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Optimal Design of Process Flexibility for General Production Systems

47 Pages Posted: 24 Oct 2016  

Xi Chen

New York University (NYU) - Leonard N. Stern School of Business

Tengyu Ma

Princeton University

Jiawei Zhang

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

Yuan Zhou

Indiana University at Bloomington

Date Written: October 22, 2016

Abstract

Process flexibility has been widely adopted as an effective strategy to improve responsiveness to demand uncertainty. Many algorithms for constructing sparse flexibility designs with good theoretical guarantees have been developed for balanced and symmetrical production systems, which assume that the number of plants equals the number of products, the supplies have the same capacity, and demands are independently and identically distributed.

In this paper, we relax these restrictions and consider a very general class of production systems. We provide a simple construction of flexibility design to fulfill (1-ε) fraction of the expected total demand with high probability (w.h.p.) with an average degree of O (ln(1/ε)). To motivate our construction, we first consider a natural weighted probabilistic construction from Chou et. al. (2011), in which the degree of each node is proportional to its expected capacity. However, we show that this strategy is sub-optimal. To obtain an optimal construction, we develop a simple, yet effective thresholding scheme. Our theoretical analysis extends the classical analysis of expander graphs by overcoming several technical difficulties. The developed techniques might be useful for other applications that require certain expansion properties of graphs with non-uniform degree sequence.

Keywords: flexible manufacturing; graph expanders; thresholding; weighted probabilistic construction

JEL Classification: C60

Suggested Citation

Chen, Xi and Ma, Tengyu and Zhang, Jiawei and Zhou, Yuan, Optimal Design of Process Flexibility for General Production Systems (October 22, 2016). Available at SSRN: https://ssrn.com/abstract=2857656

Xi Chen (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
New York, NY NY 10012
United States

Tengyu Ma

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544
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

Yuan Zhou

Indiana University at Bloomington ( email )

Lindley Hall
Indiana University at Bloomington
Bloomington, IN 47401
United States

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