Single machine scheduling with earliness-tardiness and completion time penalties

This paper considers a single machine scheduling problem with a non-restrictive common due date. The objective is to minimize the sum of earliness, tardiness and completion time penalties. For the case in which the processing time of each job is independent of its position in a schedule, we show the properties of the optimal solution and present a polynomial algorithm. Moreover, for the case where the processing time of each job is related to its position in a schedule, by calculating their positional weights, the problem can be formulated as an assignment problem in polynomial time. And a polynomial algorithm is presented.