Reply to note on The common due-date early/tardy scheduling problem on a parallel machine under the effects of time-dependent learning and linear and nonlinear deterioration

We present that the example solved for Theorems 1 and 2 proposed by Toksari and Güner [Toksari, M. D., & Güner, E. (2010). The common due-date early/tardy scheduling problem on a parallel machine under the effects of time-dependent learning and linear and nonlinear deterioration. Expert Systems with Applications 37(1), 92–112 ] in [Yunqiang Y., Dehua X., & Xiaokun H. (2011). Notes on “The common due-date early/tardy scheduling problem on a parallel machine under the effects of time-dependent learning and linear and nonlinear deterioration”. Expert Systems with Applications] is incorrect. They obtained wrong solution to example because they wrongly analyzed the both theorem. On the other hand, in the theorems proposed by Toksari and Güner (2010), a job completes on the common due date. We show that the correct solution for the given counterexample. The solution proves the Theorems 1 and 2 proposed by Toksari and Güner [Toksari, M. D., & Güner, E. (2010). The common due-date early/tardy scheduling problem on a parallel machine under the effects of time-dependent learning and linear and nonlinear deterioration. Expert Systems with Applications 37(1), 92–112 ] are correct.