Single machine scheduling with sum-of-logarithm-processing-times based deterioration

In this study we consider the single machine scheduling problems with sum-of-logarithm-processing-times based deterioration, i.e., the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. We show that even with the introduction of the sum-of-logarithm-processing-times based deterioration to job processing times, single machine makespan minimization problem remain polynomially solvable. But for the total completion time minimization problem, we show that the optimal schedule is not always V-shaped with respect to job normal processing times. Heuristic algorithms and computational results are presented for the total completion time minimization problem.