Optimal Design of Process Flexibility for General Production Systems

Xi Chen (), Tengyu Ma (), Jiawei Zhang () and Yuan Zhou ()
Additional contact information
Xi Chen: Stern School of Business, New York University, New York, New York 10012;
Tengyu Ma: Facebook AI Research, Menlo Park, California 94025;
Jiawei Zhang: Department of Information, Operations, and Management Sciences, New York University, New York, New York 10012; NYU Shanghai, 200122 Shanghai, China;
Yuan Zhou: Indiana University at Bloomington, Bloomington, Indiana 47405; University of Illinois Urbana–Champaign, Urbana, Illinois 61801

Operations Research, 2019, vol. 67, issue 2, 516-531

Abstract: Process flexibility is widely adopted as an effective strategy for responding to uncertain demand. Many algorithms for constructing sparse flexibility designs with good theoretical guarantees have been developed for balanced and symmetrical production systems. These systems assume that the number of plants equals the number of products, that supplies have the same capacity, and that demands are independently and identically distributed. In this paper we relax these assumptions and consider a general class of production systems. We construct a simple flexibility design to fulfill (1 - ɛ)-fraction of expected demand with high probability where the average degree is O (ln(1/ɛ)) . To motivate our construction, we first consider a natural weighted probabilistic construction from the existing literature where the degree of each node is proportional to its expected capacity. However, this strategy is shown to be suboptimal. To obtain an optimal construction, we develop a simple yet effective thresholding scheme. The analysis of our approach extends the classic analysis of expander graphs by overcoming several technical difficulties. Our approach may prove useful in other applications that require expansion properties of graphs with nonuniform degree sequences.

Keywords: flexible manufacturing; graph expanders; thresholding; weighted probabilistic construction (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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