On Preference Orders for Sequencing Problems Or, What Hath Smith Wrought?
When in 1956 W. E. Smith proposed the ratio rule for solving the unconstrained weighted completion time problem, he suggested an abstraction in the form of a preference order. Over the years, the concept of a preference order has been much elaborated. It is now applied to abstract problems in optimal sequencing, with general precedence constraints being dealt with by the technique of modular decomposition. This paper provides a unified and self contained exposition of these results, with some new material on the treatment of contiguity constraints.
KeywordsInternal Node Precedence Constraint Preference Order Decomposition Tree Parallel Component
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