MIT课程7

Should it look like this?
C on strain ts C e ll $C$22 $C$23 $C$24 $C$25 Nam e F u n c tion F u n c tion F u n c tion F u n c tion F in a l V a lu e 950 400 4600 4750 L a g ra n g e M u ltip lie r 3 -2 1 0

Where is Professor Orlin?

Vegas? South Beach? Amsterdam? In the first row? He is feeling just fine!

Is he OK?

2
Inspirational Quote

“On a more serious note, there's going to be a lot more information and updates on here in the coming weeks and I think this will provide you with the opportunity to get to know who I really am.”
Raw material Hours of labor Sale price

2 3 $4
3 4 $6
4 5 $7
7 6 $8
Exactly 950 total units must be produced. Customers demand that at least 400 units of product 4 be produced. Formulate an LP to maximize profit. Raw Materials Available <=4600 Labor Available <=5000
8
Our LP

Define:

X1= X2= X3= X4=
Amount Amount Amount Amount
of of of of
Creamy Gloss produced Juicy Gloss produced Dreamy Gloss produced Sunny Gloss produced
15.053 Lecture 7
Sensitivity Analysis
Created by Mike Metzger
*With help of Jim Orlin and Ollie the Owl **Guest Appearances by numerous celebrities
1
What’s Going On?
Adjustable Cells
Final Name Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease
x1 x2 x3 x4
0 400 150 400
-1 0 0 0
4 6 7 8
1 2/3 1 2
9
Solving The Initial LP
Which Method? Graphical Simplex Excel I Agree. Excel it is!

10
Solving Using Excel

Q: What does every great Magician Need?
Decision Variables: x1 0 x2 400 x3 150 x4 400
Value
Objective Function:
Total Profit:
6650
12
Sensitivity Analysis

What can go wrong with a model
(eg.
Not Kate Moss and


Hint Think of:

13
Sensitivity Analysis

The
Big Question(s):
How/when
can I determine if my current solution (or basis) is still optimal given the change without having to resolve the LP?

5
Our Problem

A Recent Letter we received:
Dear 15.053 Class, My name is Jessica Simpson. I have been going through some tough times recently and am having a real problem with one of my cosmetic lines. The info for the line is on the next page. Recently though costs are changing based on market demand in addition to highly fluctuating resource costs. My problem is this we currently have an LP that we solve to find the optimal amount to produce of each product. However, every time a parameter changes, I am always forced to resolve the LP and this takes too long. I was hoping you guys could find a better way. Lately I have just been out of it. For example, Nick and I decided to split our Hummer in half, and now I need to buy a new one. Oh yeah, about the LP it seems to have been misplaced when I was moving out of my Malibu house. Please Help! - Jessica
15
VERY Common Error’s
Forgetting to Check Assume Non-Negativity Forgetting to Check Assume Linear Model Forgetting That Chicken of the Sea is actually Tuna
6
Problem Data: See


Jessica sells four types of lip gloss. The resources
needed to produce one unit of each are known.
Creamy(1) Juicy (2) Dreamy (3) Sunny (4)
Max : subject to :
z = 4x 1 + 6x 2 + 7x 3 + 8x 4
x 1 + x 2 + x 3 + x 4 = 950
x 4 ≥ 400 2x 1 + 3x 2 + 4x 3 + 7x 4 ≤ 4600 3x 1 + 4x 2 + 5x 3 + 6x 4 ≤ 5000 x 1 , x 2 , x 3 , x 4 ≥ 0
The Sensitivity Report

A d ju s tab le C ells C e ll $C$14 $D$14 $E$14 $F$14 Nam e V alu e x1 V alu e x2 V alu e x3 V alu e x4 F in a l V a lu e 0 400 150 400 Reduced G ra d ie n t -1 .0 0 0 0 0 5 4 8 4 0 0 0

A: An Assistant!

My assistant today is very shy so lets give him a warm welcome! He will be doing the Excel today! And here he is now!


11
Our Results


Its not? At Least
it’s not
turkey!!!!
Last is for Jessica Only
Under Solver “options” Check these three things before e-mailing your TA!!!
16
The Correct Report
Why is resolving the LP so terrible?
Hint: Think about real world LP’s

14
How We Do This

M ic ro so ft E x c e l 1 1 .0 S e n sitivity R e p o rt W o rk sh e e t: [S e n sitivity L e c .x ls]Q u e stio n R e p o rt C re a te d : 2 /2 6 /2 0 0 6 7 :2 7 :5 0 P M