Quantitative Analysis Report: Linear Programming in Finance

This report delves into quantitative analysis, specifically focusing on the application of linear programming in the financial sector. It examines how institutions, such as banks, utilize linear programming to optimize operations, reduce costs, and maximize profits, particularly in managing bank loan portfolios. The report highlights the importance of linear programming in mitigating credit risk mismanagement. It outlines a business problem, recognizing potential concerns in formulating it as a linear programming problem, including linearity, constant values, scope for fractional solutions, degree complexity, and multiplicity of goals. The report then suggests ways to address these concerns, offering solutions such as using quadratic equations when linearity is not feasible and employing approximations for complex calculations. The report concludes with a reference to the application of linear programming as a tool to analyze different goals separately, given its limitation in analyzing multiple goals simultaneously. The analysis is supported by citations from relevant academic sources.

QUANTITATIVE ANALYSIS 1
Quantitative analysis
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QUANTITATIVE ANALYSIS 2
Quantitative analysis
Linear programming
Linear programming is a method used to obtain optimal solutions for a given business
problem given constraints. Most organizations use linear programming to streamline their
operations to help in the reduction of costs and profit maximization. According to ( Crane, 2011),
linear programming is a method used for making decisions in an organization under certainty and
checking and verification method for ascertaining the accuracy and reliability of decisions that
solely lies on a manager's experience.
1. Describe the business problem
Linear programming in commercial institutions helps institutions such as banks in cost
reduction procedures and profit maximization. Most banks apply linear programming methods in
the management of a bank loan portfolio. The management of bank portfolios helps the banks in
avoiding credit risk mismanagement (Fielitz and Loffler, 2010).
2. Recognize potential concerns in formulating the business problem as a linear programming
problem.
Linearity – To effectively formulate a linear programming business problem model, credit risk
management should easily represent a linear relationship between the various decision factors.
The linearity relies on the impression of the objectives stating in terms of linear expressions.
Constant values of objectives and constraint equation- The values of the objective function
and constraints equation should be known before an application of a linear programming method
to solve the credit risk management. In the process, the method assumes the values as constant

QUANTITATIVE ANALYSIS 3
during that period. In case the values change during that period, the method considers losing its
effectiveness and therefore fails to provide the optimal solution to credit risk management.
No scope for fractional optimal solutions- The solution to a linear programming method
proves no certainty in the quantification of the solution as an integer.
Degree complexity- In large scale real-life practical solving of business problems, the
application of linear programming method cannot solve some of the problems due to the
complexity and lengthy calculations.
Multiplicity of goals- Organizations long-term goals are pegged on multiple goals rather than
a single goal, and therefore the multiple goals must be attached on priority-wise for long-term
growth. These goals include profit maximization, cost minimization, retaining market share, and
provision of quality services.
Flexibility- There is difficulty in operational flexibility through the incorporation of any changes
in account of changing decisions.
3. How to address the concerns
Linearity- The credit risk management problem can be expressed in the form of quadratic
equations since the objective function and constraints cannot express linearly. For example,
Ax2+ bx +c = 0
A constant value of objectives and constraints- The restriction of linear programming methods as
the determination of objective function factors and constraints equation cannot be determined
with certainty. The likelihood of occurrence gets predicted.

QUANTITATIVE ANALYSIS 4
Degree complexity- The use of approximations and assumptions is important when solving large
calculations in the credit risk management problem.
A multiplicity of goals- The linear programming method can be used separately to analyze
different goals since it fails in analyzing multiple goals. An objective function can only
determine one goal for a linear programming technique.

QUANTITATIVE ANALYSIS 5
References
Crane, D. B. (2011). A stochastic programming model for commercial bank bond portfolio
management. Journal of Financial and Quantitative Analysis, 6(3), 955-976.
Fielitz, B. D., & Loeffler, T. A. (2010). A linear programming model for commercial bank
liquidity management. Financial Management, 41-50.
Rutkauskas, A. V., & Stankeviciene, J. (2016). Integrated asset and liability portfolio as
instrument of liquidity management in the commercial bank. Journal of business
economics and management, 7(2), 45-57.