Minimum Cost Maximum Flow Problem In Uncertain Network

Minimum cost maximum flow problem is an important issue in thefield of graph theory and networkoptimization. Until now, minimum cost maximum flow problem hasan actual application in many production, especially with logisticsmanagement, supply chain and so on, and it is widely used incommunication and many other areas. Therefore, the minimum costmaximum flow problem has great value for us to research. In real life,decision-makers need enough historical data as a reference beforemaking decisions. However, we often do not have enough historicaldata due to lacking of information or changes in conditions. In this case,we can use uncertain variables to deal with these uncertainties. Hence,it has even more practicalsignificance to study the minimum cost maximum flow problem inuncertain network.The structure of the paper is as follows: Firstly, some basicknowledge within the framework of uncertainty theory and graphtheory are introduced; Secondly, the maximum flow problem of thenetwork with uncertain arc capacities is proposed, and its uncertainprogramming model is given. Then the algorithm for solving themaximum flow problem is described and a practical application isgiven. And the minimum cost maximum flow model with uncertain unitcost is given. Finally, the expansion problem of network capacity isdiscussed, and expected value models are established under uncertaindemand of the expansion of the minimum cost maximum flow andunder cost-effectiveness framework. A numerical example is providedto interpret the model.