APPLICATION OF OPERATIONS RESEARCH TECHNIQUES IN PORTFOLIO OPTIMIZATION

Portfolio optimization is an allocation problem in which an investor seeks an appropriate balance between return, risk and practical investment restrictions. Operations Research (OR) provides a formal framework for this decision by defining decision variables, objective functions, constraints and solution procedures. This paper presents a comparative review of 17 distinct studies represented in the 18 supplied PDF files, two files contain the same article on pentagonal neutrosophic linear programming and are treated as one source. The reviewed literature covers mean–variance and mixed-integer quadratic programming, Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), linear-programming formulations, robust and multistage stochastic optimization, fuzzy and neutrosophic models, data envelopment analysis, Monte Carlo simulation, evolutionary and swarm-based metaheuristics, and a neurodynamic approach based on spiking neural networks. The comparison is qualitative rather than a pooled empirical test because the studies use different data, constraints, assumptions and performance measures. The review finds that model choice depends on the type of risk an investor wants to control, the reliability of estimated inputs, the restrictions imposed on holdings and the computational resources available. Classical mathematical programming offers transparency and, in many formulations, strong solution guarantees, metaheuristics are useful for difficult discrete search spaces but do not automatically guarantee a global optimum. Uncertainty-aware methods broaden the model but require additional assumptions and calibration. The paper concludes that no single method is universally best and that meaningful comparison requires a common out-of-sample testing framework.