'Strong'-'weak' precedence in scheduling: Extensions to series-parallel orders

Authors:
Moshe Dror;George Steiner
Affiliations:
MIS, Eller College of Management, The University of Arizona, Tucson, AZ 85721, United States;Operations Management, DeGroote School of Business, McMaster University, Hamilton, ON, Canada L8S 4M4
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

We examine computational complexity implications for scheduling problems with job precedence relations with respect to strong precedence versus weak precedence. We propose a consistent definition of strong precedence for chains, trees, and series-parallel orders. Using modular decomposition for partially ordered sets (posets), we restate and extend past complexity results for chains and trees as summarized in Dror (1997) [5]. Moreover, for series-parallel posets we establish new computational complexity results for strong precedence constraints for single- and multi-machine problems.