Two-agent group scheduling with deteriorating jobs on a single machine

This paper considers the two-agent scheduling problems with deteriorating jobs and group technology on a single machine, 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. Two agents compete to perform their respective jobs on a common single machine, and each agent has his own criterion to optimize. We introduce deteriorating jobs and group technology into the two-agent single-machine scheduling where the job processing times and group setup times are both functions of their starting times. There are two different linear deterioration functions. We propose the optimal properties and present the optimal polynomial time algorithms for two different scheduling problems, respectively.