Table 8 Case 2 - Results Monte Carlo simulations (N=1000) in case of three uniformly distributed uncertain parameters (K _m ,λ and k _cat) for robustified terminal constraint and objective function with the number of constraint violations, mean values and variances on the objective function and terminal constraint, respectively

α=1.96

\(\bar {J}\)

6.5517

13.048

12.599

8.8045

9.1717

9.1498

σ _J

0.5323

1.1015

1.0665

0.7270

0.7600

0.7600

\(\bar {c_{t}}\)

0.7023

1.0205

1.0208

1.1555

1.2254

1.2240

\(\sigma _{c_{t}}\)

0.1744

0.1659

0.1687

0.2590

0.2684

0.2690

c _t violation

470 (47.0 %)

10 (1.0 %)

13 (1.3 %)

21 (2.1 %)

7 (0.7 %)

9 (0.9 %)

α=1.65

\(\bar {J}\)

6.5517

10.079

9.6385

8.2798

8.5848

8.5683

σ _J

0.5323

0.8195

0.7762

0.6813

0.7092

0.7086

\(\bar {c_{t}}\)

0.7030

1.0259

1.0277

1.0476

1.1077

1.1056

\(\sigma _{c_{t}}\)

0.1744

0.1966

0.2042

0.2404

0.2495

0.2496

c _t violation

470 (47.0 %)

28 (2.8 %)

36 (3.6 %)

55 (5.5 %)

29 (2.9 %)

29 (2.9 %)