Process Flexibility Revisited: The Graph Expander and Its Applications

Mabel C. Chou (), Geoffrey A. Chua (), Chung-Piaw Teo () and Huan Zheng ()
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Mabel C. Chou: NUS Business School, National University of Singapore, Singapore 119245, Republic of Singapore
Geoffrey A. Chua: Nanyang Business School, Nanyang Technological University, Singapore 639798, Republic of Singapore
Chung-Piaw Teo: NUS Business School, National University of Singapore, Singapore 119245, Republic of Singapore
Huan Zheng: Antai College of Economics and Management, Shanghai Jiaotong University, 200052 Shanghai, China

Operations Research, 2011, vol. 59, issue 5, 1090-1105

Abstract: 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 (psi)-expander structure, a variant of the graph expander structure (a highly connected but sparse graph) often used in communication networks, is within (epsilon)-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.

Keywords: facilities planning; design; production; flexible manufacturing; networks/graphs; stochastic (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (36)

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