Local search algorithms for a single-machine scheduling problem with positive and negative time-lags

Positive and negative time-lags are general timing restrictions between the starting times of jobs which have been introduced in connection with the Metra potential method. Although very powerful, these relations have been considered only seldom in the literature since already for a single machine problem with positive and negative time-lags the problem of finding a feasible solution is ${\cal NP}$-complete. In this paper a local search approach for a single-machine scheduling problem with positive and negative time-lags and the objective to minimize the makespan is presented. Since the existence of a feasible initial solution for starting the search cannot be guaranteed, unfeasible solutions are incorporated into the search process. Computational results based on instances resulting from shop problems are reported.