2112 Jayanti Nath 1 , IJMCR Volume 08 Issue 08 August 2020 International Journal of Mathematics and Computer Research ISSN: 2320-7167 Volume 08 Issue 08 August 2020, Page no. - 2112-2123 Index Copernicus ICV: 57.55 DOI: 10.47191/ijmcr/v8i8.02 Portfolio Optimization in Share Market Using Multi-Objective Linear Programming Jayanti Nath 1 , Susanta Banik 2 , Debasish Bhatacharya 3 1 Department of Mathematics, National Institute of Technology, Agartala, Tripura, India-799046 2 Department of Mathematics, National Institute of Technology Agartala, Tripura, India-799046 3 Department of Mathematics, National Institute of Technology Agartala, Tripura, India-799046 ARTICLE INFO ABSTRACT Published Online: 13 August 2020 Corresponding Author: Debasish Bhattacharya Applying multi-objective linear programming formulation for the solution of portfolio optimization in share market, two methods are proposed in this paper. Here the short and long term returns as well as annual dividend received are maximized. Further, the associated risk in the form of semi-absolute deviation below the expected return is minimized. The proposed methods of solution are illustrated by a real life example based on current data collected from Bombay Stock Exchange (BSE). KEYWORDS: Portfolio Optimization, De Novo Programming, Fuzzy Multi-objective Programming, Return and risk. I. INTRODUCTION A Portfolio in finance means the combination of shares or other investments that a particular person or company has. When a potential purchaser visits a share market for purchasing securities/debentures etc. the first task he/she does is to observe the market and gathers experiences and believes regarding future performances of available securities. Having the relevant believes about future performances, the purchaser selects the portfolio of his/her choice within the available budget, Markowitz [1]. In selecting the portfolio, the investor desires to maximize the expected return and at the same time minimize the concomitant risk and hence make a balance between the return and the risk. Now the share market is unpredictable and fluctuation in the prices is a regular phenomenon. Thus the cost prices of shares and its return is random in nature. So, the selection of portfolios, without proper planning and evaluation of the alternatives is a difficult task. Naturally, question arises how the investor may select portfolio so that his/her expected return is maximized and at the same time risk is minimized. Markowitz [1] in 1952 first considered these aspects and proposed the mean-variance model for portfolio selection and it is considered as one of the best methods for addressing such problem. Markowitz’s model describes how an investor can select optimum portfolio taking into consideration the trade-off between the expected return and the market risk. However to remove some shortcomings of the said method, Markowitz [2] used semi-variance in the place of variance in 1959. Markowitz mean variance model may lead to erroneous conclusion, particularly when the security returns are asymmetric in nature. The existence of such asymmetric security return distribution was later indicated in the works of Liu, et.al.[3]; Yan and Li [4]; Guo, Q. et.al. [5], Mansini et. al. [6], Ayub, et.al. (2015)[7] and they proposed some models to minimize the risk in the way of minimizing semi-variance. Their works enriched the process of portfolio selection. Now to apply mean-variance or mean semi-variance method of optimal portfolio selection, the probability distribution of the returns is required. Again for the application of the probability theory in the portfolio selection process, the decision-maker must be provided with a reasonably large size of statistical data pertaining to the performance of the securities. Many researchers proposed an alternative way of selecting portfolios based on expert’s opinion regarding the subjective valuation of the security and their prospective returns. Their works can be broadly categorized into three ways: using Fuzzy set theory Gupta, et.al.[8] ; using Possibility theory, Carlsson, et.al.[9] ; Zhang, et.al. [10] and using Credibility theory Huang [11]; Qin, et.al.[12] These methods are used in a situation where sufficient data regarding security returns is lacking. However, these fuzzy methods are also subjected to some drawbacks. When a