On multi-state two separate minimal paths reliability problem with time and budget constraints
by Majid Forghani-Elahabad; Nezam Mahdavi-Amiri; Nelson Kagan
International Journal of Operational Research (IJOR), Vol. 37, No. 4, 2020

Abstract: In a stochastic-flow network, a (d, T, b, P₁, P₂)-MP is a system state vector for which d units of flow can be transmitted through two separate minimal paths (SMPs) P1 and P2 simultaneously from a source node to a sink node satisfying time and budget limitations T and b, respectively. Problem of determining all the (d, T, b, P₁, P₂)-MPs, termed as the (d, T, b, P₁, P₂)-MP problem, has been attractive in reliability theory. Here, some new results are established for the problem. Using these results, a new algorithm is developed to find all the (d, T, b, P₁, P₂)-MPs, and its correctness is established. The algorithm is compared with a recently proposed one to show the practical efficiency of the algorithm.

Online publication date: Fri, 13-Mar-2020

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