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

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.