A survey of results for sequencing problems with controllable processing times
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Discrete Applied Mathematics
Single machine scheduling to minimize total compression plus weighted flow cost is NP-hard
Information Processing Letters
Single machine scheduling with a variable common due date and resource-dependent processing times
Computers and Operations Research
Convex resource allocation for minimizing the makespan in a single machine with job release dates
Computers and Operations Research
Approximation schemes for parallel machine scheduling problems with controllable processing times
Computers and Operations Research
Minimizing the total weighted flow time in a single machine with controllable processing times
Computers and Operations Research
Computers and Operations Research
Task Scheduling in a Finite-Resource, Reconfigurable Hardware/Software Codesign Environment
INFORMS Journal on Computing
A survey of scheduling with controllable processing times
Discrete Applied Mathematics
A hybrid immune simulated annealing algorithm for the job shop scheduling problem
Applied Soft Computing
Genetic algorithms for a two-agent single-machine problem with release time
Applied Soft Computing
A simulated annealing heuristic for minimizing makespan in parallel machine scheduling
SEMCCO'12 Proceedings of the Third international conference on Swarm, Evolutionary, and Memetic Computing
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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.