Complexity results for single-machine problems with positive finish-start time-lags

Abstract

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 l(ij) which mean that between the finishing time of job i and the starting time of job j the minimal distance l(ij) has to be respected. New complexity results are derived for single-machine problems with constant positive time-lags l(ij) = l which also lead to new results for Bow-shop problems with unit processing times and job precedences.