Minimizing resource consumption on uniform parallel machines with a bound on makespan

With the crucial issue of environmental protection, managing natural resources efficiently and/or reducing the amount of carbon emissions have become more important than ever. In this paper, we introduce a uniform parallel machine scheduling problem where the objective is to minimize resource consumption given that the maximum completion time does not exceed a certain level. We show that the problem is strongly NP-hard. A tight lower bound and a particle swarm optimization algorithm are then developed. Finally, some computational results are provided.