An approximation algorithm for a single-machine scheduling problem with release times, delivery times and controllable processing times

The paper deals with a single-machine scheduling problem with release times, delivery times and controllable job processing times. It is assumed that the cost of performing a job is a linear function of its processing time, and the total schedule cost to be minimized is the total processing cost plus maximum completion time cost. In consequence, the processing order of jobs and their processing times are decision variables. A (ρ+1/3)-approximation algorithm for the problem is provided, where ρ is the worst-case performance bound of a procedure for solving the pure sequencing problem.