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 J 1 ,  , J n and the processing time pi p i of the i th job is given by pi=a+bisi p i = a + b i s i , where si s i is the starting time of the i th job (i=1,,n),bi ( i = 1 ,  , n ) , b i 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 u > 0 , then for each ?>0 ? > 0 a solution with the value of the goal function that is at most 1+? 1 + ? times greater than the optimal one can be found. We give a FPTAS that finds such a solution in O n 1 + 6 log 1 + u 2 1 ? 2 log 1 + u 2 time. Consequently, the problem cannot be NP-hard in the strong sense.
fptas total completion time single machine scheduling deteriorating jobs