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Reliability and transportation cost are two important indicators to measure the performance of logistics network. As a combination of reliability and transportation cost, the performance index R ( d , c ) of logistics network is defined as the probability that at least d units of flow demand can be successfully transmitted from the source to the destination with the total transportation cost less than or equal to c . In this paper, an algorithm is developed to calculate R ( d , c ) in terms of ( d , c ) -minimal paths ( ( d , c ) -MPs for short). The proposed algorithm employs a decomposition technique to divide the search space of ( d , c ) -MPs such that the search space of ( d , c ) -MPs can be dramatically reduced, and thereby ( d , c ) -MPs can be efficiently obtained. An example is provided to illustrate the proposed algorithm. Finally, computational experiments conducted on one benchmark network indicate that the proposed method has an advantage over the existing methods.

Assessing the Reliability of a Multistate Logistics Network under the Transportation Cost Constraint