Single machine due date assignment scheduling problem with customer service level in fuzzy environment

Authors:
Jinquan Li;Kaibiao Sun;Dehua Xu;Hongxing Li
Affiliations:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China;School of Electronic and Information Engineering, Dalian University of Technology, Dalian 2#, Linggong Road, Dalian, Liaoning 116024, PR China;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China;School of Electronic and Information Engineering, Dalian University of Technology, Dalian 2#, Linggong Road, Dalian, Liaoning 116024, PR China
Venue:
Applied Soft Computing
Year:
2010

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Abstract

Due date assignment scheduling problems with deterministic and stochastic parameters have been studied extensively in recent years. In this paper, we consider a single machine due date assignment scheduling problem with uncertain processing times and general precedence constraint among the jobs. The processing times of the jobs are assumed to be fuzzy numbers. We first propose an optimal polynomial time algorithm for the problem without precedence constraints among jobs. Then, we show that if general precedence constraint is involved, the problem is NP-hard. Finally, we show that if the precedence constraint is a tree or a collection of trees, the problem is still polynomially solvable.