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This paper examines the uniform parallel-machine scheduling problem in which the objective aims to minimize the total resource consumption (TRC) with a bounded makespan. A matheuristic is proposed to deal with this strongly NP-hard problem. The performance of the proposed matheuristic is compared with that of the state-of-the-art particle swarm optimization (PSO) meta-heuristic and the lower bound (LB) of TRC on a set of benchmark instances. Computational results show that the proposed matheuristic significantly outperforms the PSO meta-heuristic and its solution is very close to the tight LB. Given the critical need for environmental protection, this paper provides an effective and efficient algorithm for diminishing the gap between the theoretical progress of scheduling and the practical need for environmental protection.

Uniform Parallel-Machine Scheduling for Minimizing Total Resource Consumption With a Bounded Makespan