Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups

In this paper, we consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Previous beam search implementations use fixed beam and filter widths. We consider the usual fixed width algorithms, and develop new versions that use variable beam and filter widths. The computational results show that the beam search versions with a variable width are marginally superior to their fixed value counterparts, even when a lower average number of beam and filter nodes is used. The best results are given by the recovering beam search algorithms. For large problems, however, these procedures require excessive computation times. The priority beam search algorithms are much faster, and can therefore be used for the largest instances. Scope and purpose: We consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. In the current competitive environment, it is important that companies meet the shipping dates, as failure to do so can result in a significant loss of goodwill. The weighted tardiness criterion is a standard way of measuring compliance with the due dates. Also, the importance of sequence-dependent setups in practical applications has been established in several studies. In this paper, we present several heuristics based on the beam search technique. In previous beam search implementations, fixed beam and filter widths have been used. We consider the usual fixed width algorithms, and also develop new versions with variable beam and filter widths. The computational tests show that the beam search versions with a variable width are marginally superior to their fixed value counterparts. The recovering beam search procedures are the heuristic of choice for small and medium size instances, but require excessive computation times for large problems. The priority beam search algorithm is the fastest of the beam search heuristics, and can be used for the largest instances.