Two-agent single-machine scheduling with release dates to minimize the makespan

We consider two-agent scheduling on a single-machine with release dates. There are two agents, namely, A and B . Each agent has his own job set. Each job has a release date and a processing time. All jobs need to be scheduled on a single machine. The objective function of each agent is the makespan with respect to his jobs, i.e., the maximum completion time. We consider two problems, namely the problem to minimize the makespans of agent A with the makespan of agent B not greater than a positive number Q given in advance, and the problem to minimize the weighted sum of both agents’ makespans. For the first problem, we drive an approximation algorithm with a worst-case ratio of 3/2 . Furthermore, we show that this problem admits a fully polynomial-time approximation scheme(FPTAS). For the second problem, we propose an improved approximation algorithm with a worst-case ratio of 1 +θ/(1+θ )^2 , where θ >0 is the weight of agent B .