Homework Assignments
ORF 307
Collaboration policy: you are encouraged to discuss the homework with your
classmates. However you must submit (via Blackboard) your own copy of the homework.
Do not copy anyone else's work.
HW0
Due: 9pm on Friday, Feb 8 via Blackboard.This preliminary assignment asks you to demonstrate you are able to compile your homeworks as a single scrollable pdf that should be submitted electronically to Blackboard.
1.
Formulate the problem from Exercise 1.1a in the AMPL book
(http://ampl.com/BOOK/CHAPTERS/04-tut1.pdf page 21).
as a linear program (i.e., list the
objective function and the linear constraints of the problem).
2. Use AMPLide to solve the linear program of Problem 1. Report the optimal amount of TV and magazine advertisements and the maximal audience reached by the advertisements.
HW1
Due: 9pm on Friday, Feb 15 via Blackboard.
1.
Make an AMPL model to solve the river-crossing problem described on
slide 7 of Lecture 1.
2.
Solve Exercise 1.4, parts (a)-(d), in the AMPL book
(http://ampl.com/BOOK/CHAPTERS/04-tut1.pdf page 22).
3. Download the AMPL model PrimalSimplex2.txt. Use the AMPLide to run the code. Submit a screenshot of the output.
The following problems are from the textbook. For these problems, use the simplex method to solve the linear program. Please show the sequence of pivots, i.e. a list showing the entering and leaving variable for each pivot you make. Also give the x-values for the final result (or a screenshot of the final dictionary if the problem is unbounded or infeasible).
4. Exercise 2.2.
5. Exercise 2.5.
6. Exercise 2.8.
7. Exercise 2.10.
8. Exercise 2.11.
9. Exercise 2.12. Use 215 for the seed value. Just submit a screenshot of the last dictionary of the 10th problem.
10. Exercise 2.13. Use 215 for the seed value. Just submit a screenshot of the last dictionary of the 10th problem.
11. Exercise 2.16.
HW2
Due: 9pm on Friday Feb 22rd.1. Exercise 3.1 from the book.
2. Exercise 3.3 from the book. Use 223 as the seed value. Turn in just the screenshot of the final dictionary of the 10th problem.
3. Exercise 3.5 from the book.
4. Exercise 3.7 from the book.
5. Download the AMPL model and data files for the Markowitz portfolio
optimization problem:
6. Make a new version of the portfolio optimization called markL1_minrisk.txt in which the minimize-sum-of-squares objective is changed to a minimize-sum-of-absolute-values and is then converted to a linear optimization problem (i.e., a problem that is equivalent but has no absolute values).
7. Starting with the AMPL model in problem 5, make a new version called markL2_maxreward.txt in which the risk is expressed as a constraint and the reward is maximized.
8. Finally, make an AMPL model called markL1_maxreward.txt that combines both of the changes in problems 6 and 7. That is, this AMPL model maximizes the reward subject to a bound on risk and risk is encoded as the sum-of-absolute-values converted to linear constraints.
HW3
Due: 9pm on Friday, March 1st, via Blackboard as usual.1. Exercise 2.15 from the book.
2. Exercise 4.3 from the book.
3. Exercise 4.5 from the book. (Hint: Reading section 4.4 is useful)
4. Exercise 4.10 from the book. (Hint: you don't have to go through a theoretical proof, work your way through an example while accounting for different possible cases)
5. Solve the first AMPL problem described here.
6. Solve the second AMPL problem also described here.
HW4
Due: 9pm on Friday, March 8, via Blackboard as usual.1. Exercise 5.1 (Hint: Reading section 5.8 is useful).
2. Exercise 5.3 (Hint: Reading section 5.4 is useful).
3. Exercise 5.5 from the book. (Hint: Reading sections 5.4 and 5.5 is useful).
4. Exercise 5.6 from the LP book. (Hint: read section 5.6)
5. Exercise 5.7 from the LP book.
6. Exercise 5.9 from the LP book.
7. Exercise 5.10 from the LP book. (Hint: read section 5.7)
8. Exercise 5.11 from the LP book. (Hint: read section 5.7)
9. Solve the first AMPL problem given here. As usual you should include the mathematical formulation of the problem as part of your writeup. (Hint: for the AMPL portion you may find it easier to put the parameters into a separate .dat file - see the AMPL tutorial if you have questions on this.)
10. Solve the second AMPL problem given here.
11. Solve the third AMPL problem given here.
NOTES: For 5.6, use the dual simplex method.
For 5.10 and 5.11, use 309 as the seed value. As usual,
you only need to submit the screenshot of the optimal solution to the last problem.
HW5
Please do the following problems:1. Exercise 6.2 from the LP book. (Hint: read sections 6.1 and 6.2)
2. Exercise 7.3,
3. Exercise 7.4,
4. Exercise 7.6,
5. Exercise 7.7,
6. Exercise 7.8,
7. Solve the AMPL problem described here.
Notes: For problem 7.7, please hand in the screen shot of the last page, and use 329
for seed value, and keep the default value for dimension.
Due: 9pm on Friday March 29.
HW6
Please do the following exercises in the textbook:
1. Exercise 12.1,
2. Exercise 12.2
3. Exercise 12.8
4. Exercise 12.10(b,c).
5. Solve the first AMPL problem described in hw6ampl.pdf.
6. Solve the second AMPL problem described in hw6ampl.pdf.
For 12.8, do both the L1 and L2 regression. Make an ampl model to solve
these optimization problems.
For 12.10 part (c), instead of using the \(b_i\)-values given in the textbook, use \(b_1 = 82\), \(b_2 = 3\), \(b_3 = 11\), \(b_4 = 26\), \(b_5 = 7\) and \(b_6 = 5\).
Due: 9pm on Friday, April 5.
HW7
Please do the following exercises in the textbook:
1. Exercise 11.1
2. Exercise 11.2 (Solve the variant of the problem where each player picks a
number between 1 and 6 instead of between 1 and 100. You can
use the pivot tool or do it by hand.)
3. Exercise 11.4
4. Exercise 14.3
5. Exercise 14.4
6. Exercise 14.5
7. Write an AMPL model to solve the game in Exercise 11.2 (assuming the player
can pick 1 to 100).
HW7 is due at 9pm on Friday, April 12th.
HW8
1. Exercise 14.8
2. Solve Problem 2 described in hw8ampl.pdf.
3. Solve Problem 3 described in hw8ampl.pdf.
Note: For Exercise 14.8, use 422 for the seed value.
HW8 is due on Monday, April 22nd, at 9pm.
For convenience the problems from the textbook can be accessed here: