A Note on Two-Agent Scheduling with Resource Dependent Release Times on a Single Machine

We consider a scheduling problem in which both resource dependent release times and two agents exist simultaneously. Two agents share a common single machine, and each agent wants to minimize a cost function dependent on its own jobs. The release time of each A-agent's job is related to the amount of resource consumed. The objective is to find a schedule for the problem of minimizing A-agent's total amount of resource consumption with a constraint on B-agent's makespan. The optimal properties and the optimal polynomial time algorithm are proposed to solve the scheduling problem.