EconPapers    
Economics at your fingertips  
 

Understanding the Performance of the Long Chain and Sparse Designs in Process Flexibility

David Simchi-Levi () and Yehua Wei ()
Additional contact information
David Simchi-Levi: Engineering Systems Division, Department of Civil and Environmental Engineering, and the Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Yehua Wei: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Operations Research, 2012, vol. 60, issue 5, 1125-1141

Abstract: The long chain has been an important concept in the design of flexible processes. This design concept, as well as other sparse designs, have been applied by the automotive and other industries as a way to increase flexibility in order to better match available capacities with variable demands. Numerous empirical studies have validated the effectiveness of these designs. However, there is little theory that explains the effectiveness of the long chain, except when the system size is large, i.e., by applying an asymptotic analysis.Our attempt in this paper is to develop a theory that explains the effectiveness of long chain designs for finite size systems. First, we uncover a fundamental property of long chains, supermodularity, that serves as an important building block in our analysis. This property is used to show that the marginal benefit, i.e., the increase in expected sales, increases as the long chain is constructed, and the largest benefit is always achieved when the chain is closed by adding the last arc to the system. Then, supermodularity is used to show that the performance of the long chain is characterized by the difference between the performances of two open chains. This characterization immediately leads to the optimality of the long chain among 2-flexibility designs. Finally, under independent and identically distributed (i.i.d.) demand, this characterization gives rise to three developments: (i) an effective algorithm to compute the performances of long chains using only matrix multiplications; (ii) a result that the gap between the fill rate of full flexibility and that of the long chain increases with system size, thus implying that the effectiveness of the long chain relative to full flexibility increases as the number of products decreases; (iii) a risk-pooling result implying that the fill rate of a long chain increases with the number of products, but this increase converges to zero exponentially fast.

Keywords: flexible manufacturing; capacity pooling; facility planning; design; network flow; supermodular function; random walk (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (45)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.1120.1081 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:60:y:2012:i:5:p:1125-1141

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().

 
Page updated 2025-04-17
Handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1125-1141