Single-machine two-agent scheduling with a rate-modifying activity and weighted due-date-related functions

Abstract We analyze two-agent scheduling problems with weighted due-date-related scheduling criteria and an optional rate-modifying activity that, when completed, allows jobs to be completed faster. We start with the single-agent problem of minimizing the total weighted late work and then extend the results over to two-agent problems involving combinations of the weighted number of late jobs and the total weighted late work. We examine the properties of optimal schedules and provide efficient pseudo-polynomial time algorithms to solve these problems.