4120_lecture4 - Computational Methods for Management and...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Computational Methods for Management and Economics Carla Gomes Lecture 4 Reading: 3.3 and 3.4 of textbook
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Outline Sensitivity Analysis (summary) Linear Programming Assumptions Additional Examples
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sensitivity Analysis   0 2 4 6 8 8 6 4 2 Production rate for windows Production rate for doors Feasible region x*=(2, 6) 10 W D P = 3600 = 300D + 500W P = 3000 = 300D + 500W P = 1500 = 300D + 500W Our objective function is: maximize 3x 1 +c 2 x 2 How does the optimal solution change as c 2 changes? Optimal solution 0 <c 2 <2 x*=(4,3) Optimal solution c 2 <0 x*=(4,0) Max Z = 3 x1+ 5 x2 S.t. x1 ≤4 2 x2 ≤12 3 x1+ 2 x2 ≤18 x1 0; x2 0 D B C A E
Background image of page 4
Sensitivity Analysis   0 2 4 6 8 8 6 4 2 Production rate for windows Production rate for doors Feasible region x*=(2, 6) Optimal solution c 2 >2 10 W D P = 3600 = 300D + 500W P = 3000 = 300D + 500W P = 1500 = 300D + 500W Our objective function is: maximize 3x 1 +c 2 x 2 How does the optimal solution change as c 2 changes? Multiple Optimal solution c 2 =2 P=18 x* = (2,6) ; x*=(4,3) And any convex combination (CD) Optimal solution 0 <c 2 <2 x*=(4,3) Multiple Optimal solution c 2 =0 P=12 x*=(4,3) and (4,0) and any Convex combination (DE) Optimal solution c 2 <0 x*=(4,0) Max Z = 3 x1+ 5 x2 S.t. x1 ≤4 2 x2 ≤12 3 x1+ 2 x2 ≤18 x1 0; x2 0 D B C A E
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Linear Programming Assumptions: Proportionality Additivity Divisibility Certainty
Background image of page 6
LP Assumptions Proportionality The contribution of each activity to the value of the objective function Z is proportional to the level of the activity x j as represented by the c j x j term; The contribution of each activity to the left-hand side of each functional constraint is proportional to the level of the activity x j as represented by the term a ij . This assumption implies that all the x terms of the linear equations cannot
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
assumption Case 1 - violation occurs as a result of e.g., startup costs , associated with product 1. E.g., costs
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/25/2011 for the course AEM 4120 taught by Professor Gomes,c. during the Fall '08 term at Cornell University (Engineering School).

Page1 / 28

4120_lecture4 - Computational Methods for Management and...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online