Application of Linear Programming for Optimal Net Revenue on Bank Loan

Abstract

The primary aim of this study is to optimize the Bank's net return on loans granted to its customers. The Bank is confronted with the task of efficiently allocating funds among five distinct types of loans: Home loans, Personal loans, Car loans, Business loans, Credit Card loan, Flex i-loan and Organization loans, all of which have the potential to yield substantial net returns. Utilizing linear programming techniques, this research employs a solution approach to maximize the net return of loans disbursed by the Bank. The findings reveal an optimal allocation strategy: Home loans should receive no allocation (₦60,000000), Business Loans should be allocated ₦0 million, Personal Loans should be allocated ₦0 million, Car loans should be allocated ₦0 million, Credit Card should be allocated ₦150,000000 million and Organization loans should receive no allocation (₦90,000000). These allocations are determined from a total available loan pool of ₦300,000000 million. The calculated annual rate of return stands at 12.9%, which is slightly lower than the highest net interest rate of 58.6% observed for Personal loans . Another noteworthy observation pertains to the constraint that car and organization loans combined must account for at least 45% of the total loans (constraint 2). This requirement compels the solution to assign ₦60,000000 million to Home loans, even though they yield a lower net rate of 12.9%. It is evident that translating these insights into concerted efforts could undoubtedly enhance the Bank's profitability in terms of net return.