The attached codes are for the numerical studies in the main manuscript, in particular, for the results presented in Figures 3 and 4.

1. The file named impactofYieldUncertainty.m is for Figure 3; 
2. the file named combinesubsiy.m is for Figure 4.

The codes are written in Matlab programming language. The figure results can be easily generated by running the codes in Matlab.