Minimizing the Maximum Earliness-Tardiness on a Single Machine with Generalized Due-Dates

Abstract

This paper considers a single machine scheduling problem with generalized due-dates (GDD) to minimize the maximum earliness and tardiness. Under the assumption of GDD, due-dates are not job-dependent but rather associated with the number of jobs previously processed. First, we prove that the problem is strongly NP-hard by reduction to the well-known 3-partition problem. We then formulate three lower-bounds on the optimal solution, and develop an efficient heuristic for the problem. The heuristic is shown to perform very well through an extensive numerical study.

Keywords: Single machine; Earliness; Tardiness; Generalized due-dates