Sparse Process Flexibility Designs: Is the Long Chain Really Optimal?

Antoine Désir (), Vineet Goyal (), Yehua Wei () and Jiawei Zhang ()
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Antoine Désir: Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Vineet Goyal: Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Yehua Wei: The Fuqua School of Business, Duke University, Durham, North Carolina, 27708
Jiawei Zhang: Leonard N. Stern School of Business, New York University, New York, New York 10012; and New York University Shanghai, Shanghai, China 200122

Operations Research, 2016, vol. 64, issue 2, 416-431

Abstract: Sparse process flexibility and the long chain have become important concepts in design flexible manufacturing systems. In this paper, we study the performance of the long chain in comparison to all designs with at most 2 n edges over n supply and n demand nodes. We show that, surprisingly, long chain is not always optimal in this class of networks even for i.i.d. demand distributions. In particular, we present a family of instances where a disconnected network with 2 n edges has a strictly better performance than the long chain under a specific class of i.i.d. demand distributions. This is quite surprising and contrary to the intuition that a connected design performs better than a disconnected one under exchangeable distributions. Although our family of examples disprove the optimality of the long chain in general, we observe that the empirical performance of the long chain is nearly optimal.To further understand the effectiveness of the long chain, we compare its performance to connected designs with at most 2 n arcs. We show that the long chain is optimal in this class of designs for exchangeable demand distributions. Our proof is based on a coupling argument and a combinatorial analysis of the structure of maximum flow in directed networks. The analysis provides useful insights towards not just understanding the optimality of long chain but also toward designing more general sparse flexibility networks.

Keywords: long chain; process flexibility design; stochastic max-flow; capacity pooling (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (14)

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