Abstract
This paper considers the problem of scheduling jobs in a permutation flow shop with the objective of minimizing total earliness and tardiness. Unforced idle time is considered in order to reduce the earliness of jobs. It is shown how unforced idle time can be inserted on the final machine. Several dispatching heuristics that have been used for the problem without unforced idle time were modified and tested. Several procedures were also developed that conduct a second pass to develop a sequence using dispatching rules. These procedures were also tested and were found to result in better solutions.

Abstract
The two-machine permutation flow shop scheduling problem with the objective of minimizing total earliness and tardiness is addressed. Unforced idle time can be used to complete jobs closer to their due dates. It is shown that unforced idle time only needs to be considered on the second machine. This result is then used to extend a lower bound and dominance conditions for the single-machine problem to the two-machine permutation flow shop problem. Two branch-and-bound algorithms are developed for the problem utilizing the lower bound and dominance conditions. The algorithms are tested using instances that represent a wide variety of conditions.

Abstract
This paper considers the problem of scheduling jobs in a no-wait flow shop with the objective of minimizing total earliness and tardiness. An exact branch-and-bound algorithm is developed for the problem. Several dispatching heuristics used previously for other environments and two new heuristics were tested under a variety of conditions. It was found that one of the new heuristics consistently performed well compared to the others. An insertion search improvement procedure with speed up methods based on the structure of the problem was proposed and was found to deliver much improved solutions in a reasonable amount of time.

Abstract
This paper addresses a permutation flowshop scheduling problem, with the objective of minimizing total weighted squared tardiness. The focus is on providing efficient procedures that can quickly solve medium or even large instances. Within this context, we first present multiple dispatching heuristics. These include general rules suited to various due date-related environments, heuristics developed for the problem with a linear objective function, and procedures that are suitably adapted to take the squared objective into account. Then, we describe several improvement procedures, which use one or more of three techniques. These procedures are used to improve the solution obtained by the best dispatching rule. Computational results show that the quadratic rules greatly outperform the linear counterparts, and that one of the quadratic rules is the overall best performing dispatching heuristic. The computational tests also show that all procedures significantly improve upon the initial solution. The non-dominated procedures, when considering both solution quality and runtime, are identified. The best dispatching rule, and two of the non-dominated improvement procedures, are quite efficient, and can be applied to even very large-sized problems. The remaining non-dominated improvement method can provide somewhat higher quality solutions, but it may need excessive time for extremely large instances.

Abstract
In this paper, we consider a permutation flowshop problem, with a weighted squared tardiness objective function, which addresses an important criterion for many customers. Our objective is to find metaheuristics that can, within acceptable computational times, provide sizeable improvements in solution quality over the best existing procedure (a dispatching rule followed by an improvement method). We consider four metaheuristics, namely iterated local search (ILS), iterated greedy (IG), variable greedy (VG) and steady-state genetic algorithms (SSGA). These are known for performing well on permutation flowshops and/or on tardiness criteria. For each metaheuristic, four versions are developed, differing on the choice of initial sequence and/or local search. Additionally, four different time limits are considered. Therefore, a total of 64 sets of results are obtained. The results show that all procedures greatly outperform the best existing method. The IG procedures provide the best results, followed by the SSGA procedures. The VG methods are usually inferior to SSGA, while the ILS metaheuristics tend to be the worst performers. The four metaheuristics prove to be robust in what regards initial solution and local search method, since both have little effect on the performance of the metaheuristics. Increasing the time limit does improve the performance of all procedures. Still, a sizeable improvement is obtained even for the lowest time limit. Therefore, even under restrictive time limits, the metaheuristics greatly outperform the best existing procedure.

Abstract
Scheduling jobs in a no-wait flow shop with the objective of minimising total earliness and tardiness is the problem addressed in this paper. Idle time may be needed on the first machine due to the no-wait restriction. A model is developed that shows additional idle can be inserted on the first machine to help reduce earliness. Several dispatching heuristics previously used in other environments were modified and tested. A two-phased procedure was also developed, estimating additional idle in the first phase, and applying dispatching heuristics in the second phase. Several versions of an insertion improvement procedure were also developed. The procedures are tested on instances of various sizes and due date tightness and range. The results show the two-phase heuristics are more effective than the simple rules, and the insertion search improvement procedure can provide considerable improvements.