Stochastic dynamic job shops and hierarchical production planning
Sethi, S.; Xun Yu Zhou
Automatic Control, IEEE Transactions on
Volume 39, Issue 10, Oct 1994 Page(s):2061 - 2076
Digital Object Identifier 10.1109/9.328820
Summary:This paper presents an asymptotic analysis of hierarchical
production planning in a general manufacturing system consisting of a
network of unreliable machines producing a variety of products. The
concept of a dynamic job shop is introduced by interpreting the system
as a directed graph, and the structure of the system dynamics is
characterized for its use in the asymptotic analysis. The optimal
control problem for the system is a state-constrained problem, since the
number of parts in any buffer between any two machines must remain
nonnegative. A limiting problem is introduced in which the stochastic
machine capacities are replaced by corresponding equilibrium mean
capacities, as the rate of change in machine states approaches infinity.
The value function of the original problem is shown to converge to that
of the limiting problem, and the convergence rate is obtained.
Furthermore, near-optimal controls for the original problem are
constructed from near-optimal controls of the limiting problem, and an
error estimate is obtained on the near optimality of the constructed
controls
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