Duality, Operation Research

Assignment Help:

For every LP formulation there exists another unique linear programming formulation called the 'Dual' (the original formulation is called the 'Primal'). Same data can be used for both 'Dual' and 'Primal' formulation.  Both can be solved in a similar manner as the Dual is also an LP formulation.

The Dual can be considered as the 'inverse' of the Primal in every respect. The column coefficients in the Primal constraints become the row co-efficients in the Dual constraints. The coefficients in the Primal objective function become the right-hand-side constraints in the Dual constraints. The column of constants on the right hand side of the Primal constraints becomes the row of coefficients of the dual objective function. The direction of the inequalities are reversed. If the primal objective function is a 'Maximization' function then the dual objective function is a 'Minimization' function and vice versa.

 Example 

Consider the following 'Primal' LP formulation.

Maximize   12x1 + 10x2

subject to         2x1 +   3x2  <  18

                       2x1 +    x2   <  14

                             x1, x >    0

The 'Dual' formulation for this problem would be

Minimize      18y1 + 14y2

subject to   2y1 +   2y2    > 12

                   3y1 + y2    > 10

                   y1 > 0,  y2  >  0

Note the following:

  1. The column coefficient in the Primal constraint namely (2,2) and (3,1) have become the row coefficient in the Dual constraints.

  2. The coefficient of the Primal objective function namely, 12 and 10 have become the constants in the right-hand-side of the Dual constraints.

  3. The constants of the Primal constraints, namely 18 and 14, have become the coefficient in the Dual objective function.

  4. The direction of the inequalities have been reversed. The Primal constraints have the inequalities of < while the Dual constraints have the inequalities of >.

  5. While the Primal is a 'Maximization' problem the Dual is a 'Minimization' problem and vice versa.              


Related Discussions:- Duality

Linear programmibg, A PAPER MILL PRODUCES TWO GRADES OF PAPER VIZ., X AND Y...

A PAPER MILL PRODUCES TWO GRADES OF PAPER VIZ., X AND Y. BECAUSE OF RAW MATERIAL RESTRICTIONS, IT CANNOT PRODUCE MORE THAN 400 TONS OF GRADE X PAPER AND 300 TONS OF GRADE Y PAPER I

Game theory-, use of game theory by state bank of india

use of game theory by state bank of india

Sope, sope of operations research in a detailed manner

sope of operations research in a detailed manner

Simplex solution, difference between simplex solution procedure for maximis...

difference between simplex solution procedure for maximisation and minimisation

Trade literature - classification of documents, Trade Literature: Trad...

Trade Literature: Trade literature consists of documents that give information on the processes and materials involved in the manufacture of a product, various types of produc

Tower of hanoi problem, Step 1: Research Towers of Hanoi problem The Tow...

Step 1: Research Towers of Hanoi problem The Towers of Hanoi is a problem frequently used to teach recursive programming techniques. Step 2: Run the assembly code from Hanoim

OPERATIONS RESEARCH, Discuss the methodology of operation research

Discuss the methodology of operation research

Machine tabulation, Machine  Tabulation This methods  of tabulating i...

Machine  Tabulation This methods  of tabulating information  is generally used in  case of extensive  large scale  surveys. Mechanical sorting and tabulating equipments and su

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd