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Understanding the performance of the long chain and sparse designs in process flexibility

Publication ,  Journal Article
Simchi-Levi, D; Wei, Y
Published in: Operations Research
September 1, 2012

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. © 2012 INFORMS.

Duke Scholars

Published In

Operations Research

DOI

EISSN

1526-5463

ISSN

0030-364X

Publication Date

September 1, 2012

Volume

60

Issue

5

Start / End Page

1125 / 1141

Related Subject Headings

  • Operations Research
  • 3507 Strategy, management and organisational behaviour
  • 1503 Business and Management
  • 0802 Computation Theory and Mathematics
  • 0102 Applied Mathematics
 

Citation

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ICMJE
MLA
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Simchi-Levi, D., & Wei, Y. (2012). Understanding the performance of the long chain and sparse designs in process flexibility. Operations Research, 60(5), 1125–1141. https://doi.org/10.1287/opre.1120.1081
Simchi-Levi, D., and Y. Wei. “Understanding the performance of the long chain and sparse designs in process flexibility.” Operations Research 60, no. 5 (September 1, 2012): 1125–41. https://doi.org/10.1287/opre.1120.1081.
Simchi-Levi D, Wei Y. Understanding the performance of the long chain and sparse designs in process flexibility. Operations Research. 2012 Sep 1;60(5):1125–41.
Simchi-Levi, D., and Y. Wei. “Understanding the performance of the long chain and sparse designs in process flexibility.” Operations Research, vol. 60, no. 5, Sept. 2012, pp. 1125–41. Scopus, doi:10.1287/opre.1120.1081.
Simchi-Levi D, Wei Y. Understanding the performance of the long chain and sparse designs in process flexibility. Operations Research. 2012 Sep 1;60(5):1125–1141.

Published In

Operations Research

DOI

EISSN

1526-5463

ISSN

0030-364X

Publication Date

September 1, 2012

Volume

60

Issue

5

Start / End Page

1125 / 1141

Related Subject Headings

  • Operations Research
  • 3507 Strategy, management and organisational behaviour
  • 1503 Business and Management
  • 0802 Computation Theory and Mathematics
  • 0102 Applied Mathematics