Control of continuum models of production systems
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.
0796: Operations research