On the quadratic model for unrelated parallel machine scheduling problem with restrictive common due date

Abstract

In this paper, we deal with the unrelated parallel machine scheduling problem in which our aim is to minimize the sum of earliness and tardiness penalties with respect to the restrictive common due date. Plateau and Rios-Solis in (Eur J Oper Res 201:729–736, 2009) utilized the power of 0–1 quadratic programming model with linear constraints in order to obtain approximate optimal solutions to this problem and two other parallel machine scheduling problems. We first show that their model suffers from some deficiencies that highly affect the feasibility of the model in real problems. We then modify their model to obviate these deficiencies. To apply our proposed quadratic model to the real problems, we apply the QCR convexification technique that has been used by Plateau and Rios-Solis in wrong way. We finally test our modified quadratic model on the problems of Plateau and Rios-Solis’s paper and some other problems.