Lab 3 Review for AGEC622

Adapted from review 2010,class notes and old exams

PreperationTo prepare for the exam:

Read the relevant book sectionsTextbook: Applied Mathematical Programming Using Algebraic Systems by B. A. McCarl and T. H. Spreen

http://agecon2.tamu.edu/people/faculty/mccarl-bruce/books.htmLook at Chapter 1Assumptions Look at Chapter 2 Notable violation

Divisibility- Integer Programming

Chapter 5 Transportation (5.3)

Introduce a fundamental concept: demand and supply balance

Feed (5.4) Joint Product (5.5)

Chapter 7 Disassembly (7.2)

Chapter 15 Integer

The Basics of LP Models

What LP models are Optimization over decision variables subject to

constraints – Always an abstract of the real world Obj. F(X) S.t. G(X)ЄS

Example: Max (93-60)Xeconomy+(198-150)Xregular+(255-

200)Xfancy S.t. 0.125Xeconomy+0.26Xregular+0.30Xfancy<=30 0.40Xeconomy+0.55Xregular+0.65Xfancy<=70 Xfancy>=1 Non-Negative

Versatility of LP models And Usage

(cont.)- Objective function- Shadow price- homogeneity of units- Assumptions of the LP problem- Reduced cost

Prescriptive: What decisions should be made? Predictive: Predict the consequence of

environmental changes depicted by the parameters in the model

Sensitivity demonstration

Transportation problem

Problem Example (2008 Exam #1)

Obj. Max Profit=Revenue-Cost Revenue= Cost= Waste Disposal + Production Cost +

Shipping Cost + Purchase Cost Production Cost: YOH, YTX,, which determines the final

output but constrained by input purchase Shipping Cost: QME,OH QME,TX QWT,OH QWT,TX

Purchase Cost: BuyME, BuyTX

Crude OilMiddle

East (ME)Western

Texas (WT)

Refining PlantsTexas (TX)Ohio (OH)

OutputGasoline (GAS),

Diesel (DIE), Distillate

(DIS), Waste (WST)

Feed problem

Feed Problem

  Pork trimGround Pork Beef Trim Ground Beef

Cellousic additive Spices

Pre mixed meat   RHS

Min 0.25 0.97 0.28 1.05 0.1 10 0.9    

Protein 15 25 16 30 0 0 24 ≤ 28

Fat 25 20 25 20 0 0 21 ≤ 25

Fiber 4 10 5 10 0.7 10 7 ≤ 19

Protein 15 25 16 30 0 0 24 ≥ 21

Fat 25 20 25 20 0 0 21 ≥ 15

Fiber 4 10 5 10 0.7 10 7 ≥ 0

Spice 0 0 0 0 0 100 0 ═ 0.5

Volume 1 1 1 1 1 1 1 ═ 1

Non nega yes yes yes yes yes yes yes    

Disassembly Problem

Raw Product 1Component 1

Raw Product 2

Component 2

Component 3

Assembly disassembly problem (exam 2010)DV Cull

CowFed St Fed He Hamb Ste Ro Brisket By

products

Waste   RHS

  -135 -210 -180 1 2.5 2 1.25 0.3 -0.1    

Hambu -300 -120 -160 1           <  0

Steak -50 -180 -160   1         <  0

Roasts -100   -80     1       <  0

Brisket -50   -80       1     <  0

By p -300 -180 -160         1   <  0

Waste -200 -120 -160           1 = 0

Labor 0.5 1 1.5             <  2800

Room 1 1 1             <  600

Cull cow

1                 <  100

Fed st   1               <  300

Fed hei     1             <  200

Ham       1           <  30,000

sale bri             1     <  10,000

Non-Negativity

1, 1, 1, 1, 1, 1, 1, 1, 1, >  0

Joint product Three sets of variable: Purchase(Input), Production,

Sale(output)

Input

Possibility 1Possibility II

.

.

.

Sale 1Sale II

.

.

.

Demand-supply balance

Demand-supply balance

Class notes

Integer Programming (Chapter 15) Why do we need integer programming? Understand the use of indicator variable

Can you tell the relationship between X and Z here? Under what circumstances will such condition be needed?

Y

Integer programming (Exam 2010)

Here Y1 and Y3 must be purchased always since Y1+Y3=2. So, capacity of

0≤X1 ≤18 and the costs generated from using Y1 &Y3 are $8 and $3 respectively

If Y2 is purchased, capacity of 0 ≤X2 ≤5 and the cost generated is $5.

If Y2 is not purchased(Y2=0),X2 will not be produced (Solution 2009 exam)