Single machine scheduling to minimize total weighted late work

In the problem of scheduling a single machine to minimize total late work, there are 'n' jobs to be processed, each of which has an integer procesing time and in integer due date. The objective is to find a sequence of jobs which minimizes the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. The non-preemptive total late work problem is shown to be NP-hard, although efficient algorithms are derived for the special cases in which all processing times are equal and in which all due dates are equal. A pseudopolynomial dynamic programming algorithm is presented for the general non-preemptive total late work problem. Computational results for problems with up to 10000 jobs are given.

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http://flora.insead.edu/fichiersti_wp/inseadwp1992/92-29.pdf

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