Parallel machine scheduling problem to minimize the makespan with resource dependent processing times

This paper considers the identical parallel machine scheduling problem to minimize the makespan with controllable processing times, in which the processing times are linear decreasing functions of the consumed resource. The total resource consumption is limited. This problem is NP-hard even if the total resource consumption equals to zero. Two kinds of machines, critical machine and non-critical machine, are defined. Some theoretical results are provided. And then, a simulated annealing algorithm is designed to obtain the near-optimal solutions with high quality. To evaluate the performance of the proposed algorithm, we generate the random test data in our experiment to simulate the ingot preheating before hot-rolling process in steel mills. The accuracy and efficiency of the simulated annealing algorithm is tested based on the data with problem size varying from 200 jobs to 1000 jobs. By examining 10,000 randomly generated instances, the proposed simulated annealing algorithm shows an excellent performance in not only the solution quality but also the computation time. © 2011 Elsevier B.V. All rights reserved.