Journal of Applied Mathematics
Volume 2013 (2013), Article ID 720607, 15 pages
Research Article

A Fuzzy Nonlinear Programming Approach for Optimizing the Performance of a Four-Objective Fluctuation Smoothing Rule in a Wafer Fabrication Factory

1Department of Information Technology, Ling Tung University, No. 1, Ling Tung Road, Nantun, Taichung City 408, Taiwan
2Department of Industrial Engineering and Systems Management, Feng Chia University, No. 100, Wenhwa Road, Seatwen, Taichung City 407, Taiwan

Received 11 January 2013; Accepted 24 March 2013

Academic Editor: Yi-Chi Wang

Copyright © 2013 Horng-Ren Tsai and Toly Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In theory, a scheduling problem can be formulated as a mathematical programming problem. In practice, dispatching rules are considered to be a more practical method of scheduling. However, the combination of mathematical programming and fuzzy dispatching rule has rarely been discussed in the literature. In this study, a fuzzy nonlinear programming (FNLP) approach is proposed for optimizing the scheduling performance of a four-factor fluctuation smoothing rule in a wafer fabrication factory. The proposed methodology considers the uncertainty in the remaining cycle time of a job and optimizes a fuzzy four-factor fluctuation-smoothing rule to sequence the jobs in front of each machine. The fuzzy four-factor fluctuation-smoothing rule has five adjustable parameters, the optimization of which results in an FNLP problem. The FNLP problem can be converted into an equivalent nonlinear programming (NLP) problem to be solved. The performance of the proposed methodology has been evaluated with a series of production simulation experiments; these experiments provide sufficient evidence to support the advantages of the proposed method over some existing scheduling methods.