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

Yi-Kuei Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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.

Original languageEnglish
Pages (from-to)181-187
Number of pages7
JournalInternational Journal of Production Economics
Issue number1
StatePublished - 1 Mar 2010


  • Capacity weight
  • p-commodity stochastic flow networks
  • Supply chain
  • System capacity
  • Unreliable node

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