Document Type: Research Paper


1 School of Applied Mathematics, Zhuhai Municipal Key Laboratory of Intelligent Control, Beijing Normal University Zhuhai, Zhuhai 519087, P.R. China

2 School of Science, East China University of Technology, Nanchang 330013, P.R. China

3 School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, P.R. China


In this paper, a due date assignment scheduling problem with precedence constraints and controllable processing times
in uncertain environment is investigated, in which the basic processing time of each job is assumed to be the symmetric trapezoidal fuzzy number, and the linear resource consumption function is used.
The objective is to minimize the crisp possibilistic mean (or expected) value of a cost function that
includes the costs of earliness, tardiness, makespan and resource consumption jointly by scheduling the jobs under precedence constraints and determining the due date and the resource allocation amount
satisfying resource constraints for each job. First, the problem is shown to be NP-hard. Furthermore, an optimal algorithm with polynomial time for the special case of this problem is put forward. Moreover,
an efficient 2-approximation algorithm is presented based on solving the relaxation of the problem. Finally, the numerical experiment is given, whose results show that our method is promising.


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