How the structure of precedence constraints may change the complexity class of scheduling problems

This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. We also show that there still are many very exciting challenges in this research area

Scheduling identical jobs with chain precedence constraints on two uniform machines

The problem of scheduling identical jobs with chain precedence constraints on two uniform machines is considered. It is shown that the corresponding makespan problem can be solved in linear time