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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2349712, 9 pages
Research Article

Cooperative Strategies for Maximum-Flow Problem in Uncertain Decentralized Systems Using Reliability Analysis

1School of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran 11518-63411, Iran
2Department of Industrial Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran

Received 22 May 2016; Accepted 25 July 2016

Academic Editor: Arturo Pagano

Copyright © 2016 Hadi Heidari Gharehbolagh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study investigates a multiowner maximum-flow network problem, which suffers from risky events. Uncertain conditions effect on proper estimation and ignoring them may mislead decision makers by overestimation. A key question is how self-governing owners in the network can cooperate with each other to maintain a reliable flow. Hence, the question is answered by providing a mathematical programming model based on applying the triangular reliability function in the decentralized networks. The proposed method concentrates on multiowner networks which suffer from risky time, cost, and capacity parameters for each network’s arcs. Some cooperative game methods such as -value, Shapley, and core center are presented to fairly distribute extra profit of cooperation. A numerical example including sensitivity analysis and the results of comparisons are presented. Indeed, the proposed method provides more reality in decision-making for risky systems, hence leading to significant profits in terms of real cost estimation when compared with unforeseen effects.