Process flexibility revisited : the graph expander and its applications
Chou, Mabel C.
Chua, Geoffrey A.
Date of Issue2011
College of Business (Nanyang Business School)
We examine how to design a flexible process structure for a production system to match supply with demand more effectively. We argue that good flexible process structures are essentially highly connected graphs, and we use the concept of graph expansion (a measure of graph connectivity) to achieve various insights into this design problem. Whereas existing literature on process flexibility has focused on the expected performance of process structure, we analyze in this paper the worst-case performance of the flexible structure design problem under a more general setting, which encompasses a large class of objective functions. Chou et al. [Chou, M. C., G. Chua, C. P. Teo, H. Zheng. 2010. Design for process flexibility: Efficiency of the long chain and sparse structure. Oper. Res. 58(1) 43–58] showed the existence of a sparse process structure that performs nearly as well as the fully flexible system on average, but the approach using random sampling yields few insights into the nature of the process structure. We show that the ψ-expander structure, a variant of the graph expander structure (a highly connected but sparse graph) often used in communication networks, is within ϵ-optimality of the fully flexible system for all demand scenarios. Furthermore, the same expander structure works uniformly well for all objective functions in our class. Based on this insight, we derive design guidelines for general nonsymmetrical systems and develop a simple and easy-to-implement heuristic to design flexible process structures. Numerical results show that this simple heuristic performs well for a variety of numerical examples previously studied in the literature and compares favourably even with the best solutions obtained via extensive simulation and known demand distribution.
© 2011 INFORMS. This is the author created version of a work that has been peer reviewed and accepted for publication by Operations Research, INFORMS. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1287/opre.1110.0987].