Complexity of single machine, multi-criteria scheduling problems

The authors examine the complexity of scheduling problems when more than one measure of performance is appropriate. The criteria they study are maximal tardiness, flowtime, number of tardy jobs, tardiness and the weighted counterparts of the last three measures. The machine environment is restricted to a single machine. Complexity results are given for secondary criterion, bicriteria and weighted criteria approaches for all combinations of measures. Of the problems examined, only six remain open.