Resource allocation decisions under various demands and cost requirements in an unreliable flow network

This paper considers resource allocation decisions in an unreliable multi-source multi-sink flow network, which applies to many real-world systems such as electric and power systems, telecommunications, and transportation systems. Due to uncertainties of components in such an unreliable flow network, transmitting resources successfully and economically through the unreliable flow network is of concern to resource allocation decisions at resource-supplying (source) nodes. We study the resource allocation decisions in an unreliable flow network for a range of demand configurations constrained by demand-dependent and demand-independent cost considerations under the reliability optimization objective. Solutions to these problems can be obtained by computing the resource allocation for each demand configuration independently. In contrast, we pursue an updating scheme that eludes time-consuming enumeration of flow patterns, which is necessary in independent computation of resource allocations for different demand configurations. We show that updating is attainable under both demand-independent and demand-dependent cost constraints when demand incurs an incremental change, and demonstrate the proposed updating scheme with numerical examples.