Research on Debt Network Repayment Problem Based on Mixed Integer Linear Programming Modeling

Abstract

This study aims to optimize the payment path in the debt network by constructing a mathematical model, thereby minimizing the number of payments in the debt repayment process. The key to the study is to reduce the number of edges with non-zero weights in the network and optimize the debt repayment path. To this end, this paper divides the nodes in the debt network into two categories: debtors and creditors, and transforms the problem into a classic transportation problem. However, unlike the linear programming model of the transportation problem, the goal of this study is to minimize the number of paths in the network. Therefore, a mixed integer linear programming model is established by introducing binary variables. Finally, the model is verified to be effective through Python simulation experiments and the gurobi optimization solver is used to solve the model, demonstrating its advantages in optimizing debt networks.