Simplex Method
• It is a matrix based method used for solving linear programming problems with many variables
• It provides us with an iterative technique of examining the vertices of the feasible region that is not optimal,
but serves as a starting point (Sirug, 2012).Simplex Method Flowchart
• Transform all the constraints to equality by introducing slack, surplus, and artificial variables as follows:
• Create the initial simplex tableau
o Simplex tableau – It is a table used to keep track of the calculations made at each iteration when the
simplex method is employed
• Select the pivot/al column and determine the entering variable
o Pivot/al column – It is the column of the tableau that has the “most negative value” (for maximization)
and the “most positive value” (for minimization) element in the bottom/last row
o Entering variable– It is a variable that will be assigned a non-zero value in the next iteration so as to
increase the value of the objective function
• Select the pivot/al row and determine the leaving variable by applying the test ratio
o Pivot/al row – It is the row that corresponds to the variable that will leave the table in order to make
room for another variable. It is determined by the test ratio, expressed mathematically as:
Test Ratio of a Constraint Row = Right-hand side (RHS) ÷ Coefficient in the Pivot Column
o Pivot/al row –It is the row with the smallest non-negative result
• Apply a pivot operation to the tableau, including the bottom row
o Replacing Row = Pivot Row ÷ Pivot/al element
o Remaining Row = Previous Row – (Pivot/al element of Previous Row x Replacing Row)
• Check the simplex tableau for optimality; return to the process of selecting the pivot/al column and finding
pivot/al row and pivot/al until below are satisfied:ex:
Operation Research 