Stochastic Programming - Index of

RECOURSE PROBLEMS 215
procedure L-shaped Integer;
begin
Let z := ∞, the best solution so far;
Let P := {initial problem with K := L := 0};
while P ≠ ∅ do begin
Pickproblem(P,P); P := P\{P };
repeat (∗ for problem P ∗)
master(K, L, ˆx, ˆθ,feasible);
fathom := not (feasible) or (c Tˆx + ˆθ >z);
if not (fathom) then begin
feascut(A, ˆx,newcut);
if not (newcut) then intcut(ˆx, newcut);
if not (newcut) then begin
if ˆx integral then begin
Find Q(ˆx);
z := min{z, c Tˆx + Q(ˆx)};
fathom := (ˆθ ≥Q(ˆx));
if not (fathom) then begin
L := L +1;
Create the cut −β T L x + θ ≥ α L;
end;
end
else begin
Use branching to create 2 new problems P 1 and P 2 ;
Let P := P∪{P 1 ,P 2 };
end;
end;
end;
until fathom;
end; (∗ while ∗)
end;
Figure 27 The L-shaped decomposition method when the first-stage problem
contains integers.