A parallel-machine scheduling problem with periodic maintenance under uncertainty

A parallel-machine scheduling problem with preventive maintenance is studied in the paper. Because of the existence of indeterminacy phenomenon, the processing and maintenance time are assume to be uncertain variables. To address these uncertain parameters, two pessimistic value mathematical programming models are developed and the equivalence is proved. The worst-case bound of longest processing time (LPT) rule for the problem under an uncertain environment is obtained. To solve this problem effectively, an improved LPT rule is proposed according to the result of the theoretical analysis. Finally, numerical experiments show that the improved LPT outperforms the LPT in improving the quality of the optimal value and has a less relative error than that of the LPT.