Abstract/Details

Control of continuum models of production systems


2008 2008

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Abstract (summary)

Semiconductor factories are extremely complicated, with many machines exhibiting stochastic behavior, a large number of items, and hundreds of processing steps. This complexity causes difficulty when applying previous mathematical modeling approaches of control of production systems to semiconductor factories. In response, a continuum model consisting of a first order conservative hyperbolic partial differential equation with a non-local load-dependent velocity has been introduced that realistically describes the behavior of a semiconductor factory or other large, complex, and highly re-entrant production systems. Two different control problems are proposed, one in which a demand rate target is tracked by the outflux and another where the backlog is minimized, both through regulation of the influx and hence the load. The influx control is determined through the use of the adjoint method, an infinite dimensional constrained optimization technique that employs adjoint calculus to determine the gradient of a reduced cost functional with respect to the control. The cost functional and the gradient are then employed in a nonlinear conjugate gradient descent method to obtain a locally optimal control. The experiments ran show properties inherent to production systems and their ability to react to changes in demand, as well as the effect of influx capacity on factory operation. A description of the implementation of the technique to real-world semiconductor factories as well as to addressing open theoretical problems and possible future research areas is given.

Indexing (details)


Subject
Mathematics;
Operations research
Classification
0405: Mathematics
0796: Operations research
Identifier / keyword
Applied sciences; Pure sciences; Influx control; Production systems
Title
Control of continuum models of production systems
Author
La Marca, Michael
Number of pages
114
Publication year
2008
Degree date
2008
School code
0010
Source
DAI-B 69/06, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549679172
University/institution
Arizona State University
University location
United States -- Arizona
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3318434
ProQuest document ID
304685867
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304685867
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