System Reliability Evaluation for a Multistate Supply Chain Network With Failure Nodes Using Minimal Paths

This work devotes to the application of network methods for the reliability of a complex supply chain system, which is a set of several factories with supply-demand relationship. Two characters are considered in the proposed network: 1) nodes, and arcs all have multiple possible capacities, and may fail; and 2) the capacity weight varies with arcs, nodes, and types of commodity. The purpose of this paper is to study the systems reliability, in this case the possibility that a given quantity (
d

₁
,
d

₂
) of two types of commodities can be transmitted from the source factory to the destination factory simultaneously. Such a possibility can be treated as a performance index to measure the quality level of a supply chain network. The flow model is constructed by flow assignments, and capacity vectors. The (
d

₁
,
d

₂
) -MP, which represents the capacity of each arc/node, is a minimal capacity vector meeting the demand constraint. A simple algorithm in terms of minimal paths is first proposed to generate all (
d

₁
,
d

₂
)-MP. The system reliability can then be calculated efficiently in terms of (
d

₁
,
d

₂
)-MP. Time complexity of the proposed algorithm is also analyzed.