Single machine scheduling with a common delivery window

In this paper we consider the single machine scheduling problem of minimizing the mean absolute deviation (MAD) of job completion times from a restricted common delivery window. This problem is NP- hard. A Lagrangian relaxation procedure is proposed to solve the problem. Two efficient heuristics are also proposed. An experimental study on randomly generated problems is carried out to test the performance of the proposed methods. The computational results show that the obtained lower bounds are very good and the proposed heuristics generate near-optimal solutions.