University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415620181230SINGLE MACHINE DUE DATE ASSIGNMENT SCHEDULING PROBLEM WITH PRECEDENCE CONSTRAINTS AND CONTROLLABLE PROCESSING TIMES IN FUZZY ENVIRONMENT121143437110.22111/ijfs.2018.4371ENJinquan LiSchool of Applied Mathematics, Zhuhai Municipal Key Laboratory of
Intelligent Control, Beijing Normal University Zhuhai, Zhuhai 519087, P.R. ChinaDehua XuSchool of Science, East China University of Technology, Nanchang
330013, P.R. ChinaHongxing LiSchool of Electronic and Information Engineering, Dalian University
of Technology, Dalian 116024, P.R. ChinaJournal Article20170509In this paper, a due date assignment scheduling problem with precedence constraints and controllable processing times<br /> 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.<br />The objective is to minimize the crisp possibilistic mean (or expected) value of a cost function that<br />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<br /> 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,<br /> 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.http://ijfs.usb.ac.ir/article_4371_f8b14d686fb69693683e2e6e095379da.pdf