The reduced ability to cover debts was the frequent economic problem in the past and the problem still remains actual in present time. Insolvency is the situation in which the ability to cover the debts in exceptional economic situations (e.g., economic crisis, sudden changes in market conditions) is reduced. However, this problem can be generalized to any mutual debt compensation (e.g., mutual compensation of hours or students at the university, mutual compensation between electricity supplier and customer using own source of power, etc.). One way of dealing with this problem is mutual debts compensation.Models with optimization of mutual debt compensation are historically oriented to the application and models of mathematical programming theory. Especially these models are connected with the task of maximum circle detection in the edge-oriented graph or the maximum flow problem.There are “split the bill” applications which are offering a simple solution to mutual debt compensation within a particular group of entities. Also, the graph can be used for demonstration of relationships between individual entities that agree on the mutual compensation within a group of them. Afterwards, the problem can be solved using the mathematical programming.The paper presents the theoretical principles of generalized models of mutual debt compensation based on the graph theory and mathematical programming.
