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

Controllable Processing Times in Project and Production Management: Analysing the Trade-Off between Processing Times and the Amount of Resources

The amount of resources assigned to a task highly influences its processing time. Traditionally, different functions have been used in the literature in order to map the processing time of the task with the amount of resources assigned to the task. Obviously, this relation depends on several factors such as the type of resource and/or decision problem under study. Although in the literature there are hundreds of papers using these relations in their models or methods, most of them do not justify the motivation for choosing a specific relation over another one. In some cases, even wrong justifications are given and, hence, infeasible or nonappropriated relations have been applied for the different problems, as we will show in this paper. Thus, our paper intends to fill this gap establishing the conditions where each relation can be applied by analysing the relations between the processing time of a task and the amount of resources assigned to that task commonly employed in the production and project management literature