Scheduling problems with rejection and piece-rate maintenance to minimise the total weighted completion time

This paper addresses the single machine scheduling problems with simultaneous consideration of rejection and piece-rate maintenance. Each job is either accepted to be processed on the machine, or rejected in which case a rejection penalty will be incurred. The piece-rate maintenance refers that the machine performs maintenance activity every time it completes a given number of jobs. The objective is to minimise the sum of weighted completion …