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In this paper we consider a total penalty for the n job, one machine scheduling problem in which all jobs have a common due date. This penalty function is based on the due date value and on the earliness or the lateness of each job in the selected sequence. The main objective is to determine the optimal value of this due date and an optimal sequence to minimize a total penalty function. We prove that the optimal due date result can be generalized to the parallel machine problem. The problem ofdoi:10.18052/www.scipress.com/bsmass.1.6 fatcat:satlunbcmfdcbhiikpgbmyrlnm