Appraoch 1 Risk Model

The first approach adopts the classical Markowitz s MV model to handle randomness in the objective function coefficients of prices, in which the expected profit is maximized while an appended term representing the magnitude of operational risk due to variability or dispersion in price, as measured by variance, is minimized (Eppen, Martin, and Schrage, 1989). The model can be formulated as minimizing risk (i.e., variance) subject to a lower bound constraint on the target profit (i.e., the mean return). 

Malcolm and Zenios (1994) presented an application of the MV approach by adopting the robust optimization framework proposed by Mulvey, Vanderbei, and 

Zenios (1995) to the problem of capacity expansion of power systems. The problem was formulated as a large-scale nonlinear program with variance of the scenario-dependent costs included in the objective function. Another application using variance is employed by Bok, Lee, and Park (1998), also within a robust optimization framework of Mulvey, Vanderbei, and Zenios (1995), for investment in the long-range capacity expansion of chemical process networks under uncertain demands. 

---