MINIMIZING WEIGHTED NUMBER OF TARDY JOBS AND WEIGHTED EARLINESS TARDINESS PENALTIES ABOUT A COMMON DUE DATE

We consider the n-job, non-preemptive, single-machine scheduling problem of minimizing the weighted sum of tardy jobs and earliness-tardiness penalties about a common due date. We study the case of job-dependent penalties under a certain condition on the radio of processing times and weights. Two instances of the problem, one when the due date is a decision variable and the other when the due date is given parameter, are considered. We provide dynamic programming algorithms to solve both instances. For the special case when the weights are independent of jobs, we propose more efficient algorithms.