Dual Simplex method reciprocal method Operation research Lec 16 by Professor Maqsood Ali Abbas

#Dual_simplex_method #reciprocal_method #Dualsimplexmethod #reciprocal_method #Dualsimplex #math #physics #economics #math #bs #ms

[awaisshahid]

Dual simplex method.
This method start better than optimal but infeasible and moves to achieve feasibility while maintaining the optimality.

[tayyabanaz]

• dual simplex method:
In dual simplex method, the LP starts with an optimum (or better) objective function value which is infeasible.

•Dual feasibility solution:
The leaving variable xr' is the basic variable having the most negative value. If all the variable are non negative then algorithm ends.

• dual optimal solution:
Take the ratio of left hand side of the z equation to the corresponding coefficient in the equation is associated with the leaving variable.
Smallest absolute value of the ratio if the problem is maximization. If the denominator are all +ve or zero then the problem has no feasible solution.

[mrbuddies]

Dual simplex method.
This method starts better than optional but infessble and move to enhance feasibility while maintaining thw optimality..
Dual feasibility condition..
The learning variable is the basic variable having the most - ve value in the solution colume ( ties are broken arbitrary ). If all the basic variablez arw non- negative, the algorithm ends.

[sarasakhawat]

Dual optimal sloution :
Take the ratio left hand sidr of z to crossponding coefficent in equation is associated with the leaving variable.

[muzammiliqbaljappa]

Dual optimal solution :-
Take the ratio of LHS of the z equation to the corresponding coefficient in the equation is associated with the leaving Variable.
Smallest absolutely value of the ratio of the problem is maximization.

Dual optimility condition :-
Due to our realignment of the objective function, the most negative value in the z row of the simplex table will always be the entering Variable for the next iteration and is called dual optimility condition.

[shanzayaseen]

1.In z row the most -ve value will always be the incoming variable for next iteration this is called optimility condition.

2.The leaving variable is the basic variable having the most negative value, if all the basic variables are non negative, then algorithm end.

3.Simplex method start with infeasibility & works towards feasibility.

[muhammadaftab]

Dual simplex method
This method is infeasible but move to achieve feasibility while maintaining the optimally.
Dual feasibility condition.
The leaving variable is the basic variable having the most negative value in the solution column. If all the basic variable non negative then algorithm ends.
Dual optimalitiy condition.
Take the ratio of Z equation to the equation associated with leaving variable. Smallest ratio is the entering variable.

[ZEESHANHAIDER-vkkq]

Dual simplex method:
The Linear Programming starts with an optimum (or better) objective function value which is infeasible. Iterations are designed to move toward feasibility without violating optimality.
Dual feasible solution:
The leaving variable xr, is the basic variable having the most negative value.if all the variable are non negative then algorithm ends.
Dual optimal solution:
Take the ratio of left hand side of z equation to the corresponding coefficient in the equation is associated with the leaving variable.

[sarasakhawat]

Dual feasible sloution :
The leaving variable xr is the basic variable heaving the most of negative value and if all variable are negative the algorithm ends.

[tahirali]

Dual optimality condition:
In fact, due to our realignment of the objective function, the most negative value in the z-row of the simplex table will always be the entering variable for the next iteration. This is called optimality condition.

[zeeshannawaz]

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem.

[maliksunny]

Dual optimal solution :-
Take the ratio of left hand side of the z equation to the corresponding coefficient in the equation is associated with with the leaving variable .

[ghmaths]

DUAL SIMPLEX METHOD
This method starts better than optimal but infeasible and moves to achieve feasibility while maintaining the optimality.
DUAL FEASIBLE CONDITION
The leaving variable is the basic variable having the most negative value in the solution column.If all the basic variables are non negative then algorithm ends.
DUAL OPTIMALITY CONDITION
Take the ratio of the L.H.S co efficient of z equation to the corresponding co efficient in the equation associated with the leaving variable ignore the ratios with positive or zero denominators.The entering variable is the non basic variable associated with the smallest ratio if the problem is minimized or the smallest absolute value of the ratio if the problem is maximization.
ALGORITHM
TO START LP OPTIMAL AND INFEASIBLE TWO REQUIREMENTS MUST BE MET,
1)The objective function must satisfy the optimality condition of the regular simplex method.
2) All the constraints must be of type (<=). To convert (>=) to (<=) simply multiply both sides of (>=) inequality by -1.If LP includes (=) constraints, the equation can be replaced by two inequalities.

[logicandfun]

Dual feasibility condition

The leaving variable is the basic variable having most Negitive value in the solution column (Lies are broken arbitrary) if all the basic veriable are non negative the algorithm ends.

[mahramchudhary]

Dual fisibility condition:
) Remains feasible (i.e. satisfies Ax=b, when the primal is in standard form). 2) Remains dual feasible. Meaning that yA≤c where c is the cost vector for the objective function of the primal, and y is the solution vector for the objective function of the dual.

[umkwogu]

Dual optimality:
Due to our relighment of objecty function the most negative value in the z row of simplex table will always be entering varibale.


The dual simplex method will pivot from dual fiseable dictionary working towards feasibility. This new pivot strategy is called dual simplex method.

[aneeskamboh]

Fareeha shahzadi 5666
Q#1: Dual simplex method:
In dual simplex method, the LP starts with an optimum (or better) objective function value which is infeasible.
Q#2: Dual feasibility solution:
The leaving variable 'xr' is the basic variable having the most negative value.If all the variable are non negative then algorithm ends.
Q#3: Dual optimality condition:
Due to our realignment of the objective function the most negative Value in the z-row of the simplex table will always be the entering variable for the next iteration.
Q#4: Dual optimal solution:
Take the ratio of left hand side of the z equation to the corresponding coefficient in the equation is associated with with the leaving variable.

[NaveedAhmad-fblg]

Dual optimility condition;
Due to our realignment of objective function, the most -ve value in the z-row of simplex table is always the entering variable for next iteration, is called dual optimilty condition.

[yousafarshad]

The Dual Simplex Method will pivot from dual feasible dictionary to dual feasible dictionary working towards feasibility. This new pivoting strategy is called the Dual Simplex Method because it really is the same as performing the usual Simplex Method on the dual linear problem

[dramaseriesurdu]

Dual optimility condition:
Due to our realignment of the objective function, the most negative value in the z-row of the simplex table will always be the entering variable for the next iteration. This is known as the optimality condition.