This paper considers the problem of scheduling parallel machines for split jobs to minimize the total tardiness. Accepting a new job, each machine needs to be set up and the setup times depend on the sequence of jobs. To solve the above problem, a new approach is suggested and a number of theorems are provided and proved regarding resource planning and job sequencing for the given problem in hand. Then, the proposed algorithm is verified and evaluated with a number of test problems. The associated results are analyzed and compared with the results obtained by the Lingo software.
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