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

Abstract

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 $$O(n^3)$$ 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 $$O(n^3/\epsilon )$$ time. $$\mathcal {NP}$$ -hardness proof is proved for a very special case and fast FPTASes with $$O(n^2/\epsilon )$$ running time are identified for two special cases.