Example $10\mathrm{.}6($Newsvendor problem revisited$)$ Suppose the demand $D$ in the

newsvendor problem has a discrete distribution. More precisely, suppose the

scenarios for the demand $D$ are $D_1,$dots,$D_S$ and $P(D=D_i)=p_i$ for $i=1,$dots,$S.$

Hence the newsvendor problem $mi{n}_{x}0E[F(x,D)]$ where

$F(x,D)=c*x+p*max(D-x,0)+h*max(x-D,0)$

has the following deterministic equivalent:

$mi{n}_{x,y,z},c*x+p*{\displaystyle \underset{k=1}{\overset{S}{}}}{p}_i{y}_i+h*{\displaystyle \underset{k=1}{\overset{S}{}}}{p}_i{z}_i$

$s.t.y_i{D}_i-x,i=1,$dots,$S$

$,z_{i}x-D_i,i=1,$dots,$S$

$,x0$

$,y,z0$