




































Indian Journal of Finance and Banking 

 Vol. 4, No. 4; 2020 

                                       ISSN 2574-6081   E-ISSN 2574-609X 

Published by CRIBFB, USA 

 

1 

MATHEMATICAL MODELING OF ASSET LIABILITY 

MANAGEMENT IN BANKS USING GOAL PROGRAMMING 

AND AHP 
 

 

Jyoti Tanwar 

Research Scholar 

Department of Economics and Finance 

BITS-Pilani, Pilani Campus 

Jhunjunu, Rajasthan- 333031, India 

E-mail: jyotanwar@gmail.com 

 

Arun Kumar Vaish 

Assistant Professor 

Department of Economics and Finance 

BITS- Pilani, Pilani Campus 

Jhunjunu, Rajasthan- 333031, India 

 

N V M Rao 

Professor 

Department of Economics and Finance 

BITS-Pilani, Pilani Campus 

Jhunjunu, Rajasthan- 333031, India 

 

 

ABSTRACT 

Asset Liability Management has gained popularity in the banking sector. Earlier banks focused 

on asset allocation, but now the management of assets and liabilities is equally essential. Asset 

liability management targets the optimum distribution of funds in assets and managing liabilities 

so that banks can earn higher profits and minimize risk. In this paper, the optimization of assets 

and liabilities of Indian banks has been concentrated using mathematical models. Combining the 

Analytical Hierarchy Process (AHP) and Goal Programming (GP) model has been used to solve 

the optimization problem. AHP is a multi-criteria decision-making approach for deriving 

priority weights. Goal Programming is a linear programming model to solve complex issues 

having multiple objectives. In this paper, the primary data gathered from Bank senior managers 

have been analyzed using the AHP approach to derive weights for criteria. These weights are 

assigned to goals in goal programming to prioritize the goals. Secondary data on OBC bank is 

used in goal programming from 2010-2019 collected from OBC bank's annual reports and RBI 

websites. The findings show that OBC bank has the scope of improving its assets and liabilities 

position to increase its profit and minimize the risk. The model generates an optimum balance 

sheet that achieves the set goals and satisfies all the statutory and planning constraints. The 

same model can be useful for scheduled commercial banks in India with modifications 

concerning banks' targets and controls. The model developed in this paper is helpful for bank 

managers in planning and forecasting. AHP and GP's combined approach is unique in this 



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paper, which uses experts' knowledge and applies it in the model. The model is created on the 

bank's realistic goals and constraints after carefully considering the issues faced by bank 

officials. The paper is limited to the Indian Banking system as other countries have different 

balance sheet structures and constraints. 

 

Keywords: Asset-Liability Management, Goal Programming, Analytical Hierarchy Process, 

Indian Banking. 

 

INTRODUCTION 
The history of banking in India is as old as Vedic civilization, where usury has been commonly 

referred to money lenders. Banking in India originated in the 18th century and has evolved over 

the years to the present shape ( Tanwar, Seth, Vaish, and Rao, 2020). Some of RBI's significant 

reform events led to greater competition and strengthening of the Indian banking sector. In 1969, 

14 major Indian Scheduled Commercial banks were nationalized to serve the development of the 

economy. In 1970, RBI prescribed a minimum interest rate to be charged by banks on advances. 

In response to inflation, RBI took strong measures to increase bank rates and raised the Statutory 

Liquidity Ratio (SLR) from 25% to 28%. In 1992, RBI introduced income recognition and asset 

classification norms, putting most of the banks under severe Non-Performing Assets (NPAs) 

stress. The capital adequacy standards were specified to be fulfilled by Indian banks by 1996. In 

1993, RBI released new guidelines that aimed at increasing competition by establishing private 

sector banks. In 2003, the risk-based supervision of banks was introduced (Chronology of events, 

n.d.).  

The banking sector has undergone many structural changes, from well defined, directed 

norms to prudence-based compliance to move towards greater consistency. Deregulation and 

intense competition have led Indian banks to compete on the asset side and the liability side of 

the balance sheet, forcing them to assume greater and newer risk in their quest for higher returns. 

The composition and risk profile of banks' assets and liabilities have a direct effect on their 

performance and profitability. The process of managing assets and liabilities of a bank while 

achieving the bank's objectives and satisfying the constraints is known as Asset Liability 

Management (ALM). ALM is a process where risks and benefits go hand in hand. On one side, 

the risk is minimized, and on the other side, financial goals are maximized by optimally 

allocating the fund in assets and managing liabilities (Samuel, 2011).  As banking regulations 

and management's plans change from time to time; therefore, ALM needs continuous 

formulation, implementation, and control. Based on the results, strategies need to be revised to 

improve performance and reduce risk (Romanyuk, 2010). 

ALM policy framework targets achieving higher profitability and minimizing risks after 

considering the statutory and regulatory constraints such as liquidity, credit quality, capital 

adequacy, etc. Therefore ALM aims to improve the quality of assets and balance the number of 

assets and liabilities in addition to focusing on the riskiness in the future ( Naderi, Minouei, & 

Gashti, 2013). 

In this research paper, an attempt has been made to optimize the assets and liabilities of 

Indian banks using the example of the Oriental Bank of Commerce (OBC). A combination of the 

Analytical Hierarchy Process (AHP) with weighted goal programming is used to optimize the 

assets and liabilities while simultaneously fulfilling the statutory and regulatory compliance. The 

model developed here tries to satisfy multiple goals that are desired by all banks. 

 



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LITERATURE REVIEW 
ALM is an essential tool for banks and other financial institutions to establish sound financial 

management that can target higher profits and lower bank risk. A bank faces market risk, 

operational risk, liquidity risk, interest rate risk, counterparty risk, financial risk, etc.  ALM was 

introduced in the Indian Banking industry with effect from 1st April 1999
1
. Even in the absence 

of a formal asset-liability management program, understanding these concepts is of value to an 

institution as it provides a more authentic picture of the risk/reward trade-off in which the 

institution is engaged (Fabozzi & Konishi, 1991). The study of ALM develops a clearer picture 

of risk and return trade-off for banks. Risk and reward are complementary to each other. If banks 

desire to increase profits, then it has to take a calculated risk. Banks and other institutions have to 

create a balance between risk and reward. Therefore, ALM deals with narrowing the unfavorable 

effects of risk in parallel to managing the assets-liabilities. 

As discussed, the bank's managers face the problem of improving profitability with their 

limited resources. In past decades, many techniques have been developed to assist bank officials. 

Various studies considered an optimization problem of selecting an optimal portfolio that can 

yield adequate returns while minimizing risk. A suggested by Kosmidou and Zopounidis (2002) 

ALM techniques can be deterministic or Stochastic. Chambers and Charnes (1961) applied 

deterministic linear programming in the model bank to resolve banks' functional problems. The 

study focuses on implementing the requirements Federal Reserve System while developing the 

best profitable portfolio plan. This model focuses on actual problems and optimizing the fund 

allocation within the defined limits of bank examiners. Fielitz and Loeffler (1979), Cohen and 

Hammer (1967), and many others have implemented Chambers and Charner’s model with 

modifications. However, they all had a single objective function, i.e., maximizing profitability 

within defined constraints. A Linear Programming model concentrates on maximization or 

minimization of objective function within a set of relevant constraints. Fielitz and Loeffler 

(1979) describe a mathematical model that deals with the liquidity management of commercial 

banks. Liquidity supports the operation of the bank, but if appropriately governed, it can also 

generate profits. The study aims to maximize the profits that resulted from managing liquidity 

variables subject to external and internal constraints. Cohen and Hammer (1967) explain an 

analytical model using linear programming to improve profitability subject to policy constraints. 

The model endeavor to create a balance between the assets and liability compositions of the 

bank. Eatman and Sealey (1979) developed a multi-objective linear programming model to 

improve commercial banks' profitability and solvency. The bank managers have solvency and 

risk minimization as other goals which are employed in the paper. Liquidity and risk are 

measured by capital adequacy ratio and risk-weighted assets to capital, respectively. Dash and 

Pathak (2011) proposed a linear programming model for Indian banks to optimize the assets and 

liability mix. The objective of the study is to maximize the profitability subject to liquidity and 

statutory constraints. 

Apart from deterministic models, various stochastic models were also proposed after the 

1970s. Markowitz (1959)introduced the Portfolio selection theory, which led to the origination of 

the stochastic model, also known as the static mean-variance method. Ziemba and Mulvey 

(1998) determined a multi-period stochastic linear program that defines the target over the 

                                                 
1
Reserve Bank of India, Bombay, Asset-Liability Management (ALM) System, DBOD Circular 

BP.BC.8/21.04.098/99 dtd. Feb. 10, 1999 



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planning period. Russell-Yasuda at the Frank Russell Company used stochastic programming to 

develop a model that can maximize wealth and income. 

Many scholars have used the goal Programming technique for generating an optimized 

solution for multiple goals. In the real world, a problem deals with numerous goals. Every 

business, bank, a household has not just one but many goals to achieve. Goal Programming (GP) 

is one such model that deals with multiple objectives decisions. In this model, many objectives 

can be achieved while seeking an optimal and feasible solution. In this model, goal constraints 

are set equal to target values that need not be achieved. 

 D. Giokas and Vassiloglou (1991) developed multi-objective programming for bank 

assets and liabilities management. They argued that banks have multiple goals. Bank 

management not only strives to maximize revenue but also put effort to reduce risk. Apart from 

revenue/profit, banks try to gain market share of deposits and credits. As linear programming can 

only handle a single objective function, goal programming is the right approach for multiple 

goals. Kruger (2011) used a single-period approach and multi-period approach to finds that it is 

possible to optimize the balance sheet using advanced software. Viswanathan and 

Balasubramanian (2007)applied the preemptive GP model and studied optimal deployment of 

funds across different asset classes of varying risk and return characteristics to attain the profit 

goals. The regulatory and other constraints are also satisfied while pursuing objectives. Sedzro, 

Marouane, and Assogbavi (2012) use goal programming models for asset allocation. The authors 

incorporated the investor's risk profile and future economic scenarios while optimizing asset 

allocation. Jain, Dalela, and Tiwari (2010) presented the ALM model for pensioners. The study 

discussed the fuzzy programming approach to control the risk of volatility on investment returns 

and liabilities.  

  Viswanathan, Ranganatham and Balasubramanian (2014) used the goal programming 

model in ALM. Goal programming optimally allocated the assets to achieve the target goals, 

namely Other Income, Deposits, Investments, and Advances. Halim et al. (2015)applied the GP 

model to attain six goals: asset accumulation, liability reduction, equity wealth, earning, 

profitability, and optimum management of a bank in Malaysia. The proposed model is capable of 

supporting financial decision making while dealing with diverse economic scenarios. Rezaei, 

Ameleh, Ghalmegh, and Ramezanzadeh (2013), studied assets and liabilities management by 

comparing the model value with actual values using Fuzzy AHP and goal programming. 

Goal Programming assists in structured decision-making; however, it has no method of 

evaluating the priority in goals or assigning weights to goals. All goals do not have the same 

importance. Some goals are more important than others and have to be fulfilled. Analytical 

Hierarchy Process (AHP) allows pair-wise comparison and shows the domination of one element 

concerning others. AHP reckon the judgment of experts to obtain priority scales. The AHP is 

first introduced by Saaty (2008)as the most common multi-criteria decision-making method.  

The use of AHP in the banking industry for ranking and assigning weights is extensive. 

Hunjak & Jakovčević (2001) evaluated bank performance by integrating quantitative and 

qualitative data. The AHP assisted in the activity of comparing and deriving bank ratings. AHP 

was used to assess the best applicant for irrigation and equipment loans. The purpose is to 

allocate the loan to rank one applicant and distribute the remaining fund to the best candidate. 

AHP assisted in ranking based on service, loan history, and insurance (Srdevic, Blagojevic, and 

Srdevic, 2011). Kamil, Ismail, and Shahimi (2013) tried to establish that Islamic banking 

operates to realize society's socio-economic objectives. AHP method is used to derive the 



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priorities for financial resource allocation (ALM) while considering economic and social 

objectives. 

Similarly, the bank decision-maker can use AHP to increase customer base and customer 

satisfaction by understanding their preferences (Javalgi, Armacost, & Hosseini, 1989).  

Tummala, Smith, and Uppuluri (1983) evaluated companies' credit risk belonging to the 

construction industry, which applied for loans. The ranking of the criteria was estimated with 

AHP. The requirements were character, capitalization, collateral, capacity, and conditions. 

Combing AHP with GP will provide a systematic approach to rank/prioritize or weight the 

goals.AHP can establish relative importance among goals, which can be readily used in the GP 

model to solve the problems (Naderi et al., 2013; Sedzro et al., 2012; Wang & Chin, 2008). The 

combination of (AHP) with GP to gain an ideal solution is the best approach. 

 

OBJECTIVE 

There are very few studies in the Indian banking industry that has applied AHP and GP together. 

Most of the studies have either used AHP to derive the ranking/weights or used GP to solve a 

multi-decision-making problem. In the Indian banking industry, the combined used of AHP and 

GP to optimize Asset-Liability Management is not yet focused. Therefore, in this paper, the 

weights for the goals or objectives are attained using AHP. Those weights are assigned to goals 

while optimizing the bank's assets and liabilities in the study. The paper aims to determine the 

optimal structure of assets and liabilities for Indian commercial banks. The targets for goals have 

to be achieved while simultaneously satisfying the constraints. Secondly, to analyze whether the 

model can provide banking management with policy inputs. 

 

METHODOLOGY 

The main objective of this paper is to design a mathematical model that can optimize the assets 

and liabilities of the Oriental Bank of Commerce (OBC Bank) using Goal Programming. The 

relative importance of the goals of Indian scheduled commercial banks is determined with AHP. 

 

Analytical Hierarchy Process 
Interviews were conducted with banks' management in risk profile and balance sheet 

management to identify the goals or criteria for the banks. The interviews were conducted with 

OBC bank, Allahabad Bank, Punjab & Sind Bank, ICICI Bank, Axis Bank, and Bank of Baroda. 

The seven main goals were then arranged in a questionnaire for further processing to obtain the 

priority and weights for the goals from banks' management.AHP used pairwise comparison and 

relies on the experts' judgments to obtain priority scales (Saaty, 2008). The comparison depicts 

the relative importance of one element over another. The process of AHP follows: 

1. Define the problem 

2. Determine the decision hierarchy from top to intermediate level and to the lowest level (if 

any). 

3. Construct pair wise comparison matrices. 

4. There is n (n-1)/2 judgments required, and reciprocals are assigned automatically. 

5. Obtain the experts' judgment and calculate the priority scale. 

6. Check for inconsistency. CR is determined using the Consistency index. To determine 

Consistency Ratio: Lambda-max = Σ (weighted sum value/ criteria weight)/ n. 

Consistency Index (CI) = (Lambda-max – n) / (n – 1). Consistency Ratio = CI/RI 

 



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Table 1. Random Index table 

 

Size of Matrix 1 2 3 4 5 6 7 8 9 10 

RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 

 

The data collected from the questionnaires are analyzed using MS Excel. After that, the 

consistency ratio (CR) and the relative weights vector of goals are calculated. The CR must be 

less than 0.1 for each pairwise comparison; otherwise, the questionnaire has to be sent again to 

be filled by experts (Vaidya & Kumar, 2004). Each expert's judgment is combined using 

geometric means to derive outcomes, as suggested by Saaty (2008).  Table 2 below shows the 

pairwise comparison scale for AHP preferences: 

 

Table 2. Pairwise Comparison Scale  

 

Judgment of Preferences Numerical Value 

Equally important 1 

Moderately important 3 

Strongly important 5 

Very strongly important 7 

Extremely important 9 

Intermediate values  

Equally to moderately preferred 2 

Moderately to strongly preferred 4 

Strongly to very strongly preferred 6 

Very strongly to extremely preferred 8 

 

The goals for the banks, as suggested by experts, are liquidity risk, Capital Adequacy, 

Market share of the deposit, Market share of Credit, Return on Asset, Return on Equity, and 

reducing Non-Performing Assets. 

 

Table 3. Goals for Banks 

 

Goals Definition 

Liquidity Liquidity risk is the inability of a bank to meet its obligation when it 

arises. Banks manage their liquidity risk through ALM. 

Capital Adequacy Capital Adequacy ratio determines the extent of capital a bank 

requires against its risk-weighted credit exposure to protect it against 

losses before the risk of insolvency. 

Market share of the deposit It shows the bank's share of customer deposits in an aggregate 

deposit of scheduled commercial banks in India. 

Market Share of credit It shows the credit available to banks from the aggregate credit 

facility available to all scheduled commercial banks in India. 

Return on Asset It shows the profit-generating capacity of a bank from its total asset 

available. The higher the ratio better it is for the bank. 

Return on Equity It measures the return on investment invested by shareholders. The 

higher the ratio the better it is for the company. 



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Non-Performing Asset (NPA) The banks want to reduce their nonperforming asset. It is calculated 

by dividing Gross NPA with Gross Advances. The lower the ratio, 

the better it is for the bank. 

 

The results of the AHP are given below in table 4: 

 

Table 4. Weights of Goal as per AHP 

 

Goals Weights (using AHP) 

Market share of credit 0.0504 

Market share of deposits 0.0446 

Return on assets 0.138 

Return on equity 0.133 

Capital adequacy ratio 0.229 

Liquidity risk 0.208 

Non-Performing Asset 0.107 

 

Goal Programming 

The priority scale obtained from AHP is used to weight goals and optimize the assets and 

liabilities. The GP data is obtained from annual reports of OBC banks over the last ten years, i.e., 

from 2010 to 2019 from its website. Secondary data has also been collected from the Reserve 

Bank of India website for analysis. Goal Programming is used for solving the asset-liability 

management problem with the help of LINGO version 17 software. 

Ignizio (1981)developed the following steps to formulate the GP model: 

1.    Define the decision variables 

2.    Define the structural constraints and goal constraints 

3.    Determine the relative weight 

4.    Define the objective function 

5.    State the non-negative requirement 

 

The structural constraints are the statutory constraints and management constraints in the 

bank for the assets and liabilities. Goal constraints are the target to be achieved with positive and 

negative deviations. The objective function in the GP model is to minimize the variations. In this 

paper, weighted goal programming is used where the objective is to minimize the weighted sum 

of goal deviations.   

The weighted Goal Programming as given by Charnes & Cooper (1977)is given below: 

Minimize  

  (1) 

Subject to linear constraints-  

Goal Constraints: 

  (2) 



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Structural constraints: 

  (3) 

With  

 
Where m, p, and n represent goals, structural constraints, and decision variables, respectively.  

Wi negative represents weight assigned to negative deviation and Wi positive represent weight 

assigned to positive deviations. 

Di negative represents the negative deviational variable of the i
th

 goal (underachievement of 

goal). 

Di positive represents the positive deviational variable of the i
th

 constraints (overachievement of 

goal). 

Bi represents the aspiration level or the target value. 

Z= objective function 

Aij= The coefficient associated with variable j in the i
th

 goal  

Xj= the j
th 

decision variables 

 

Decision Variables 

Identification of the decision variables: 

The Indian bank balance sheet has assets and liabilities. These assets and liabilities are the 

decision variables. 

 

Assets 

Cash and Bank Balance 

YA1 = Cash in hand 

YA2 = Balance with RBI 

YA3 = Balance with Banks & Money at call & short notice in India 

YA4 = Balance with Banks & Money at call & short notice outside India 

 

Investments 

YA5 = Investment in government securities 

YA6 = Investment in approved securities 

YA7 = Shares 

YA8 = Debentures 

YA9 = Investment in Subsidiaries/Joint Ventures 

YA10 = Others (Commercial papers, Mutual funds, etc.) 

 

Advances 

YA11 = Bills Purchased & discounted 

YA12 = Cash Credit, Overdrafts, Loans repayable on demand 

YA13 = Term Loans 

YA14 = Advances in Priority Sector 

YA15 = Advances in Banks in India 

 



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FA = Fixed Assets and Intangible assets 

OA = Other Assets 

 

Liabilities 

Shareholders fund 

XL1 = Capital 

XL2 = Reserves & Surplus 

 

Deposits 

XL3 = Demand Deposit 

XL4 = Saving Deposits 

XL5 = Term Deposits 

 

Borrowings 

Borrowings from India 

XL6 = Borrowings from RBI 

XL7 = Borrowings from Banks and other institutions & Agencies 

Borrowings outside India 

XL8 = Borrowings outside India 

 

XL9 = Other Liabilities  

XL10 = Others (including provisions) 

 

Decision Constraints 

1. Total Assets = Total Liabilities 

13                     10  

i= 1YAi + FA + OA = j= 1XLj 

Total Asset (TA) = 2719095661 

 

2. Cash Reserve Ratio = 4% 

YA2 0.04(Net demand and Time Liability) 

YA2 0.04 (XL3 + XL4 + XL5 + XL6 + XL7 + XL9 -YA3 – YA15) 

 

3. Statutory Liquidity Ratio = 19.5% 

Liquid Asset = excess cash and balance with RBI over CRR + investment in govt. 

securities + Investment in approved securities  

 

Liquid Assets (LA) = YA1 + (YA2)– 0.04 (XL3 + XL4 + XL5 + XL6 + XL7 + XL9 -YA3 – 

YA15) + (YA3 + YA5 + YA6 

 

NTDL = XL3 + XL4 + XL5 + XL6 + XL7 + XL9 -YA3 – YA15 

 

YA1 + (YA2)– 0.04 (XL3 + XL4 + XL5 + XL6 + XL7 + XL9 -YA3 – YA15) + (YA3 + YA5 

+ YA6 19.5% (XL3 + XL4 + XL5 + XL6 + XL7 + XL9 -YA3 – YA15) 

 

4. Priority Sector Lending = 40% of the Adjusted Net Banking Credit 



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YA14  0.40 (YA11 + YA12 + YA13) 

5. Investments 

 13         13  

%(i= 1YAi + FA + OA)  (YA5 + YA6 + YA7 +YA8 +YA9 + YA10)  %(i= 1YAi + FA + 

OA) 

               13                   13  

0.26 (i= 1YAi + FA + OA)  (YA5 + YA6 + YA7 +YA8 +YA9 + YA10)  0.30 (i= 1YAi + 

FA + OA) 

 

6. Investments in Government Securities & approved securities 

% (YA5 + YA6 + YA7 +YA8 +YA9 + YA10)  (YA5 + YA6)  % (YA5 + YA6 + YA7 +YA8 

+YA9 + YA10) 

 

0.75 (YA5 + YA6 + YA7 +YA8 +YA9 + YA10)  (YA5 + YA6)  0.85 (YA5 + YA6 + YA7 

+YA8 +YA9 + YA10) 

 

7. Investments in Non-SLR securities 

% (YA5 + YA6 + YA7 +YA8 +YA9 + YA10)  (YA7 +YA8 +YA9 + YA10) %(YA5 + YA6 

+ YA7 +YA8 +YA9 + YA10) 

 

0.15 (YA5 + YA6 + YA7 +YA8 +YA9 + YA10)  (YA7 +YA8 +YA9 + YA10)  0.25 (YA5 + 

YA6 + YA7 +YA8 +YA9 + YA10) 

 

8. Cash & Balance with RBI 

       13      13  

%(i= 1YAi + FA + OA)  (YA1 + YA2)  %(i= 1YAi + FA + OA) 

               13      13  

0.045(i= 1YAi + FA + OA)  (YA1 + YA2)  0.06(i= 1YAi + FA + OA) 

 

9. Balance with Banks & Money at call & short notice in India 

       13         13  

%(i= 1YAi + FA + OA)  (YA3)  %(i= 1YAi + FA + OA) 

 

                13     13  

0.001(i= 1YAi + FA + OA)  (YA3)  0.05(i= 1YAi + FA + OA) 

 

10. Balance with Banks & Money at call & short notice outside India  

      13        13  

%(i= 1YAi + FA + OA)  (YA4)  %(i= 1YAi + FA + OA) 

       13    13  

0(i= 1YAi + FA + OA)  (YA4)  0.01(i= 1YAi + FA + OA) 

 

11. Advances 

      13            13  

%(i= 1YAi + FA + OA)  (YA11 + YA12 + YA13)  %(i= 1YAi + FA + OA) 

               13       13  



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0.58 (i= 1YAi + FA + OA)  (YA11 + YA12 + YA13)  0.65(i= 1YAi + FA + OA) 

 

12. Bills Purchased & discounted 

% (YA11 + YA12 + YA13)    (YA11)  %(YA11 + YA12 + YA13) 

0.006 (YA11 + YA12 + YA13)    (YA11)    0.035 (YA11 + YA12 + YA13) 

 

13. Cash Credit, Overdrafts, Loans repayable on demand 

%(YA11 + YA12 + YA13)    (YA12)    %(YA11 + YA12 + YA13) 

0.35(YA11 + YA12 + YA13)    (YA12)    0.50 (YA11 + YA12 + YA13) 

 

14. Term Loans 

%(YA11 + YA12 + YA13)    (YA13)     % (YA11 + YA12 + YA13) 

0.48 (YA11 + YA12 + YA13)    (YA13)    0.62 (YA11 + YA12 + YA13) 

 

15. Fixed Assets 

        13        

FA = 0.01(i= 1YAi + FA + OA) 

 

16. Other Assets 

13     13  

%(i= 1YAi + FA + OA)  (OA)  %(i= 1YAi + FA + OA) 

13      13  

0.035(i= 1YAi + FA + OA)  (OA)  0.065 (i= 1YAi + FA + OA) 

 

17. Deposits 

        13       13  

%(i= 1YAi + FA + OA)  (XL3 + XL4 + XL5)  %(i= 1YAi + FA + OA) 

              13                 13  

0.85(i= 1YAi + FA + OA)  (XL3 + XL4 + XL5)  0.90(i= 1YAi + FA + OA) 

 

18. Demand Deposit 

%( XL3 + XL4 + XL5)  (XL3)  %( XL3 + XL4 + XL5) 

0.06 (XL3 + XL4 + XL5)  (XL3)  0.09 ( XL3 + XL4 + XL5) 

 

19. Saving Deposit 

%( XL3 + XL4 + XL5)  (XL4)  %( XL3 + XL4 + XL5) 

0.17( XL3 + XL4 + XL5)  (XL4)  0.25( XL3 + XL4 + XL5) 

 

20. Term Deposit 

%( XL3 + XL4 + XL5)  (XL5)  %( XL3 + XL4 + XL5) 

0.68( XL3 + XL4 + XL5)  (XL5)  0.78( XL3 + XL4 + XL5) 

21. Borrowing Limits 

 

13      13  

%(i= 1YAi + FA + OA)  (XL6 + XL7 + XL8)  %(i= 1YAi + FA + OA) 



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                 13     13  

0.025(i= 1YAi + FA + OA)  (XL6 + XL7 + XL8)  0.06(i= 1YAi + FA + OA) 

 

22. Borrowings from RBI 

%( XL6 + XL7 + XL8)  (XL6)  %( XL6 + XL7 + XL8) 

0 ( XL6 + XL7 + XL8)  (XL6)  0.3( XL6 + XL7 + XL8) 

 

23. Borrowings from Banks And other institutions & Agencies 

%( XL6 + XL7 + XL8)  (XL7)  %( XL6 + XL7 + XL8) 

0.64 ( XL6 + XL7 + XL8)  (XL7)  0.98( XL6 + XL7 + XL8) 

 

24. Borrowings outside India 

%( XL6 + XL7 + XL8)  (XL8)  %( XL6 + XL7 + XL8) 

0 ( XL6 + XL7 + XL8)  (XL8)  0.27 ( XL6 + XL7 + XL8) 

 

25. Other liabilities  

       13    13  

%(i= 1YAi + FA + OA)  (XL9)  %(i= 1YAi + FA + OA) 

  13             13  

0.0034(i= 1YAi + FA + OA)  (XL9)  0.0084(i= 1YAi + FA + OA) 

 

26. Provisions 

       13          13  

%(i= 1YAi + FA + OA)  (XL10)  %(i= 1YAi + FA + OA) 

                13     13  

0.014(i= 1YAi + FA + OA)  (XL10)  0.026(i= 1YAi + FA + OA) 

 

Goal Constraints 

1. Market Share of Credit 

Total Credit of Bank = YA15 + YA16 + YA17 

Aggregate Credit (AGCREDIT)= 97674300000 

YA11+ YA12+ YA13+ d1
- 
- d1

+ 
 = Share in aggregate Credit of Scheduled commercial bank 

YA11+ YA12+ YA13+ d1
- 
- d1

+ 
 = 0.018(97674300000) 

YA11+ YA12+ YA13+ d1
- 
- d1

+ 
 = 1758137400 

 

2. Market Share of Deposit 
Total deposit of bank = XL3 + XL4 + XL5 

Aggregate Deposit (AGDEPOSIT )=  125725860000 

XL3 + XL4 + XL5 + d2
- 
- d2

+ 
 = Aggregate deposit of Scheduled commercial bank 

XL3 + XL4 + XL5 + d2
- 
- d2

+ 
 = 0.0185(125725860000) 

XL3 + XL4 + XL5 + d2
- 
- d2

+ 
 =2325928410 

 

3. Return on equity 
0.0046(XL1 + XL2) + d3

- 
- d3

+ 
 = Net Profit 

 

 



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4. Return on Asset 

  13      

0.0004 (i= 1YAi + FA + OA) + d4
- 
- d4

+ 
= Net Profit 

 

5. Capital adequacy ratio 
Capital + reserves = 11.5 % (risk weighted assets) 

 

XL1 + XL2 >= 0.115*( 0*( YA1 + YA2 + YA3 + YA4) + 0.5*( YA5 + YA6) + 1.25*( YA7 

+ YA8 + YA9 + YA10) + 1*( YA11 + YA12) + 1.25*YA13) 

 

XL1 + XL2 + d5
- 
- d5

+ 
= 0.115*( 0*( YA1 + YA2 + YA3 + YA4) + 0.5*( YA5 + YA6) + 

1.25*( YA7 + YA8 + YA9 + YA10) + 1*( YA11 + YA12) + 1.25*YA13) 

 

6. Liquidity risk- (liquidity coverage ratio) 
HQLA= Cash+ excess balance with RBI over CRR + Excess govt. securities over SLR + 

15% of NTDL 

Cashflow in 30 days = 374319700 

 

LCR = HQLA/ Cashflow in 30 days 

LCR>=100% 

HQLA + d6
- 
- d6

+ 
= 374319700 

HQLA= YA1 + EXCASH + YA5 - 0.195*NTDL + 0.15*NTDL 

EXCASH= YA2 - 0.04*NTDL 

 

7. Gross NPA NPA<= 10% of Gross Advances (YA11 YA12 + YA13) 

 

NPA + d7
- 
- d7

+
 = 10% (YA11 YA12 + YA13) 

 

The % is the multiplier symbol here and it is estimated on the basis of the past 10-year 

data of OBC bank. 

 

Objective function 

MIN = Z 

Where, 

Z= 0.0504*D1MINUS+ 0.0446*D2MINUS+ 0.138*D3MINUS + 0.133*D4MINUS + 

0.229*D5MINUS + 0.208*D6MINUS + 0.107*D7PLUS 

 

RESULTS AND ANALYSIS 

The model developed can be applied to any bank by modifying the multiplier that appears in 

front of each expression as per their balance sheet structure. The multiplier can be derived after 

examining the past balance sheet items. In the case of OBC bank, the data for the past 10-years 

has been studied from 2010-2019. All the figures are presented in ‘000. In this paper, the real 

balance sheet of 2019 has been compared with the model value for 2019. Any deviation in real 

value and model value is recorded. Optimized assets and liabilities of OBC banks have been 

calculated, which shows that the bank can reallocate its assets and liabilities and achieve more 

than its current position. The model has statutory constraints such as Cash Reserve Ratio (CRR), 



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14 

Statutory Liquidity Ratio (SLR), Priority Sector Lending (PSL), and Capital Adequacy Ratio 

(CAR). In 2019, CRR was 4%, SLR was 19.5%, PSL was 40% and CAR was 11.5%. It also 

shows at what level the bank can be optimized. Table 5 presents the results of the model 

developed in the methodology section. 

 

Table 5. Real value Vs. Model Value  

 

Oriental Bank of Commerce 2019 

figures in '000 

    Real Model Deviation 

Assets         

Cash and bank YA1 & YA2 111938820 122359300 -10420480 

Money at call YA3 & YA4 52822048 2719096 50102952 

SLR investment YA5 & YA6 583275898 600920200 -17644302 

Non SLR investment 

YA7, YA8, YA9, 

YA10 209402321 106044700 103357621 

Advances  

YA11, YA12, 

YA13 1592848135 1758137410 -165289275 

Fixed asset FA 25892722 33746640 -7853918 

Other assets OA 142915717 95168350 47747367 

Total Asset   2719095661 2719095696 -35 

          

Liabilities         

Capital & reserves XL1 & XL2 189012435 277877600 -88865165 

Demand deposit XL3 142610850 209333600 -66722750 

Saving deposit XL4 541258880 534963500 6295380 

Term deposit XL5 1642584046 1581631000 60953046 

Borrowing in India XL6, XL7 141193671 67977388 73216283 

Borrowing outside India XL8 0 0 0 

Other liabilities XL9 16850484 9245268 7605216 

Provisions XL10 45585295 38067340 7517955 

Total liabilities   2719095661 2719095696 -35 

          

Bills Purchased and 

Discounted YA11 31570620 61534810 -29964190 

Cash Credits, Overdrafts, 

and Loans repayable on 

demand YA12 756933270 795908500 -38975230 

Term loans YA13 804344245 900694100 -96349855 

Priority lending YA14 591650822 703255000 -111604178 

Net profit   549938 1087638 -537700 

 



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Table 6. Computation of major goals and constraints 

 

Modal Values of Goal Constraints and 

Statutory constraints 

Constraints 

Model 

Values 

CRR % 5.13 

SLR % 26.47 

NTDL 2382850000 

HQLA 374319700 

Cash Flow For 30 Days 374319700 

Return on Asset % 0.04 

Return on Equity % 0.39 

Liquid Asset 630684500 

Market Share of Credit 1.80 

Market Share of Deposit 1.85 

Capital Adequacy Ratio 11.50 

Risk-Weighted Asset 2416327000  

Liquidity Coverage Ratio % 100 

Priority Sector Lending 40 

 

The above table 6 shows that the model has satisfied all the statutory constraints and 

decision constraints. The CRR achieved here is 5.13%, and SLR is 26.47%. The credit in priority 

sector lending is 40%. The total asset is also equal to the total liability. In the model, the total 

asset's value was kept the same as real total assets in 2019. The model has successfully achieved 

all seven goals. The objective is to minimize the deviations that negatively affect the bank's 

performance. There is no underachievement of goals. The actual market share of the credit of 

OBC bank is 1.63%, whereas we have achieved 1.80% in the model. It shows that the bank can 

increase its market share of credit, i.e., to reach the optimization level. The real and model 

market share of the deposit is 1.85% for the bank. It shows that the bank has no scope to increase 

the market share of the deposit without affecting its performance.  

Likewise, the bank generates a 0.04% return on an asset, which is better than the actual 

value, i.e., 0.02%. Here the bank can earn a higher profit if using its assets and liabilities 

judiciously. The bank targets to achieve a 0.46% return on equity. However, it has acquired 

0.39% (0.4% approximately). This figure is still better than the real return on equity of 0.3%. If 

the bank could generate 190598.7 more profit, it could achieve the target of 0.46%. However, 

their model return on equity is higher than the actual value. In the model, the bank has a capital 

adequacy ratio of 11.50%, as targeted. The liquidity coverage ratio is 100%, which shows that 

the bank has no risk of liquidity. The Gross NPA is kept 10% and achieved by the model. In real 

bank has 12.66% of GNPA ratio to gross advances.  

Table 7 presented below shows that the objective value is 0, which depicts that deviation 

is minimized to value 0. Therefore, it can be said that banks can increase their credit share in the 

market and generate more interest income and satisfy all the statutory constraints. 

 



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Table 7. Achievement of goals 

 

  GOALS OBJECTIVE VALUE 

D1 MINUS Market share of credit 0 

D2 MINUS 

Market share of the 

deposit 0 

D3 MINUS Return on equity 0 

D4 MINUS Return on Asset 0 

D5 MINUS Capital Adequacy  0 

D6 MINUS Liquidity risk 0 

D7 PLUS NPA 0 

 

The ability to test the sensitivity of the model is the best advantage of goal programming. 

The variables can be changed to test the effect on the optimal solution. The model has tested 

sensitivity to arrive at the optimal solution where the deviation is minimized to 0. Any change in 

the constraint may lead to a solution where deviations from the target may arise. It is an integral 

part of the solution to test the effect of parameters for sensitivity. There are high chances of 

frequent change in goals, priorities, and available resources in the real world. Any change will 

result in the alteration of the optimum solution (Lee, 1981). 

 

FINDINGS 
The Goal Programming model is an effective and straightforward method to set targets and 

constraints to generate an optimum solution. In goal programming, the goal constraints are set 

equal to the target, which may or may not achieved. However, the model will generate an 

optimum solution with deviations that shows all goals are not attainable, yet the best available 

solution is derived. In this paper, the model has developed the asset and liability mix that fulfill 

all the goals and constraints. The bank can deploy its resources to generate more returns. If a 

bank can increase its market share of deposits from 1.63% to 1.8%, it can create more revenue 

and achieve higher profitability. The bank can restructure its assets and liabilities. A decline in 

money at call with other banks, and an increase in investment will accelerate the income-earning 

capacity of the bank. The bank should decrease its fund in non-income generating assets and 

reinvest those funds in income-generating assets. The optimum utilization of fixed and current 

assets can also increase the efficiency of the bank (Tanwar et al., 2020).This model reveals areas 

that need focus to attain an optimal level. No institution can run at an optimal level until it knows 

the particular domain where it can improve. This model helps in pointing out such items in the 

balance sheet, which need more attention. 

This model can be used by banks' management to set its target and management 

constraints to generate an optimal mix of assets and liabilities. This model is helpful in planning, 

forecasting, and budgeting for banks and other institutions. Even a bank can prioritize its goals 

using the Preemptive Goal Programming method, where the most important goals are optimized 

before lower-level goals are considered. The bank's management can analyze how to achieve the 

targets and how it affects the bank's performance and regulations. 

 

 

 



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LIMITATIONS 
The model has used past data to arrive at risk weights of assets. The risk weight is difficult to 

derive for all assets’ components. The model can be used more precisely by bank officials as 

they know the risk weights and other regulations. The effect of interest rate on profitability has 

not been considered. In future work, I will use weighted lexicographic goal programming and 

derive the impact of interest rate on the bank's profitability. It can also avoid upper bound on 

decision variables and determine how it will impact the asset and liability mix.  

  

REFERENCES 
Chambers, D., & Charnes, A. (1961). Inter-Temporal Analysis and Optimization of Bank 

Portfolios. Management Science, 7(4), 393–410. https://doi.org/10.1287/mnsc.7.4.393 

 

Charnes, A., & Cooper, W. W. (1977). Goal programming and multiple objective optimizations: 

Part 1. European Journal of Operational Research, 1(1), 39–54. 

https://doi.org/https://doi.org/10.1016/S0377-2217(77)81007-2 

 

Chronology of events. (n.d.). Reserve Bank of India. 

https://www.rbi.org.in/Scripts/chro_1968.aspx 

 

Cohen, K. J., & Hammer, F. S. (1967). Linear Programming and Optimal Bank Asset 

Management Decisions. The Journal of Finance, 22(2), 147–165. 

https://doi.org/10.2307/2325551 

 

D. Giokas, & Vassiloglou, M. (1991). A goal programming model for bank assets and liabilities 

management. European Journal of Operational Research, 50(1), 48–60. 

https://doi.org/https://doi.org/10.1016/0377-2217(91)90038-W 

 

Dash, M., & Pathak, R. (2011). A Linear Programming Model for Assessing Asset- Liability 

Management in Banks. The IUP Journal of Financial Risk Management : IJFRM, 8(1), 50–

67. 

 

Eatman, J., & Sealey, C. (1979). A multiobjective linear programming model for commercial 

bank balance sheet management. Journal of Bank Research, 9, 227–236. 

 

Fabozzi, F. J., & Konishi, A. (1991). Asset/liability Management: Investment Strategies, 

Liquidity Requirements, and Risk Controls for Banks and Thrifts. Probus Publishing 

Company. 

 

Fielitz, B. D., & Loeffler, T. A. (1979). A Linear Programming Model for Commercial Bank 

Liquidity Management. Financial Management, 8(3), 41–50. https://doi.org/DOI: 

10.2307/3665037 

 

Halim, B. A., Karim, H. A., Fahami, N. A., Mahad, N. F., Nordin, S. K. S., & Hassan, N. (2015). 

Bank Financial Statement Management Using A Goal Programming Model. Procedia - 

Social and Behavioral Sciences, 211(November), 498–504. 

https://doi.org/10.1016/j.sbspro.2015.11.066 



https://www.cribfb.com/journal/index.php/ijfb                               Indian Journal of Finance and Banking                    Vol. 4, No. 4; 2020 

 

18 

 

Hunjak, T., & Jakovčević, D. (2001). AHP Based Model for Bank Performance Evaluation and 

Rating. Proceedings of 6th International Symposium on Analytic Hierarchy Process 

(ISAHP 2001), 149–158. 

 

Ignizio, J. P. (1981). Linear Programming in Single and Multiple Objective Systems. Prentice-

Hall International Series in Industrial & Systems Engineering). 

 

Jain, M. K., Dalela, A. K., & Tiwari, S. K. (2010). Application of Fuzzy Mathematical Model in 

Assets-Liabilities. International Journal of Trade, Economics and Finance, 1(3), 247–253. 

https://doi.org/10.7763/ijtef.2010.v1.45 

 

Javalgi, R. G., Armacost, R. L., & Hosseini, J. C. (1989). Using the analytic hierarchy process 

for bank management: Analysis of consumer bank selection decisions. Journal of Business 

Research, 19(1), 33–49. https://doi.org/10.1016/0148-2963(89)90039-8 

 

Kamil, K. H., Ismail, A. G., & Shahimi, S. S. (2013). Use of the Analytic Hierarchy Process ( 

AHP ) to Derive Priorities in the Management of Assets and liabilities in Accordance with 

Islamic Banking Objectives. Malaysian Management Review, July-December, 39–51. 

 

Kosmidou, K., & Zopounidis, C. (2002). An optimization scenario methodology for bank asset 

liability management. Operational Research, 2(2), 279–287. 

https://doi.org/http://dx.doi.org/10.1007/BF02936331 

 

Kruger, M. (2011). A Goal Programming Approach to Strategic Bank Balance Sheet 

Management. SAS Global Forum 2011 Banking, Financal Services and Insurance, 1–11. 

 

Lee, S. M. (1981). Goal Programming. In A. G. Holzman (Ed.), Mathematical Programming for 

Operations Researchers and Computer Scientists. Marcel Dekker Inc. 

 

Markowitz, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. John 

Wiley & Sons. 

 

Naderi, S., Minouei, M., & Gashti, H. P. (2013). Asset and Liability Optimal Management 

Mathematical Modeling for Bank. Journal of Basic and Applied Scientific Research, 3(1), 

484–493. 

 

Rezaei, S. T., Ameleh, K. N., Ghalmegh, K., & Ramezanzadeh, A. (2013). Management of 

Balance Sheet Bank Using Goal Programming Model (GP) and Fuzzy Analytic Hierarchy 

Process (FAHP). Semantic Scholar. 

 

Romanyuk, Y. (2010). Asset-Liability Management : An Overview. In Bank of Canada 

Discussion Paper. 

 

Saaty, T. L. (2008). Decision making with the Analytic Hierarchy Process. International Journal 

of Services Sciences, 1(1), 83–98. https://doi.org/10.1504/ijssci.2008.017590 



https://www.cribfb.com/journal/index.php/ijfb                               Indian Journal of Finance and Banking                    Vol. 4, No. 4; 2020 

 

19 

 

Samuel, G. (2011). The effect of Asset liability management on profitability of National 

Investment Bank in the New Jyabeng municipality. 1–61. 

 

Sedzro, K., Marouane, A., & Assogbavi, T. (2012). Analytical Hierarchy Process and Goal 

Programming Approach for Asset Allocation. Journal of Mathematical Finance, 02(01), 

96–104. https://doi.org/10.4236/jmf.2012.21012 

 

Srdevic, Z., Blagojevic, B., & Srdevic, B. (2011). AHP based group decision making in ranking 

loan applicants for purchasing irrigation equipment: A case study. Bulgarian Journal of 

Agricultural Science, 17(4), 531–543. 

 

Tanwar, J., Seth, H., Vaish, A. K., & Rao, N. V. M. (2020). Revisiting the Efficiency of Indian 

Banking Sector: An Analysis of Comparative Models Through Data Envelopment Analysis. 

Indian Journal of Finance and Banking, 4(1), 92–108. 

https://doi.org/10.46281/ijfb.v4i1.585 

 

Tummala, V. M. R., Smith, J. R., & Uppuluri, V. R. R. (1983). Evaulating Commercial Credit 

Decisions by Analytical Hierarchy Process. ASCI Journal of Management, 12(1 & 2), 48–

56. 

 

Viswanathan, P. K., & Balasubramanian, G. (2007). Modelling asset allocation for banks- A goal 

programming approach. Journal of National Institute of Bank Management-Prajnan, 

XXXVI(1), 135–145. 

 

Viswanathan, P. K., Ranganatham, M., & Balasubramanian, G. (2014). Modeling asset 

allocation and liability composition for Indian banks. Managerial Finance, 40(7), 700–723. 

https://doi.org/10.1108/MF-10-2013-0276 

 

Wang, Y. M., & Chin, K. S. (2008). A linear goal programming priority method for fuzzy 

analytic hierarchy process and its applications in new product screening. International 

Journal of Approximate Reasoning, 49(2), 451–465. 

https://doi.org/10.1016/j.ijar.2008.04.004 

 

Ziemba, W. T., & Mulvey, J. M. (1998). Worldwide Asset and Liability Modeling. Publications 

of the Newton Institute. 

 

 

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