This preview shows pages 1–2. Sign up to view the full content.
solution of homework 9
Problem 1
a.
Let
f
n
(
x
) denote the minimal cost from n to the end of the planning hori
zon given that x is the cumulative requisitions after the requisitions of the nth
period have arrived. Because you could choose either processing the requisitions
or not. The dynamic program should be as the following:
f
n
(
x
) = min
{
K
+
X
j
P
j
f
n
+1
(
j
)
,cx
+
X
j
P
j
f
n
+1
(
x
+
j
)
}
The boundary condition is:
f
N
+1
(
x
)
≡
K
b.
From the dynamic program, we can see that in the nth period:
if
K
+
∑
j
P
j
f
n
+1
(
j
)
> cx
+
∑
j
P
j
f
n
+1
(
x
+
j
), we will decide not processing
the requisitions
if
K
+
∑
j
P
j
f
n
+1
(
j
)
< cx
+
∑
j
P
j
f
n
+1
(
x
+
j
), we will decide processing the
requisitions.
K
+
∑
j
P
j
f
n
+1
(
j
) is a constant value we do not know.
cx
+
∑
j
P
j
f
n
+1
(
x
+
j
)
is nondecreasing in x, this could be explained in two ways: 1) By intuition. More
requisitions will cause the cost nondecreasing 2) By induction. Since
f
N
+1
(
x
)
≡
K
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '12
 Richard

Click to edit the document details