Scheduling with common due date assignment to minimize generalized weighted earliness-tardiness penalties

We investigate a single-machine common due date assignment scheduling problem with the objective of minimizing the generalized weighted earliness/tardiness penalties. The earliness/tardiness penalty includes not only a variable cost which depends upon the job earliness/tardiness but also a fixed cost for each early/tardy job. We provide an O(n3) time algorithm for the case where all jobs have equal processing times. Under the agreeable ratio condition, we solve the problem by formulating a series of half-product problems, which permits us to devise a fully polynomial-time approximation scheme with O(n3/ similar to) time. NP-hardness proof is proved for a very special case and fast FPTASes with O(n2/ similar to) running time are identified for two special cases.