OPTIMIZING INVESTMENT PORTFOLIOS IN BANKING USING INTEGER PROGRAMMING TECHNIQUES

Abstract

In the modern banking system, optimizing the allocation of capital across various loan aspects is a critical task that directly impacts profitability and risk management. Traditional portfolio optimization methods often rely on linear programming techniques that assume continuous investment decisions. However, real-world banking constraints—such as regulatory limits, discrete investment units, and risk thresholds—demand more realistic and implementable models. This thesis explores the application of Integer Programming (IP) techniques to optimize investment portfolios in the banking domain. The primary objective is to maximize net profit from three major loan categories—Home Loans, Personal Loans, and Business Loans—while adhering to operational constraints such as investment caps, borrower creditworthiness, and diversification rules. The dataset used in this study was manually created to simulate realistic banking scenarios, including data on expected profits, borrower creditworthiness, and administrative costs. A Mixed Integer Linear Programming (MILP) model was formulated to reflect these constraints, with investment decisions modelled in discrete ₹1 lakh units. The results indicated an optimal allocation of ₹50 lakhs each to Home and Personal Loans, yielding a maximum net profit of ₹8.50 lakhs. Business loans, though offering a competitive return, were excluded from the final allocation due to relatively lower risk-adjusted performance and constraint tightness. Graphical visualizations were used to interpret allocation patterns and profit contributions, while sensitivity analysis highlighted the binding nature of budget and diversification constraints. The study demonstrates that Integer Programming not only improves the practical feasibility of financial decisions but also allows banks to manage risk while achieving profitability. The model’s structure provides a robust foundation for extending into multi-period investment strategies, stochastic interest rate environments, or incorporating credit scoring models in future work.