# What is the role of the recourse variable in stochastic programming?

What is the role of recourse variable in stochastic programming?

I often see two-stage stochastic programming problems with recourse, written as follows:

Stage 1 $$$$\begin{array}{rrclcl} \displaystyle \min_{x} \,\,\,{c^T x} +E_{\zeta}[Q(x,\zeta)]\\ \textrm{s.t.} & A x & \leq & b \\ &\displaystyle \sum_{i=0}^{n} x_i & = & 1 \\ \end{array}$$$$

Stage 2 $$$$\begin{array}{rrclcl} \displaystyle \min_{y} \,\,\,Q(x,\zeta)={q^T y} \\ \textrm{s.t.} & Tx+Wy=h \\ &\displaystyle y\ge0 \\ \end{array}$$$$