The batch scheduling of unrelated parallel machine is discussed by Kim et al., (2003) and their objective is to minimize the total weighted tardiness of jobs. Liaw et al., (2003) conducted research on finding a schedule for a single machine total weighted tardiness problem with sequence dependent setup times. They conducted computational experiments on benchmark problems to check how well the proposed heuristics are working. Similarly, Lin and Ying (2007) conducted research on the same problem and showed metaheuristics find upper bound values for benchmark problems. The Single machine scheduling problem is not restricted to a single machine but also a group of machines can also be considered as single machine.
2.2. Dispatching rules
The earliest weighted due date (EWDD) rule and shortest weighted processing time (SWPT) rules are used by Kim et al., (2003) but they concluded these rules are not as good as other heuristics as they concentrate on job scheduling but not the job level sequencing. Two-level batch scheduling heuristic (TH) yielded didnt perform well when the job size increases. In construction phase of a heuristic all the dispatching rules are used to provide an initial solution. For a single machine total weighted tardiness problem with sequence dependent setup times, the apparent tardiness cost with setups (ATCS) is the best construction heuristic (Liaw et al., 2003). There are two rules which are easy to apply for minimizing our problem such as EDD and SPT rules (Lin and Ying, 2007). If all the jobs are tardy the SPT rule is the best whereas, if there is only one tardy job the EDD rule holds good to minimize the total tardiness.
Kim et al., (2003) said, Metaheuristics are used to solve complicated combinatorial problems. In their research, Simulated Annealing algorithm (SA) outperformed all the search heuristics. Another literature by Lin and Ying (2007) shows approaches like SA, Genetic Algorithm (GA) and TABU search applied to solve SMS problems with sequence dependent setup times. The computation times using these heuristics for 60 jobs are same.
2.4. Mathematical models and exact algorithms
According to Liaw et al., (2003), mathematical models like Mixed integer models and branch and bound techniques are used by many researchers for minimizing the total tardiness on a single machine with sequence dependent setup times. Their work also shows application of Lagrange relaxation in solving similar problems with total weighted squared tardiness. They proved that the performance of branch and bound technique is good with problems up to 18jobs and 4 machines.