A FPTAS for minimizing total completion time in a single machine time-dependent scheduling problem
In this paper a single machine time-dependent scheduling problem with total completion time criterion is considered. There are given n jobs J1,...,Jn and the processing time pi of the ith job is given by pi=a+bisi, where si is the starting time of the ith job (i=1,...,n),bi is its deterioration rate and a is the common base processing time. If all jobs have deterioration rates different and not smaller than a certain constant u>0, then for each [epsilon]>0 a solution with the value of the goal function that is at most 1+[epsilon] times greater than the optimal one can be found. We give a FPTAS that finds such a solution in time. Consequently, the problem cannot be NP-hard in the strong sense.
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- Biskup, Dirk, 2008. "A state-of-the-art review on scheduling with learning effects," European Journal of Operational Research, Elsevier, vol. 188(2), pages 315-329, July.
- Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
- Ji, Min & Cheng, T.C.E., 2008. "Parallel-machine scheduling with simple linear deterioration to minimize total completion time," European Journal of Operational Research, Elsevier, vol. 188(2), pages 342-347, July.
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