Two-agent single-machine scheduling with position-dependent processing times

A new scheduling model in which both two-agent and position-dependent processing times exist simultaneously is considered in this paper. Two agents compete to perform their respective jobs on a common single machine, and each agent has his own criterion to optimize. The job position-dependent processing time is characterized by increasing or decreasing function dependent on the position of a job in the sequence. We introduce an aging effect and a learning effect into the two-agent single-machine scheduling, where the objective is to minimize the total completion time of the first agent with the restriction that the maximum cost of the second agent cannot exceed a given upper bound. We propose the optimal properties for the considered scheduling problems and then present the optimal polynomial time algorithms to solve the two scheduling problems, respectively.