Dispatching heuristics for the single machine early/tardy scheduling problem with job-independent penalties

Abstract

In this paper, we consider the single machine earliness/tardiness scheduling problem with job-independent penalties, and no machine idle time. Several dispatching heuristics are proposed, and their performance is analysed on a wide range of instances. The heuristics include simple scheduling rules, as well as a procedure that takes advantage of the strengths of each of those rules. We also consider early/tardy dispatching procedures, and a heuristic method based on existing adjacent precedence conditions. An improvement procedure that can be used to improve the schedules generated by the heuristics is also proposed.The computational tests show that the best results are given by the early/tardy dispatching rules. These heuristics are also quite fast, and are capable of quickly solving even very large instances. The use of the improvement procedure is recommended, since it improves the solution quality, with little additional computational effort.

Beam search heuristics for the single machine early/tardy scheduling problem with no machine idle time

“…Three alternative dispatching heuristics were considered, in order to analyse the effect of using different rules on the performance of the beam search algorithms. These three heuristics are the EDD, LES_AS and LINET_vk dispatching rules analysed in Valente (2007). The EDD rule is not only quite well-known, but also widely used in practice for problems with due dates.…”

“…The LES_AS heuristic combines the EDD rule with two other simple and commonly used heuristics, and provides a significant improvement over these simpler rules. The LINET_vk heuristic was the best-performing of all the dispatching rules considered in Valente (2007). Therefore, we considered three versions (corresponding to these three rules) for each type of beam search procedure.…”

“…The lower bound of the node is then set equal to the sum of the cost of the existing partial schedule and the lower bound for the unscheduled jobs. Finally, for the recovering phase we used the improvement procedure proposed in Valente (2007). This procedure uses the dominance conditions developed by Szwarc (1993), in order to generate a sequence that cannot be further improved through adjacent swaps.…”

“…The objective is then to find a schedule that minimizes the sum of weighted earliness and weighted tardiness costs P n j¼1 ðhE j þ wT j Þ, subject to the constraint that no machine idle time is allowed. This problem has been previously considered by Szwarc (1993), Azizoglu, Kondakci, and Kirca (1991) and Valente (2007). Szwarc (1993) developed time-dependent precedence relations that hold for adjacent jobs in an optimal schedule, and presented a branching scheme based on these adjacent ordering conditions.…”

“…They proposed a lower bounding procedure, as well as a branch-and-bound algorithm. Valente (2007) presented and analysed several dispatching heuristics, and also proposed an improvement procedure that incorporates Szwarc's adjacent ordering conditions.…”