Note on the sequence dependent setup scheduling problem (SDSSP) with earliness and tardiness penalties

In the paper: "Minimizing the Sum of Earliness/Tardiness in Multi-machine Scheduling: A Mixed Integer Programming Approach" by Zhiwei Zhu and Ronald B. Heady, published in Computers & Industrial Engineering 38 (2000) 297-305, they present two formulations. Both their triple index and double index mathematical formulations address the sequence dependent setup scheduling problem (SDSSP) with earliness and tardiness penalties. These formulations were compared to the network flow based formulation of Anderson et al. in the paper: "An Efficient Network-Based Formulation for Sequence Dependent Setup Scheduling on Parallel Identical Machines", published in Mathematical and Computer Modeling, Volume 57, Issues 3-4, February 2013, p. 483-493. Through this comparative analysis, an omission in the double index Zhu and Heady formulation was discovered. (C) 2014 Elsevier Ltd. All rights reserved.