New Precedence Theorems for One-Machine Weighted Tardiness

New Precedence Theorems for One-Machine Weighted Tardiness

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Article ID: iaor200954125
Country: United States
Volume: 32
Issue: 3
Start Page Number: 579
End Page Number: 588
Publication Date: Aug 2007
Journal: Mathematics of Operations Research
Authors:
Abstract:

In an earlier paper by Emmons (1969), the problem of sequencing jobs on a single machine in order to minimize total tardiness was analyzed. Emmons provided three theorems for specifying precedence relations for pairs of jobs. His theorems apply when the tardiness penalty for each job grows at the same rate. Rinnooy Kan et al. (1975) later extended Emmons's theorems to the case when job tardiness penalties can grow at different rates for different jobs. Provided here is a set of theorems, stronger than those of Rinnooy Kan et al., that more fully exploits the special properties of the weighted tardiness function, allowing for greater reduction of the solution space.

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