15.060  Data, Models, and Decisions

Rooms for the Final

Hello everyone,

There was a small typo in the previous announcement for section E. The final exam will take place in the following rooms:
Section A: E51-345
Section B: E51-315
Section C: E51-325
Section D: E51-335
Section E: E51-395
Section F: E51-376

Sorry for that and have a good evening,
Jean

Announced on 18 December 2017  3:23  p.m. by Jean A. N Pauphilet

Important information about the Final

Hi everyone,

A few important information about the DMD final tomorrow:
- Final will take place tomorrow from 9am to noon in E51.
Section A: E51-345
Section B: E51-315
Section C: E51-325
Section D: E51-335
Section E: E51-395
Section F: E51-376
- Try to be 5 minutes early so we can start sharp on schedule.
- Formula sheet will be provided so you do not need to bring your own.
- Bring a non-communicating calculator (graphing calculators are okay). Any other device or material is not allowed.
- Last-minute office hours today
Mon 2pm-3:30pm in E51-242 Barry
Mon 4:30-6pm in E40-175A Jean
- Get a good night's sleep!

See you tomorrow,
The DMD Team

Announced on 18 December 2017  1:39  p.m. by Jean A. N Pauphilet

Update on Office Hours

Good evening everyone,

We will be holding office hours on Sunday and Monday afternoon.
Sun 2pm-3pm in E62 cafeteria Matthew
Sun 3pm-4pm in E62 cafeteria Isabelle
Sun 4pm-5pm in E62 cafeteria Hari
Mon 2pm-3:30pm in E51-242 Barry
Mon 4:30-6pm in E40-175A Jean

Have a good weekend,
The TA team

Announced on 15 December 2017  6:19  p.m. by Jean A. N Pauphilet

Formula sheet, Final Review session and Office Hours

Good morning everyone,

- The formula sheet for the final is available on Stellar.

- Tomorrow, your TA will be conducting a Final Review session (lecture time, lecture room).

- We uploaded 'Final Review' slides on Stellar in the 'Recitation' folder. Do not hesitate to have a look at them to study for the final.

- We will be holding a special Office Hours schedule this week:
Tue 5pm-6pm in E51-242 Matthew
Wed 3pm-4pm in E51-395 Isabelle
Thu 2:30om-3:30pm in E51-242 Kara
Fri 9am-10am in E40-166 Jean
Fri 3pm-4pm in E62-233 Hari
Sun 2pm-3pm in E62 cafeteria Matthew
Sun 3pm-4pm in E62 cafeteria Isabelle
Sun 4pm-5pm in E62 cafeteria Hari
Mon 2pm-3:30pm in E51-242 Barry

Have a good day,
The TA team

Announced on 12 December 2017  9:44  a.m. by Jean A. N Pauphilet

Feedback on Endurance and Homework 4

Good afternoon everyone,

We have graded the Endurance case and Homework 4 and wanted to give you some general feedback on your assignments.

Endurance case
- In non-linear optimization, keep in mind that Lagrange multipliers have no valid range. The sign of the multiplier indicates whether an increase in the RHS of a constraint would increase or decrease the objective value. The actual value of the Lagrange multiplier then gives you a rough estimate of the magnitude of this increase/decrease. But you should not take it at face value.

- A word of caution about units (again…) and percentage. In the sensitivity analysis, you might have written sentences like “increasing the RHS of the constraint by one unit will increase the objective value …”. However, in the case (e.g., question a), the unit for the RHS of the “Standard deviation” constraint was percentage (annual returns were given in percentage). Replacing the word “unit” by “percent” in the previous sentence, many of you wrote that “increasing the 13%-standard deviation threshold by one percent could increase the annual profit by…”. This sentence is highly ambiguous. Does it mean increasing from 13% to 14% (so literally adding one unit) or from 13% to 13.13% (i.e., adding 1% of 13%)? Be careful! It can be very misleading and cause of a lot of confusion in real life (not only in DMD). The best way to avoid any ambiguity is to be very explicit. For instance, you can:
A) Use the word “percentage point” to refer to percentage as a unit, and not as a relative change, as in “increasing the 13%-standard deviation threshold by one percentage point”.
B) Use “increase/decrease from … to …” instead of “increase/decrease by …” as in “increasing from 13% to 14%”.
C) Specify if you are talking about an absolute or relative increase as in “An absolute increase of 1% in the 13%-standard deviation threshold”.

Homework 4
- Question 1: Always specify what the decision variables are in your optimization model. If variables are not part of the objective function or the constraints, then they are not decision variables. For instance, in question 1, if Ep and Em are no longer part of the objective function or constraints, then they are not decision variables.

- Question 2: Be careful about units. For instance, project profit is in $k, so when subtracting the cost of engineering salaries, you should subtract 150*x_i, not 150,000*x_i. Similarly, the constraint “total profit at least $1.1 million” in 2.b should be modeled as “Profit >= 1,100”.

- Question 2b: There was a lot of confusion in the formula for the objective function so we encourage all of you to go over the solutions (available on Stellar). Many of you calculated the variance of a random variable which takes 6 potential values with equal probability, which was totally unrelated to the question; or computed the “variance of the expected profit”, which makes no sense. Make sure you clearly define what the random variables are (in this case, there were 6 of them, corresponding the profit from each project) and derive step by the step the expression for the objective function. Do not hesitate to introduce “intermediate variables” such as the probability of success or the expected profit for each project, to make the formula look nicer!

- Question 3/4: Being binary or integer is a constraint, to be specified with the other constraints (just like non-negativity)

- Question 3/4: Label your constraints, e.g., “Comedy/Drama Constraint”

- Question 3/4: It is incorrect to define a binary variable using an “IF” statement (and you will not be granted points if you do so in the final). Instead, you should add valid constraints that ensure the binary variable takes the desired values. For instance in Question 3, many people created a binary variable for violent shows (which was intended to equal 1 when all 4 violent shows were aired). However, many people did not “activate” it with a constraint: D+L+J+N <= V+3. Similarly in Question 4, B_Carolina should equal 1 when Carolina>0, which can be enforced by the constraint “Carolina <= 1,000*B_Carolina”. When Carolina=0, the constraint is satisfied whether B_Carolina equals to 0 or 1. Since you aim at minimizing cost, it will equal 0.

Enjoy the snow and have a good week,

The TA Team

Announced on 10 December 2017  2:58  p.m. by Jean A. N Pauphilet