Common due-date assignment problems with fixed-plus-linear earliness and tardiness costs

We study single machine scheduling and common due-date assignment problems. The cost considered is fixed plus linear, i.e., jobs are penalized by two cost components: (i) a variable cost which is proportional to their earliness/tardiness values, (ii) a fixed cost which is independent of their actual earliness/tardiness values. For the general version of this problem, three heuristics are introduced and tested. We also study a number of modifications and special cases. We focus first on the special case of identical job processing times. Both versions of minsum and minmax are shown to have a polynomial time solution, even with the additional option of job rejection. Another special case of variable earliness cost and fixed tardiness cost is also studied. For this NP-hard problem, a pseudo-polynomial dynamic programming algorithm is introduced and tested. An extension to the case of bounded rejection cost, and a modified version with an additional bound on the total tardiness cost, are also studied. The solution algorithms for these problems are tested numerically as well. The last studied problem is that of job-independent cost components. This version, which generalizes the first and most cited due-date assignment model, is shown to have a polynomial time solution.