SIMPLEX METHOD ( LPP) IN EASY WAY IN HINDI

In this video we will learn simplex method in hindi in operations research with solved numerical problem.
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SIMPLEX METHOD

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Test for Optimality

Calculate the values of cj - zj .There may arise three cases:-

a). If all the values of cj - zj row is less than or equal to 0, then the current basic feasible solution is the optimal solution.

b). If at least one column ak of coefficient matrix for which ck – zk is greater than 0 and all elements of ak column are negative then there exist an unbounded solution to the given problem.

c). If there are one or more positive values in cj - zj row, then
current initial basic feasible solution is not optimal.(i.e. it can be improved)

Select the variable to enter the basis (incoming variables) and Test for Feasibility (variables to leave the basis(outgoing variables))

1. Incoming Variable:- select the most positive value in cj - zj row and the element corresponding to these positive value is incoming variable, and column containing these incoming variables is called key column.

2. Outgoing Variable:- Divide the values under b column by the corresponding positive element in the key column, and compare the ratios. The row that indicates the minimum ratio is called the key row (and corresponding variable is termed as outgoing variable). However, division by zero or negative coefficients in the key column is not allowed. In the case of a tie, break the tie arbitrarily.

Important note: If all these ratio are negative then problem has an unbounded solution and we stop the procedure.

Identify the Pivot Element (Key Element)
The number that lies at the intersection of the key column and key row of a given table is called the key element. It is always a non-zero positive number.

Finding the New Solution
If key element is 1 then row remains the same in the new simplex table.
If the key element is other than 1, then divide each element in the key row (including element in b- column) by the key element, to find the new values for that row.
Convert all the element of the key column to zero (key element is 1) by performing elementary row operation.

Repeat the Procedure

Go to step TEST FOR OPTIMALITY and repeat the procedure until all the values of are cj - zj row either zero or negative.

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Please watch: "UNBALANCED ASSIGNMENT PROBLEM IN OPERATION RESEARCH | USING HUNGARIAN METHOD | Lecture 03"
   • Unbalanced Assignment Problem | Using Hung...  
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