Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Scheduling parallel machines to minimize total weighted and unweighted tardiness
Computers and Operations Research
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
Scheduling unrelated parallel machines to minimize total weighted tardiness
Computers and Operations Research
Computers and Industrial Engineering
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A branch and bound algorithm (B&B) has been widely used in various discrete and combinatorial optimization fields. To obtain optimal solutions as soon as possible for scheduling problems, three tools, which are branching, bounding and dominance rules, have been developed in the B&B algorithm. One of these tools, a branching is a method for generating subproblems and directly determines size of solution to be searched in the B&B algorithm. Therefore, it is very important to devise effective branching scheme for the problem. In this note, a survey of branching schemes is performed for parallel machines scheduling (PMS) problems with n independent jobs and m machines and new branching schemes that can be used for identical and unrelated PMS problems, respectively, are suggested. The suggested branching methods show that numbers of generated subproblems are much smaller than that of other methods developed earlier and therefore, it is expected that they help to reduce a lot of CPU time required to obtain optimal solutions in the B&B algorithm.