This paper considers a kind of scheduling setting where both delivery times and processing times are dependent on the jobs already processed. The delivery times are formulated as an exponential function of the sum of the logarithm of actual processing times of jobs already processed. The actual processing time is formulated as a basic processing time multiplied by a factor which is also an exponential function of the sum of the logarithm of actual processing times of jobs already processed. In the setting, the authors study the single-machine scheduling problems to minimize makespan, total completion time, weighted total completion time, and maximum tardiness. They show that all the problems are polynomially solvable and give corresponding optimal rules.