Suppose the demand D in the

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

scenarios for the demand D are D$1,...,$DS and P$($D $=$ Di$)=$ pi for i $=1,...,$ S$.$

Hence the newsvendor problem min x$>=0$

E$[$F$($x$,$ D$)]$ where

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

has the following deterministic equivalent:

min

x$,$y$,$z c $$ x $+$ p $$

S

k$=1$

piyi $+$ h $$

S

k$=1$

pizi

s$.$t$.$ yi $>=$ Di $$ x$,$ i $=1,...,$S

zi $>=$ x $$ Di$,$ i $=1,...,$S

x $>=0$

y$,$ z $>=0$