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.
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.
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.
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.
