Abstract
In this paper, we present an approach to weighted tardiness job-shop scheduling problems (JSP) using a graph decomposition technique. Our method decomposes a JSP into a series of sub-problems by solving a variant of the generalized assignment problem which we term "VAP". Given a specified assignment cost, VAP assigns operations to mutually exclusive and exhaustive subsets, identifying a partially specified schedule, Compared to a conventional, completely specified schedule, this partial schedule is more robust to shop disturbances, and therefore more useful for planning and control. We have developed assignment heuristics which iteratively update the problem parameters using lower and upper bounds computed from the corresponding schedule. The heuristics are tested on standard test problems. We show that the proposed approach provides a means for extending traditional scheduling capabilities to a much wider spectrum of shop conditions and production scenarios.
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