An Application of Graph Theory in the Process of Mutual Debt Compensation

In our paper, the class of graph tractable problems of mutual debt compensation (MDC) among firms is introduced. We demonstrate that the debt compensation is related to the optimization problems maximizing the circulation of the consecutive compensation in the digraph of debts. Each optimization problem is firstly formulated by linear programming methods. It is subsequently redeveloped in order to apply the more efficient Klein's cycle-cancelling algorithm. The class of the formulated compensation problems consists of the following models: (i) the model maximizing the returns of the MDC organizer; (ii) the model of profitable subsidies and (iii) the model minimizing the claims exposition of the MDC organizer.