
Linear Optimization under Uncertainty 297
Example 8.2
Solving DPM using scenario 2 data for the demand gives the optimal
production decisions x
1
= 400, x
2
= 225, and x
3
= 300. These values represent
x
∗
(ξ) and then are used as the first-stage values in the stochastic program
(8.1)-(8.19). The recourse values are then given as follows
Scenario Home PC Pro PC Workstation PC
low (s=1) surplus 100 purchase 275 surplus 100
average (s=2) purchase 425
high (s=3) purchase 100 purchase 575 purchase 100
The expected recourse cost is $192,500. Thus, E
ξ
f(x
∗
(ξ), ξ) is the cost of
the first stage 225(400)+350(225)+250(300) + $192,500 = $436,250. Then,
V SS = $436, 250 −