‘Strong’–‘weak’ precedence in scheduling: Extensions to series–parallel orders

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.