Complexity Results for Single-Machine Problems with Positive Finish-Start Time-Lags

In a single-machine problem with time-lags a set of jobs has to be processed on a single machine in such a way that certain timing restrictions between the finishing and starting times of the jobs are satisfied and a given objective function is minimized. We consider the case of positive finish-start time-lags which mean that between the finishing time of job i and the starting time of job j the minimal distance has to be respected. New complexity results are derived for single-machine problems with constant positive time-lags which also lead to new results for flow-shop problems with unit processing times and job precedences. Received: May 13, 1998; revised November 23, 1998