Sparse Process Flexibility Designs: Is Long Chain Really Optimal?

28 Pages Posted: 14 Jun 2014 Last revised: 5 Oct 2017

See all articles by Antoine Désir

Antoine Désir

INSEAD

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Yehua Wei

Decision Sciences Area, Fuqua School of Business, Duke University

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: June 12, 2014

Abstract

Sparse process flexibility and long chain has became an important concept in design flexible manufacturing systems since the seminal paper of Jordan and Graves (1995). In this paper, we study the performance of long chain in comparison to all designs with at most 2n edges over n supply and n demand nodes. We show that, surprisingly, long chain is not 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 2n edges has a strictly better performance than long chain even for i.i.d. demand distributions. This is quite surprising and contrary to the intuition that a connected design performs better than a disconnected one for symmetric distributions. Moreover, our family of instances show that the optimal design depends on the particular demand distribution.

We also study the performance of long chain in comparison to connected designs with at most 2n arcs. We show that 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 towards designing more general sparse flexibility networks.

Keywords: long chain, process flexibility design, stochastic max-flow, capacity pooling

Suggested Citation

Désir, Antoine and Goyal, Vineet and Wei, Yehua and Zhang, Jiawei, Sparse Process Flexibility Designs: Is Long Chain Really Optimal? (June 12, 2014). Available at SSRN: https://ssrn.com/abstract=2449944 or http://dx.doi.org/10.2139/ssrn.2449944

Antoine Désir

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Yehua Wei (Contact Author)

Decision Sciences Area, Fuqua School of Business, Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States

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