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A stochastic model to study the system capacity for supply chains in terms of minimal cuts

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  • Lin, Yi-Kuei

Abstract

For a single-commodity stochastic flow network, the system capacity is the maximum flow from the source to the sink. We construct a p-commodity stochastic flow network with unreliable nodes, in which branches and nodes all have several possible capacities and may fail, to model a supply chain. Different types of commodities, transmitted through the same network simultaneously, consume the capacities of branches and nodes differently. That is, the capacity weight depends on branches, nodes and types of commodity. We first define the system capacity as a vector and propose a performance index, the probability that the upper bound of the system capacity is a given pattern. Such a performance index can be easily computed in terms of upper boundary states meeting the demand exactly. An efficient algorithm based on minimal cuts is thus presented to generate all upper boundary states. The manager can apply this performance index to measure the transportation level of a supply chain.

Suggested Citation

  • Lin, Yi-Kuei, 2010. "A stochastic model to study the system capacity for supply chains in terms of minimal cuts," International Journal of Production Economics, Elsevier, vol. 124(1), pages 181-187, March.
    • Handle: RePEc:eee:proeco:v:124:y:2010:i:1:p:181-187
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    References listed on IDEAS

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    1. Lin, Yi-Kuei, 2007. "Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity," International Journal of Production Economics, Elsevier, vol. 107(2), pages 572-580, June.
    2. Lin, Yi-Kuei, 2007. "On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint," European Journal of Operational Research, Elsevier, vol. 176(1), pages 347-360, January.
    3. Yeh, Wei-Chang, 2004. "Multistate network reliability evaluation under the maintenance cost constraint," International Journal of Production Economics, Elsevier, vol. 88(1), pages 73-83, March.
    4. Lin, Yi-Kuei, 2006. "Evaluate the performance of a stochastic-flow network with cost attribute in terms of minimal cuts," Reliability Engineering and System Safety, Elsevier, vol. 91(5), pages 539-545.
    5. Bailey, Kate & Francis, Mark, 2008. "Managing information flows for improved value chain performance," International Journal of Production Economics, Elsevier, vol. 111(1), pages 2-12, January.
    6. B. Rothschild & A. Whinston, 1966. "On Two Commodity Network Flows," Operations Research, INFORMS, vol. 14(3), pages 377-387, June.
    7. T. C. Hu, 1963. "Multi-Commodity Network Flows," Operations Research, INFORMS, vol. 11(3), pages 344-360, June.
    8. Yeh, Wei-Chang, 2005. "A new approach to evaluate reliability of multistate networks under the cost constraint," Omega, Elsevier, vol. 33(3), pages 203-209, June.
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    Cited by:

    1. Lin, Yi-Kuei & Yeh, Cheng-Ta, 2010. "Optimal carrier selection based on network reliability criterion for stochastic logistics networks," International Journal of Production Economics, Elsevier, vol. 128(2), pages 510-517, December.
    2. Cheng-Ta Yeh & Yi-Kuei Lin & Cheng-Fu Huang, 2016. "Vehicle glass distribution reliability measurement under transportation cost constraint," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 10(2), pages 243-263.
    3. Yi-Kuei Lin & Cheng-Ta Yeh & Cheng-Fu Huang, 2016. "A simple algorithm to evaluate supply-chain reliability for brittle commodity logistics under production and delivery constraints," Annals of Operations Research, Springer, vol. 244(1), pages 67-83, September.

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