Sample Average Approximation Method for Chance Constrained ...

not show the corresponding Figures for other values of γ, but the pattern observed inthe portfolio problem repeated: with γ = 0 almost every point was feasible but far fromthe optimal, with γ = α = 0.05 almost every point was infeasible. The parameter choicethat generated the best candidate solutions was γ = α/2 = 0.025. We also show theγN-plot for the SAA of problem (22). We tested γ values in the range 0, 0.005, . . ., 0.05and N = 60, 70, . . ., 150. We included a plane representing the optimal value of problem(22) for α = 0.05, which is readily obtained by applying formula (23).In accordance with Figure 7, in Figure 9 the best candidate solutions are the oneswith γ around 0.025. Even for very small sample sizes we have feasible solutions (darkgray triangles) close to the optimal plane. On the other hand, this experiment givesmore evidence that the SAA with γ = 0 is excellent to generate feasible solutions (darkgray triangles) but the quality of the solutions is poor. As shown in Figure 9, the highpeaks associated with γ = 0 persist for any sample size, generating points far form theoptimal plane. In agreement with Figure 7, the candidates obtained for γ > α are intheir vast majority infeasible.29