Stochastic Programming - Index of

160 STOCHASTIC PROGRAMMING
Figure 1 A map showing potential plant sites and actual fishing grounds for
Southern Norway and the North Sea.
The function Q(x, ξ) is called the recourse function, andQ(x) therefore the
expected recourse function.
In this chapter we shall look at only the case with fixed recourse, i.e. the
case where W (ξ) ≡ W . Let us repeat a few terms from Section 1.4, in order
to prepare for the next section. The cone pos W , mentioned in (4.17) of
Chapter 1, is defined by
pos W = {t | t = Wy, y ≥ 0}.
The cone pos W is illustrated in Figure 2. Note that
Wy = h, y ≥ 0isfeasible ⇐⇒ h ∈ pos W.
Recall that a problem has complete recourse if
Among other things, this implies that
pos W = R m .
h(ξ) − T (ξ)x ∈ pos W for all ξ and all x.
But that is definitely more than we need in most cases. Usually, it is more
than enough to know that