Minimizing earliness and tardiness subject to total completion time in an identical parallel machine system

This study addresses the identical parallel machine scheduling problem in which the total earliness and tardiness about a common due date are minimized subject to minimum total flowtime, P∥(E+T)/∑CiP∥(E+T)/∑Ci. The problem is demonstrated to be transformed into a simplified version of the parallel machine problem with the objective of minimizing makespan subject to minimum total flowtime, P∥Cmax/∑CiP∥Cmax/∑Ci. Several properties are considered to solve optimally the restricted version of the problem. A streamlined binary integer programming model is developed to solve the P∥Cmax/∑CiP∥Cmax/∑Ci problem and the P∥(E+T)/∑CiP∥(E+T)/∑Ci problem. Computational experiments indicate that the binary integer programming model is superior to the existing optimization algorithm for the P∥Cmax/∑CiP∥Cmax/∑Ci problem in the literature.