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 asτ-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.
Purpose
Maximum-flow of an uncertain multi-owner network has become very important recently. This study aims to evaluate the maximum flow on a cooperated logistic system in the presence of uncertainties, raised by travel time, capacity, cost and failures.
Design/methodology/approach
To consider different uncertainties and to promote network efficiency, the proposed model is enriched with a cooperative game methodology and a reliability method. A scenario-based method covers optimistic, pessimistic and most likely estimates time, cost and capacity of each route as well as applies a prior failure pattern for breakdown of any resource.
Findings
A linear optimization model, which is enriched with target reliability estimation, is presented. Results on a water distribution network indicate more revenue performance for players. Carrying out sensitivity analysis shows the importance of the model parameters.
Originality/value
Modeling maximum-flow problem in the presence of many sources of uncertainty with the aim of a cooperative game is the main contribution of the present study. Also, a novel method based on the reliability theory is applied to close the chasm on evaluating the real maximum flow in a shared decentralized network which suffers from risky conditions on arcs and nodes.
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