GOMORY'S Cutting plane method in Englis|Mixed-Integer cutting plane method INTEGER LINEAR PROGRAMING

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INTEGER LINEAR PROGRAMING
INTEGER LINEAR PROGRAMING
In linear programming, each decision variable as well as slack and/or surplus variable is allowed to take any real or fractional value. However, there are certain real-life problems in which the fractional value of however, be obtained by rounding off the optimum value of the variables to the nearest integer value. This be working on a project or 1.6 machines will be used in a workshop. The integer solution to a problem an integer solution. This solution however may not satisfy all the given constraints. Secondly, the value if the given problem, where an integer solution is required, is solved by integer programming techniques.
. An integer LP problem has important applications. Capital budgeting, construction scheduling, plant problems that demonstrate the areas of application of integer programming.
7.2 TYPES OF INTEGER PROGRAMMING PROBLEMS
Linear integer programming problems can be classified into three categories:
(1) Pure (all) integer programming problems in which all decision variables are restricted to integer
values.
(ii) Mixed integer programming problems in which some, but not all, of the decision variables are
restricted to integer values.
(ii) Zero-one integer programming problems in which all decision variables are restricted to integer values
of either 0 or 1.

The broader classification of integer LP problems and their solution methods are summarized in
: (i) Gomory's cutting plane method and
(ii) Branch and Bound method, for solving integer programming problems

7.4.2 Steps of Gomory's All Integer Programming Algorithm

Step 1: Initialization Formulate the standard integer LP problem. If there are any non-integer coefficients in the constraint equations, convert them into integer coefficients. Solve the problem by the
simplex method, ignoring the integer requirement of variables.

Step 2: Test the optimality

(a) Examine the optimal solution. If all basic variables have integer values, the integer optimal solution has been derived and the procedure should be terminated. The current optimal solution
obtained in Step 1 is the optimal basic feasible solution to the integer linear programming.
(b) If one or more basic variables with integer requirements have non-integer solution values, then go to
Step 3.

Step 3: Generate cutting plane Choose a row r corresponding to a variable xr, that has the largest fractional value fr, Now generate the cutting plane (a Gomory constraint) .
If there are more than one variables with the same largest fraction, then choose the one that has the smallest contribution to the maximization LP problem or the largest cost to the minimization LP problem.

Step 4: Obtain the new solution Add the cutting plane generated in Step 3 to the bottom of the optimal simplex table, as obtained in Step 3. Find a new optimal solution by using the dual simplex method,
i.e. choose a variable that is to be entered into the new solution having the smallest ratio:
and return to Step 2. The process is to be repeated until all basic variables with integer requirements
assume non-negative integer values.

GOMORY'S ALL INTEGER CUTTING PLANE METHOD HINDI EXPLANATION
GOMORY'S ALL INTEGER CUTTING PLANE METHOD URDU EXPLANATION
GOMORY'S ALL INTEGER CUTTING PLANE METHOD ENGLISH
Fractional Cut method
Fractional Cut method
Fractional Cut method
Fractional Cut method
Fractional Cut method
Fractional Cut method
Fractional Cut method
Fractional Cut method
GOMORY'S CUT
GOMORY'S CUT
GOMORY'S MIXED-INTEGER CUTTING PLANE METHOD HINDI
GOMORY'S MIXED-INTEGER CUTTING PLANE METHOD ENGLISH
GOMORY'S MIXED-INTEGER CUTTING PLANE METHOD URDU.
MIXED CUT
MIXED CUT
MIXED CUT
BRANCH AND BOUND METHOD URDU
BRANCH AND BOUND METHOD HINDI
#MIXEDCUT
#MIXEDCUT
#BRANCHANDBOUNDMETHODURDU
#BRANCHANDBOUNDMETHODHINDI
#FractionalCutMethod
Simplex method Hindi

Dual simplex method Hindi/Urdu

Dual simplex method English

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