Note on “A note on single machine scheduling with time-dependent deterioration and exponential learning effect”

Abstract

A result in a recent paper Huang et al. (2010) is incorrect because job processing times are variable due to both deteriorating jobs and learning effects, which is not taken into account by the authors. In this note, we show by a counter-example that the published result is incorrect. From the counter-example, we know that the classical SPT rule or LPT rule cannot give an optimal solution for the problem 1pj[r]=pj(1+∑i=1r-1pi)aαr-1,wj=θpj∑wjCj, then we provide a revised model.