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In problems of portfolio selection the reward-risk ratio criterion is optimized to search for a risky portfolio offering the maximum increase of the mean return, compared to the risk-free investment opportunities. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several polyhedral risk measures, being linear programming (LP) computable in the case of discrete random variables represented by their realizations under specified scenarios, have been introduced and applied in portfolio optimization. The reward-risk ratio optimization with polyhedral risk measures can be transformed into LP formulations. The LP models typically contain the number of constraints proportional to the number of scenarios while the number of variables (matrix columns) proportional to the total of the number …