Neighborhood search algorithm for one-machine scheduling problem with time lags

The one-machine scheduling problem with time lags while minimizing the completion time is NP-hard. The problem typically arises in a manufacturing where the next job has to be carried out in a specific time window after the completion of the immediately proceeding job. Scheduling the jobs is to find a shortest path that passes all the nodes and meets all precedence constraints and time lags constraints on AON (activity-on-node) net. A nonlinear mathematic optimization model is established based on AON net. A neighborhood search algorithm is proposed to convert the nonlinear model into a linear programming model that could be solved by standard software. Computational results prove that the proposed neighborhood search algorithm is effective.