A comparison of two V-shaped schedule-builder EAs for the common due date problem

Abstract

The restricted single-machine common due date problem can be stated as follows: A set of <i>n</i> jobs with deterministic processing times <i>p</i><SUB>i</SUB> and a common due date <i>d</i> are given. The jobs have to be processed on one machine. For each of the jobs an individual earliness α<SUB>i</SUB> and tardiness β<SUB>i</SUB> penalty is given, which is incurred, if a job is finished before or after the common due date <i>d</i>, respectively. The goal is to find a schedule for the <i>n</i> jobs which jointly minimizes the sum of earliness and tardiness penalties. Even simple in the formulation, this model leads to an optimization problem that is NP-Hard.