Abstract
A semiconductor manufacturing system that involves a large number of items and many steps can be modelled through conservation laws for a continuous density variable on a production process. In this paper, the basic hyperbolic partial differential equation (PDE) models for multiple re-entrant manufacturing systems are proposed. However, through numerical examples, the basic continuum models do not perform well for small-scale multiple re-entrant systems, so a new state equation taking into account the re-entrant degree of the product is introduced to improve the basic continuum models. The applicability of the modified continuum model is illustrated through a numerical example. Based on the modified continuous model, this paper studies the optimal control problems for multiple re-entrant manufacturing systems. The gradient of the cost function with respect to the influx is solved by the adjoint approach, and then the optimal influx is computed by the steepest descent method. Finally, numerical examples on optimal influx profiles for steps in demand rate, linear demand rate and periodically varying demand rate are given. The relationships among influx, outflux and demand are also discussed in detail.
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