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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.17 No.2 pp.311-317
DOI : https://doi.org/10.7232/iems.2018.17.2.311

# Design and Optimization of the Asset and Liability Model based on the Multiple-Objective Decision-Making View

Faculty of Management and Accounting, Yadegar-e-Emam Branch, Islamic Azad University, Shahre-Rey, Iran
Corresponding Author, E-mail: a.dehghan@aftermail.ir
July 26, 2017 October 29, 2017 November 3, 2017

## ABSTRACT

Nowadays, asset-liability management is a strategic method of planning and by turning it into short-term operating plans a targeted profit and risk control can be ensured. The main purpose of this research is to provide a mathematical model for optimizing assets and liabilities in an Iranian bank. In this research, considering the objectives of the studied bank, the structural and ideological constraints were considered as well as the legal requirements of the ideal planning model. At first, using fuzzy hierarchical analysis, goals were defined and priorities and their orders of significance are specified. Then, using the ideal planning of model within three years the balance sheet was tested and the results of the model were compared to actual results. Obtained results of the model and comparing with the actual results and evaluating the deviation between the ideal and actual values of variables, indicated the increased efficiency of resource allocation optimization model in the bank. The results of the model will help to optimize the efficient allocation of resources.

## 1. INTRODUCTION

The development of business activities has brought up the requirement to the services of banking institutions. Therefore the necessity of existence of a payment means to measure the value and collection of receivables from customers, despite the potential risks arising from the transfer of money, became more tangible. So the banks emerged.

Today, banking plays an important role in microeconomics and macroeconomics of countries. In fact, banks are levers that implement government’s macroeconomic policies and control the main economic issues such as inflation and unemployment. Thus, it is clear that the success of banks in execution of their duties has significant and positive impact on the entire economy of the country and caused sustainable economic growth. Conversely, if banks are not able to show their positive performance and good results in the loss of financial resources, negative results of poor performance will be destructive for the whole economy (Khalili, 2007).

For this reason, banks must continually monitor their assets and liabilities. Bank’s assets and liabilities management means the planning for all assets and liabilities of the bank under different requirements and through the combined balance sheets of banks and bank management objectives. Legal and administrative requirements and market conditions is done in order to reduce interest rate risk, liquidity and strengthening of the bank. In addition Assets and Liability Management (ALM) is an index of the relationship between risk and reward. Therefore, using effective and sometimes innovative solutions in order to achieve the desired reward, always begins with an analysis of the balance sheet and internal and external check items and if the bank be successful in risk control, Not only they perpetuate their survival, but also protect their critical conditions.

In fact asset-liability management is a set of designed management tools to be exposed to the risks which reduce banks profits and efficiency. In ALM, expenses related to the performance of loans, deposits and investment portfolio management are considered as the main components of the balance sheet. In general all financial decisions of a bank or a financial institution are reflected in the balance sheet and in fact the institution statues at certain times are determined. That is why the balance sheet management are considered equivalent to assets and liabilities management (Alhumaidah, 2015).

ALM strategies can be referred to mathematical planning. Mathematical planning includes the expression of various limitations in the form of mathematical equations which take all the essential aspects of the ALM into account in mathematical form. The most successful mathematical models are used for ideal planning (Mehrabi, 2014). The main purpose of this research is to investigate the rate of deviation of the performance of Iran’s public banks from the goals set using the mathematical model for each of the objectives. For this purpose, we first assume that determining the optimal answer using the model for satisfactory bank performance is possible. Also, the amount of deviation from the goals of the bank is favorable by using the model for each of the goals.

## 2. LITERATURE REVIEW

### 2.1. ALM

In the process of developing a global bank and financial activities, the issue of how to manage assets and liabilities in banks and financial institutions has always been regarded as an important matter and it is an integral part of this activity. For example, between 1940-1950, when the banks with large amounts of funds and with low costs were faced by various forms of deposits and savings, management attention is focused on managing these funds and thus “asset management” was regarded as a dominant in this period. Lack of progress of this situation and reducing bank funds and financial institutions over subsequent years and during 1960s, led the managers to manage the funds at their disposal more economical to implement. Thu economic prosperity demand for borrowing and lending from banks are increased. Books responses to the growing demands and financing, were forced to run in new debts and their debts management adopted. Thus, in the 1960s and early 1970s, dominant procedures of “debt management” in the management of banks’ balance sheets occurred. Global inflation, volatility in interest rates and a severe economic downturn in the years led to the mid-1970s attracted the attention of banks on both assets and liabilities and they consider comprehensive management of both columns of balance sheet. Use the simultaneous management practices assets and liabilities as "assets and liabilities management (ALM), mentioned years as a key issue in the activities of banks and financial.

So that during the 1980s, the bank faced with the volatility of interest rates and inflation, while intense competition between them rose in the financial markets and deregulation. Management techniques with liabilities and assets formed dominant funds for funds management. The situation in the 1990s as banks faced with an economic and financial environment has changed the agenda of many countries. In recent years, capital flows between countries benefit of a strong growth and banks were exposed to more competition and different types of risks. Advances in technology and the use of financial instruments and the complexity of the tools and create a variety of different items liabilities and assets in banks and financial institutions, has increased the importance of management of these areas more than ever (Armand, 2013).

### 2.2. Decision-Making Models with Multiple Goals

In the past, many decision-making models were used based on the assumption that the objective of each company is maximizing shareholders’ wealth. But today’s companies are complex sets and have multiple stakeholders interacted with each other. In such circumstances, maximizing shareholders’ wealth is facing constraints such as risk, liquidity, social responsibility, environmental protection, employee’s welfare and other issues which should be considered. In this case one of the best methods is using multi-criteria decision-making model. In recent years, various models of operations research in the field of financial management using multi-criteria decisionmaking models is extended. Several purposes can be considered using multi-criteria decision-making models. Traditionally, two-objectives of risk versus return and the balance between risk and return in order to achieve the ultimate goal has been raised. The solution to such a situation is the application of the decision-making model of a criterion, which is well-documented in many text books. What are unclear, are new solutions that they can accomplish more than two goals. In such circumstances, goal programming model as a multi-criteria decision-making model can be used (Khalili, 2007).

### 2.3. Concepts of Ideal Planning

One method of decision-making with multiple objectives is ideal planning which was discussed for the first time in 1967 by “Charnes” and “Cooper” to remove the impossible conditions to meet the objectives in the linear planning problems resulting from conflicts. This method later was developed with ideal planning theory priorities by “Lee.” Ideal planning is a special type of linear programming with multiple and contradictory goals, in terms of importance in a way that low level targets are taken into consideration when the high-level goals are met. In other words, Goal Programming (GP) shows a move toward several objectives at the same time. Unlike the linear planning that maximizes or minimizes the targets, GP minimizes deviation between targets and actual results. Ideal planning has many attractions because it match more with practical decision-making (Islami and Talangy, 2000).

In order to create a clear understanding of ideal planning, understanding following concepts and terms is essential:

Purpose: The terms and mathematical relations that reflect the interests of decision makers. These demands may be “to maximize profits” or “to minimize the cost.”

Tendency level: specified value that the decision maker is seeking. In other words, the decision for any purpose, determines an optimum level of numerical targets for assigning or deformation to the number of ideals used.

Ideals: the goal defined for that level tends to be target phrase associated with any desired level of number is called ideal.

Deviation from ideal: Since all appropriate levels cannot be met simultaneously, it can be resulted in deviate from the ideal. In other words, the difference between wants and what the resulting deviation from the ideal is called deviation from ideal. Deviation from the ideal is shown with “d”. Excess amount of goals with d+ and the fraction of the desired ideal with d- is shown (Mehregan, 2015).

### 2.4. Steps of Ideal Planning

• Defining decision variables

• Defining deviation variables from the ideal

• Formulation of constraint equations

• Formulation of the objective function

### 2.5. Fuzzy Analytic Hierarchy Process (FAHP)

Analytic Hierarchy Process (AHP) is one of the MADM methods in order to decide and choose an option from multiple-decision options used. The method was invented in 1980 by Saati. This complicated technique based on mutual works examination. AHP method is based on pair wise comparisons. In this method of decision-making by providing a decision hierarchy tree, the work begins, tree, indices and options shows the decision. Then a series of paired comparisons is formed, the weight comparison of each factor in line with competition options specified. Finally AHP combined matrix of pair wise comparisons so that determine the optimal decision (Azar and Faraji, 2013).

In Studying he AHP, it should be noted that in traditional analytic hierarchy process, there is not the possibility of reflecting the style of human thinking. Using fuzzy numbers is more compatible with verbal expressions, and sometimes human vague, so it is better to investigate using fuzzy numbers to make decisions in the real world.

In view of the shortcomings of the first phase of AHP method, Buckley in 1985 developed a new method for fuzzy AHP technique (Habibi et al., 2014).

In 1992, a method entitled analysis method was developed by Chang. Later, the technique was improved by Chang. Chang developed the method for computing the fuzzy analytical hierarchy. The numbers used in this method is fuzzy triangular numbers. Chang generalized AHP technique to phase space using the concept of the feasibility.

In fact, fuzzy logic is a very powerful tool that can be used to quantify the incomplete data. Generally, it can be said that the theory of fuzzy sets can be a valuable tool in addressing issues through multi-objective decisionmaking (Ramanathan and Ganesh, 1995).

### 2.6. Integration of Ideal Planning Model with Fuzzy Analytical Hierarchy

Ideal planning is a structured approach for identifying and evaluating solutions based on the priorities or weights assigned to the goals.

Ideal planning is a systematic method for determination of the relative importance and priority when ranking is not ideal. However, “AHP” has the ability to use it and fix its weakness by ideal planning model. Figure 1 shows the decision-making process based on an integrated system of two mathematical models (Lawrence et al., 2000).

### 2.7. Literature Review

Alizadeh (2016), using ALM and an ideal planning model found the optimal balance sheet composition in order to maximize profits with optimal risk. The results of optimizing the balance sheet of the five banks admitted to the Stock Exchange showed that the optimum combination of assets and liabilities of banks were not significant .

Izadi et al. (2013), proposed to acquire the balance sheets of commercial banks in 2011, with the goal of maximizing shareholders’ wealth, as well as taking into account the limitations of the existing structure, using multi-objective decision making methods. The results of the study showed that all expected targets for market risk, and deviations from ideals were fully realized except for market risk which was zero.

Islami et al. (2011), examined ideal planning model in their study in one of the banks. The results showed that using ideal planning model can be more efficient in order to assist the efficient allocation of resources .

Ebrahimi (2010), using hierarchical analysis technique of ideal planning model to manage assets and liabilities corresponding to Tejarat bank and goals such as capital adequacy and liquidity maximized .

In Alhumaidah (2015) research, two optimization models were provided for the withdrawal of deposits from the central bank of Arabia and has been regularly substantial amount. Both the volume and the possibility of accidental outflow of deposits as a possible event in the study of its capital structure are considered. The second model includes external loans and as an option to increase liquidity. The results of the study showed that the cost of borrowing cash and its non-linearly is increased .

Arewa et al. (2013), examined the ALM studying UBA Bank’s financial statements and based on the ideal planning techniques, the result showed that it is not possible for the bank to reduce its debt or raise other indicators included in the financial statements, reduced. Accordingly, they concluded that the bank must convert quickly their debt to assets.

The analysis of asset and liability management at the Bank of India by Dash et al. (2011) was performed. They provide a linear model for the evaluation of assets and liabilities and they found that public sector banks are the best positioned considering asset-liability management, maintaining profitability, liquidity constraints satisfaction and reducing exposure to interest rate risk .

## 3. METHODOLOGY

This study is practical research and a case in which the structure of the financial system and the relationship between the variables of balance sheet items of public banks are recognized in order to identify the prevailing balance sheet items and then according to the goals, limitations and requirements governing the banking system and the studied bank, the model constraints are defined. Constraints and objectives presented in the model has been accounted mainly through distributing questionnaires among distinguished banking experts and based on the financial information and requirements set by the Central Bank of Iran.

In terms of performance, the study included the literature review related to the research and quantitative models, problem statement, selecting the desired model, modeling and solving the model. This study is conducted using data obtained from the bank’s financial statements in the period of 2013 to 2015. Data collected from the documents obtained in these banks and banking regulations of the Central Bank of the Islamic Republic of Iran, while the obtained information was provided by the questionnaire among the managers who were associated with the subject.

## 4. RESULTS AND DISCUSSION

The model used in this research is the hybrid model of FAHP and GP. The analysis phase is to extract the hierarchical priorities and by engaging them in the target function and restrictions according to Central Bank regulations and bank policies which were collected and compiled in a goal-programming model, the model simulations assessed by using the software Lingo©.

Finally, the obtained data from model is compared to actual data in the financial statements of the bank. On the basis of a strategy document announced by Iranian Ministry of Economic Affairs and Finance to promote the country’s wealth creation, State-owned banks were obliged to reduce their non-current receivables and to increase their capital by selling surplus property and transfer their surplus power company’s facilities to increase their ratings.

Based on interviews with top managers of the bank who were all banking elite, intended goals based on the declared strategy document aims identified and to determine the weighting of their priorities and objectives, the questionnaire was developed. Then, using fuzzy hierarchical analysis and their weights the priority targets were determined which are as Table 1:

### 4.1. The Decision Variables

With regard to the items in the balance sheet, Goal programming model parameters are extracted. In this regard, the operating variables used are introduced in Table 2:

### 4.2. Goals and Limitation

$M i n z = 0.45 d 1 − + 0.22 d 2 − + 0.15 ( d 3 + + d 3 − ) + 0.13 d 4 + + 0.05 ( d 6 + + d 6 − )$
(1)

$( i1 × x4 ) + ( i2 × x5 ) + ( i3 × x7 ) + ( i4 × x6 ) + ( i5 × x12 ) − ( i × y5 ) − ( 1 . 5 % × ( x4 + x5 ) ) + d 1 − + d 1 + = 0$
(2)

$99 .0 66 / [ 0 % ( x1 + x2 + x4 ) + 2 0 % ( x1 0 + x3 ) + 1 00 % ( x3 + x7 + x8 + x9 ) + ( 2 0 % × ( x11 + x12 ) ) + ( 1 00 % × ( x13 ) ) ] + d 2 − + d 2 + = 1$
(3)

(4)

$X1 − 1 . 5 % ( Y3 + Y4 + Y5 + Y6 + Y1 ) + d 4 − + d 4 + = 0$
(5)

$X8 − ( 0. 3 × Y9 ) + d 6 − + d 6 + = 0$
(6)

$X1 ≤ 3 % × ( Y1 + Y3 + Y4 + Y5 + Y6) ≥ 2 % × ( Y1 + Y3 + Y4 + Y5 + Y6 )$
(7)

$X2 = 13 . 5 % ( Y1 + Y3 + Y4 + Y5 + Y6 )$
(8)

$X3 ≥ 3 % × ( Y1 + Y3 + Y4 + Y5 + Y6 )$
(9)

(10)

(11)

(12)

(13)

(14)

$X9 = 0.0 3 × Y5$
(15)

$0.0 7(99 .0 66) ≥ Y8 ≥ 0$
(16)

$X11 = Y1 0$
(17)

$X12 = Y11 − Y12$
(18)

$X13 = Y12 − Y13$
(19)

$X14 = Y13 − Y14$
(20)

(21)

(22)

The objective function (equation (1)) represents at least the amount of deviation of each of the ideals that have been defined as unequal. Equation 2 represents the objective earnings performance (increased profits). In the second constraint (Equation 3) the purpose of capital adequacy is determined by dividing the capital base which is calculated based on the weighted assets.

The objective defined in Equation 4, is facility to deposit ratio.

Equation 5 represents the liquidity target which is 1.5% of the total resources and should be allocated for cash with a high degree of liquidity. Equation 6 shows the relationship between the model and the amount of fixed assets in the Bank.

Equation 7 is the introduction of limitation of cash with the explanation that at least 3% of total deposits and liability existed at the central bank.

Equation 8, disinfection relationship is determined how that the law should deposit ratio of 13.5% of total resources. According to equation 9, it is required that the receivables from banks and other institutions be at least 3% of total deposits. According to equation 10, grants in the public sector lays between 20%-23%. Equation 11 defined facilities in the private sector amount between 77%-88%. Equation 12 represents maximum order bonds and investments. This variable should be 40% of the bank’s capital base (capital base of the bank: 99.066 billion Rials). Equation 13 determines that investment and partnerships must be between 2.5 and 3% of the balance sheet. Equation 14, considers fixed-asset up to 30% in capital base Bank. Equation 15, considers the other assets equivalent to 3% of the balance sheet. Equation 16 calculated items between 0 to 7% of the bank’s capital base.

Equation 17 to 20, considered the model requires that the balance sheet for equality before the following items. Equation 21 represents the relationship between accounting principle, equality of resources and the balance sheet. Equation 22 defines the scope of variables.

The values of the parameters and variables of the model in real bank balance sheets between 2012 and 2014 are obtained and presented in Table 3.

## 5. CONCLUSION

Regarding liquidity should be noted that high liquidity in banks and credit institutions perceived as cost and revenue-generating opportunities in other areas of banking will become maintenance costs. Deviation in additional liquidity in 2012 was the opportunity for such investments from the bank. The deviation in long-term investment deposit indicates the appropriate utilization of resources and should not be injected to the deviation in costs of banks. The high volume of fixed assets should also be considered. Bank by decreasing fixed assets to 30% of equity (the regulations) could invest in assets such as investments and partnerships and to take action to increase profitability. The bank managers can use the model to identify surplus funds with the approval of the Central Bank of the funds invest at higher rates. By comparing the results of the actual balance sheet in the years 2012, 2013 and 2014 respectively, 39.901, 59.816, and 67.978 billion Rials surplus funds were calculated, which can be used by the managers to increase revenue.

## Figure

Process of decision-making in ideal planning model.

## Table

Priorities and normal weights of the FAHP model

Decision-making variables of the model

Forecast balance sheet items using goal programming model

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