**Apr 25**End-of-semester announcements:**Projects:**Due Monday April 28 in class**Final Exam:**Friday May 2, 7:55- For more information, see the "Exams" section below
- Exam EI on Thursday May 1, 1900-2000, CH348

**GMPL exercises:**Due Friday May 2 at noon- I will send you the status of your GMPL exercises electronically on Monday April 28 and Wednesday April 30

**Mar 28**Exam 2 is on Friday April 4. For more information, see the "Exams" section below.- Review in class on Wednesday April 2
- Exam EI on Thursday April 3, 1900-2000, CH348

**Mar 26**GMPL clinic rescheduled for Thursday March 27, 2000-2100, CH348**Mar 24**GMPL clinic on Thursday March 27, 1900-2000, CH348**Mar 17**Instructions for the course project have been posted; see below. Due dates:- Preliminary problem statement due Monday March 31
- Final report due Monday April 28

**Feb 19**Solutions to Exam 1 have been posted.**Feb 5**Exam 1 is on Friday February 14. For more information, see the "Exams" section below.- GMPL clinic on Tuesday February 11, 1900-2000, CH348
- Review in class on Wednesday February 12
- Exam EI on Thursday February 13, 1900-2000, CH348

**Jan 7**Welcome!

Note: Now that the semester is over, I have taken down the homework solutions.

Solutions are only available within USNA.

**GMPL exercises are starred.* For GMPL exercises, formulate a model on paper and write accompanying GMPL code. Submit your GMPL code, using the instructions above.**

**Apr 18**rock-paper-scissors [solutions]**Apr 16**pirates*: Write a linear program for Example 1 in Lesson 33 using symbolic input parameters. This is the last GMPL exercise of the semester. [solutions: see completed notes for Lesson 33 below]- Your model file should be named
__pirates.mod__ - Your data file should be named
__pirates.dat__ - The folder name should be
__pirates__

- Your model file should be named
**Apr 14**~~2.30* — This is the last GMPL exercise of the semester.~~Updated on April 15**Apr 11**cars [solutions]**Apr 9**9.5ab [solutions]**Apr 7**9.1, 9.2, 9.3, 9.4 [solutions: 9.1, 9.2, 9.3, 9.4]**Mar 28**8.11ab, 8.12ab [solutions: 8.11ab, 8.12ab]- Note: part b of 8.11 and 8.12 are somewhat tedious, since the
LPs are rather large for solving with the simplex method by hand.
Nevertheless, they do serve as good practice for reinforcing the
mechanics of the simplex method. Make sure you know how to
**interpret**an optimal solution and the optimal value of a Phase I LP.

- Note: part b of 8.11 and 8.12 are somewhat tedious, since the
LPs are rather large for solving with the simplex method by hand.
Nevertheless, they do serve as good practice for reinforcing the
mechanics of the simplex method. Make sure you know how to
**Mar 26**8.3, 8.8 [solutions: 8.3, 8.8]**Mar 24**8.1, 8.2 [solutions: 8.1, 8.2]**Mar 21**Work on diet-part2 if you haven't completed it yet. Here's a hint.**Mar 19**7.16, 7.17 [solutions: 7.16, 7.17]**Mar 7**7.14 [solutions]**Mar 5**7.4 [solutions]**Feb 28**7.2, 7.3 [solutions: 7.2, 7.3]**Feb 24**6.14, 6.18 [solutions: 6.14, 6.18]**Feb 21**6.1, 6.2, 6.8, 6.9 [solutions: 6.1, 6.2, 6.8, 6.9]**Feb 19**diet-part2* Updated on February 20- Partial GMPL model file, GMPL data file

**Feb 10**2.20, 2.22 using symbolic input parameters [solutions: 2.20, 2.22]**Feb 7**redo 2.9 and 2.10 using symbolic input parameters [solutions: 2.9, 2.10]**Feb 5**redo 2.6 using symbolic input parameters [solutions]- Solutions updated with a correction on February 10

**Feb 3**2.13*, 2.14, 2.16, using symbolic input parameters [solutions: 2.13, 2.14, 2.16]- For 2.13, submit a GMPL model file (2.13.mod) and a GMPL data file (2.13.dat)

**Jan 31**redo 2.3; 2.24, diet-part1. Bring your laptop to class on Monday. [solutions: 2.3, 2.24, diet-part1 (updated on March 26)]- For these exercises,
**use symbolic input parameters**. For example, in 2.3, let:- F = set of film types
- M = set of machines
- r
_{i}= revenue of one square yard of film type i, for i ∈ F - a
_{ij}= minutes needed on machine j to make one square yard of film type i, for i ∈ F and j ∈ M - etc.

- For these exercises,
**Jan 29**sets. Bring your laptop to class on Friday. [solutions]**Jan 27**inventory, finco [solutions: inventory, finco]**Jan 24**2.10* [solutions]**Jan 22**2.9 [solutions]**Jan 17**2.11*, 2.12 [solutions: 2.11, 2.12]**Jan 15**2.6 [solutions]**Jan 13**2.1, 2.3* [solutions: 2.1, 2.3]**Jan 10**1.1abcd, 1.2. Use the graphical method we discussed in Lesson 3 for 1.1. Bring your laptops on Monday. [solutions]**Jan 8**1.1abcd: By trial-and-error — for each linear program, find a few feasible solutions and determine their values. Try to find the best feasible solution you can.**Jan 7**Read the course policy statement. Watch out for an e-mail from POET and follow its instructions to set up an account at the POET website. Bring your laptop to class on Wednesday.

- 1. Introduction (Jan 7)
- 2. Introduction to optimization modeling (Jan 8)
- 3. Graphical solution of optimization models (Jan 10)
- 4. Solving optimization models with a computer, resource allocation models (Jan 13)
- 5. Work scheduling models (Jan 15)
- 6. Blending models (Jan 17)
- 7. Production process models (Jan 22)
- 8. Production process models, cont. (Jan 24)
- 9. Multiperiod models (Jan 27)
- 10. Sets, summations, for statements (Jan 29)
- 11. Resource allocation models, revisited (Jan 31)
- 12. Blending models, revisited (Feb 3)
- 13. Work scheduling models, revisited (Feb 5)
- 14. Production process models, revisited (Feb 7)
- 15. Multiperiod models, revisited (Feb 10)
- 16. Introduction to algorithm design (Feb 19)
- 17. Improving search: finding better solutions (Feb 21)
- 18. Improving search: convexity and optimality (Feb 24)
- 19. Improving search: review (Feb 26)
- 20. Geometry and algebra of corner points (Feb 28)
- 21. Geometry and algebra of corner points, cont. (Mar 5)
- 22. Linear programs in canonical form (Mar 7)
- 23. Basic solutions in canonical form LPs (Mar 19)
- 24 + 25. The simplex method (Mar 21, Mar 24)
- 26. The simplex method: review (Mar 26)
- 27. Finding an initial BFS (Mar 28)
- 28. Degeneracy, convergence, multiple optimal solutions (Mar 31)
- 29. Bounds and the dual LP (Apr 7)
- 30. Weak and strong duality (Apr 9)
- 31. An economic interpretation of LP duality (Apr 11)
- 32. Maximin and minimax objectives (Apr 14)
- 33. Maximin and minimax objectives, cont. (Apr 16)
- 34. LP duality and game theory (Apr 18)
- 35. Review

Note: Now that the semester is over, I have taken down the quiz solutions.

- 1. Jan 15
- 2. Jan 22
- 3. Jan 29
- 4. Feb 5
- 5. Not really a quiz
- 6. Feb 26 - see Lesson 19
- 7. Mar 7
- 8. Mar 28
- 8a. Mar 31
- 9. Apr 16
- 10. Apr 23

Note: Now that the semester is over, I have taken down the sample exams, review problems and solutions.

- Exam 1 (Feb 14)
- Information and review problems
- Solutions to review problems
- Solutions

- Exam 2 (Apr 4)
- Information and review problems
- Solutions to review problem
- Last year's Exam 2
- Solutions to last year's Exam 2
- Solutions

- Final Exam (May 2)
- Information
- Last year's Final Exam - Ignore 6d, 6e
- Solutions to last year's Final Exam