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Abstract-In economic and finance, function of modelling and optimization is substantial. In fact, by using modelling we can implement, analyze, and control different theories of economic and finance in the market. Bank's asset and liability management is one of the most important areas of study in finance. In this structure, bank's asset and liability portfolio including lending, bonds and received deposit is optimized by expressing objective and constraint regarding different contract positions. In this paper, the application of Operation Research in the structure of modelling and optimization of bank's asset and liability management is so obvious. In fact, it is an instrument to find the highest level of utility. In this research, we start with defining the concept of special finance ratio in bank's balance sheet, then we consider notation for any decision variable. With due attention to these definitions, we wrote ratio in the form of mathematics formula and this is of importance in the body of this paper; and its distinction from other researches is the using of financial ratio for optimization. In the construction of this ratio formulation, some ratio are objectives and others are constraints guiding us to find mathematical programming and then to optimize it. In the construction of this formulation, there are absolute phrases and some objectives with goal, so we have goal fractional multi-objectives problems that in the part of the solving method of the paper, we present a method by change of variables. After solving this problem, we design bank's behavioral policies and/or we can compare the optimized state with what has happened. Index Terms-Modelling and optimization, fractional programming, goal programming, Asset and liability management. I. INTRODUCTIONIn every society, the bank is one of the main economic entities. Collecting the funds and allocating them correctly and injecting them to the industries are among of the main jobs in which banks play the important role. Undoubtedly, correctly allocating these financial resources is a substantial principle and a consolidated support for the banks so that they are directed in a way to get rid of any doubt and then be more extensively present in micro-and macro-economy. Banks can be exemplified to a thermometer in society that indicates a number based on the temperature of environment; hence, it is possible to measure the economic situation of the society according to banks' situation. The banks' presence in Manuscript

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