MATP6960 Stochastic Programming, Homework 6

Revised: November 16th and 17th.

Due: Thursday, November 21, 2002.

1.

Birge and Louveaux, page 244, question 2.

2.

Birge and Louveaux, page 244, question 4.

3.

Let $Q(x,\xi)=\vert x-\xi\vert$, with $\xi$ uniformly distributed on [0,6] and $0 \leq x \leq 10$. Show that the E-M upper bound and the Jensen lower bound both equal Q(x) for $x \geq 6$.

4.

For the second stage problem defined in question 4 on page 102, find the minimizers x for the E-M and Jensen bounds. What do you conclude?

5.

For the second stage problem defined in question 1 on page 101, find the minimizers for the UB^mean, E-M, and Jensen bounds. You can assume $1 \leq x_1 \leq 2$ and $1 \leq x_2 \leq 2$.

6.

For the second stage problem defined in question 1 on page 101, restrict $1 \leq x_1 \leq 2$ and $1 \leq x_2 \leq 2$. Further, drop the upper bound constraints $y_1 \leq 1$ and $y_2 \leq 1$. For the resulting problem, find a minimizer for the upper bound on Q(x) derived using the scheme of section 9.5(b).

	John Mitchell	Amos Eaton 325
	x6915.	mitchj@rpi.edu
	Office hours:	Tuesday: 2pm - 4pm.