proximity. An
individual-based model for this system needs to capture the spatial attributes
of every agent and monitor the interaction between each pair of them. As a
result, the cost of simulating this model grows exponentially as the number of
agents increases. For this reason, a patch-based model with more abstraction
but better scalability is advantageous. In a patch-based model, instead of
representing each agent separately, we model the agents in a patch as an
aggregation. This property significantly enhances the scalability of the model.
In this paper, we convert an individual-based model for a spatially distributed
network system for wild-life monitoring, ZebraNet, to a patch-based stochastic
HYPE model with accurate performance evaluation. We show the ease and
expressiveness of stochastic HYPE for patch-based modelling of hybrid systems.
Moreover, a mean-field analytical model is proposed as the fluid flow
approximation of the stochastic HYPE model, which can be used to investigate
the average behaviour of the modelled system over an infinite number of
simulation runs of the stochastic HYPE model.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Discrete event simulation tool for analysis of qualitative models of continuous processing systems
An artificial intelligence design and qualitative modeling tool is disclosed for creating computer models and simulating continuous activities, functions, and/or behavior using developed discrete event techniques. Conveniently, the tool is organized in four modules: library design module, model construction module, simulation module, and experimentation and analysis. The library design module supports the building of library knowledge including component classes and elements pertinent to a particular domain of continuous activities, functions, and behavior being modeled. The continuous behavior is defined discretely with respect to invocation statements, effect statements, and time delays. The functionality of the components is defined in terms of variable cluster instances, independent processes, and modes, further defined in terms of mode transition processes and mode dependent processes. Model construction utilizes the hierarchy of libraries and connects them with appropriate relations. The simulation executes a specialized initialization routine and executes events in a manner that includes selective inherency of characteristics through a time and event schema until the event queue in the simulator is emptied. The experimentation and analysis module supports analysis through the generation of appropriate log files and graphics developments and includes the ability of log file comparisons
New variational and multisymplectic formulations of the Euler-Poincar\'e equation on the Virasoro-Bott group using the inverse map
We derive a new variational principle, leading to a new momentum map and a
new multisymplectic formulation for a family of Euler--Poincar\'e equations
defined on the Virasoro-Bott group, by using the inverse map (also called
`back-to-labels' map). This family contains as special cases the well-known
Korteweg-de Vries, Camassa-Holm, and Hunter-Saxton soliton equations. In the
conclusion section, we sketch opportunities for future work that would apply
the new Clebsch momentum map with -cocycles derived here to investigate a
new type of interplay among nonlinearity, dispersion and noise.Comment: 19 page
HYPE with stochastic events
The process algebra HYPE was recently proposed as a fine-grained modelling
approach for capturing the behaviour of hybrid systems. In the original
proposal, each flow or influence affecting a variable is modelled separately
and the overall behaviour of the system then emerges as the composition of
these flows. The discrete behaviour of the system is captured by instantaneous
actions which might be urgent, taking effect as soon as some activation
condition is satisfied, or non-urgent meaning that they can tolerate some
(unknown) delay before happening. In this paper we refine the notion of
non-urgent actions, to make such actions governed by a probability
distribution. As a consequence of this we now give HYPE a semantics in terms of
Transition-Driven Stochastic Hybrid Automata, which are a subset of a general
class of stochastic processes termed Piecewise Deterministic Markov Processes.Comment: In Proceedings QAPL 2011, arXiv:1107.074
A discrete invitation to quantum filtering and feedback control
The engineering and control of devices at the quantum-mechanical level--such
as those consisting of small numbers of atoms and photons--is a delicate
business. The fundamental uncertainty that is inherently present at this scale
manifests itself in the unavoidable presence of noise, making this a novel
field of application for stochastic estimation and control theory. In this
expository paper we demonstrate estimation and feedback control of quantum
mechanical systems in what is essentially a noncommutative version of the
binomial model that is popular in mathematical finance. The model is extremely
rich and allows a full development of the theory, while remaining completely
within the setting of finite-dimensional Hilbert spaces (thus avoiding the
technical complications of the continuous theory). We introduce discretized
models of an atom in interaction with the electromagnetic field, obtain
filtering equations for photon counting and homodyne detection, and solve a
stochastic control problem using dynamic programming and Lyapunov function
methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be
found at http://minty.caltech.edu/papers.ph
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