A note on single-machine total completion time problem with general deteriorating function

In this paper, we consider the single-machine scheduling problem with a deteriorating function. By the deteriorating function, we mean that the actual job processing time is a function of jobs already processed. We show that the total completion time minimization problem for a ≥ 1 remains polynomially solvable under the proposed model, where a denotes the deterioration rate. For the case of 0 < a < 1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times. We use the classical smallest processing time first rule as a heuristic algorithm for the case of 0 < a < 1 and analyze its worst-case bound.