Setting due dates to minimize the total weighted possibilistic mean value of the weighted earliness-tardiness costs on a single machine

Authors:
Jinquan Li;Xuehai Yuan;E. S. Lee;Dehua Xu
Affiliations:
School of Applied Mathematics, Research Center of Fuzzy Systems, Beijing Normal University, Zhuhai, Guangdong, 519087, PR China;School of Control Science and Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China;Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506, USA;School of Science, East China Institute of Technology, Fuzhou, Jiangxi 344000, PR China
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, it is investigated how to sequence jobs with fuzzy processing times and predict their due dates on a single machine such that the total weighted possibilistic mean value of the weighted earliness-tardiness costs is minimized. First, an optimal polynomial time algorithm is put forward for the scheduling problem when there are no precedence constraints among jobs. Moreover, it is shown that if general precedence constraints are involved, the problem is NP-hard. Then, four reduction rules are proposed to simplify the constraints without changing the optimal schedule. Based on these rules, an optimal polynomial time algorithm is proposed when the precedence constraint is a tree or a collection of trees. Finally, a numerical experiment is given.