Single machine scheduling problem in a Just-in-time environment

In this work we discusses the deterministic single machine scheduling problem in a just in time environment. We study the non regular objective of minimizing the earliness-tardiness cost, which is consistent with the just-in-time environment, when processing times and the common due date are known in advance. This problem is known to be NP-hard, so we propose a heuristic that do well for small restrictive due date compared to existing benchmarks. In addition to present methods for solving this classical problem, we discuss also the problem with periodic preventive maintenance and present a mixed integer linear program to solve it to optimality.