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Mathematical Problems in Engineering
Volume 2016, Article ID 4329613, 15 pages
Research Article

An Improved L-Shaped Method for Solving Process Flexibility Design Problems

1Department of Industrial Engineering, Tsinghua University, Beijing 100084, China
2University of Alabama in Huntsville, Huntsville, AL 35899, USA
3Logistics Engineering and Simulation Laboratory, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China

Received 2 March 2016; Revised 17 July 2016; Accepted 21 July 2016

Academic Editor: Xiangyu Meng

Copyright © 2016 Huasheng Yang et al. 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.


Process flexibility, where a plant is able to produce different types of products, is introduced to mitigate mismatch risk caused by demand uncertainties. The long chain design proposed by Jordan and Graves in 1995 has been shown to be able to reap most benefits of full-flexibility structure (where each plant is able to produce all products) in balanced systems (where the numbers of products and plants are equal). However, when systems are not balanced or asymmetric or when response dimension is taken into consideration, long chain design may not be the best configuration. Therefore, this paper models the process flexibility design problem in more general settings. The paper considers both balanced and unbalanced systems with asymmetric plants considering response dimension. The problem is formulated as a two-stage stochastic program which is solved by an adapted L-shaped method, combining it with several enhancements. To the best of our knowledge, this is the first time L-shaped method is used to solve the process flexibility design problem. The effectiveness and efficiency of the proposed method and enhancements are evaluated. Finally, the comparison between design methods proposed in this paper and in existing literature shows the superiority of the former.