Algorithm to Calculate Basic Feasible Solution using Simplex Method
Algorithm to Calculate Basic Feasible Solution using Simplex Method
Abstract:
The problem of maximization/minimization deals with choosing the ideal set of values of variables in order to find the extrema of an equation subject to constraints. The simplex method is one of the fundamental methods of calculating the Basic Feasible Solution (BFS) of a maximization/minimization. This algorithm implements the simplex method to allow for quick calculation of the BFS to maximize profit or minimize loss, depending on the requirement. It provides an intuitive user interface which can be used to provide all the input and then performs the required calculations, presenting the results in a clean format.
Methodology:
The application will take the equations from the user in an easy-to-use GUI. There will be limits to the number of terms that each equation can be composed of and the number of constraint equations.
Once the equations have been input, the algorithm appends the temporary variables onto the constraint equations. It then creates the table. The following table shows the format of the table that will be generated.
CB
Basis
X1
X2
S1
S2
S3 b θ
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
This will be used to calculate Zj and then Cj-Zj. The BFS will now be checked to see if it’s the absolute extrema for the problem. If not, the process will be repeated in order to find the true extrema values.
Program Details:
The program will be written in Python and will use wxPython for GUI construction. This will allow it to be run on both UNIX based and Windows based PCs.
On starting the application, the user will be presented with a GUI where the equations can be entered. On clicking the submit button, the table will be displayed with step-by-step processing.
Algorithm:
1) Read in the values in the text box to respective variables.
2) Append slack variables to each equation.
3) Take column of largest coefficient and divide b by the
Abstract:
The problem of maximization/minimization deals with choosing the ideal set of values of variables in order to find the extrema of an equation subject to constraints. The simplex method is one of the fundamental methods of calculating the Basic Feasible Solution (BFS) of a maximization/minimization. This algorithm implements the simplex method to allow for quick calculation of the BFS to maximize profit or minimize loss, depending on the requirement. It provides an intuitive user interface which can be used to provide all the input and then performs the required calculations, presenting the results in a clean format.
Methodology:
The application will take the equations from the user in an easy-to-use GUI. There will be limits to the number of terms that each equation can be composed of and the number of constraint equations.
Once the equations have been input, the algorithm appends the temporary variables onto the constraint equations. It then creates the table. The following table shows the format of the table that will be generated.
CB
Basis
X1
X2
S1
S2
S3 b θ
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
This will be used to calculate Zj and then Cj-Zj. The BFS will now be checked to see if it’s the absolute extrema for the problem. If not, the process will be repeated in order to find the true extrema values.
Program Details:
The program will be written in Python and will use wxPython for GUI construction. This will allow it to be run on both UNIX based and Windows based PCs.
On starting the application, the user will be presented with a GUI where the equations can be entered. On clicking the submit button, the table will be displayed with step-by-step processing.
Algorithm:
1) Read in the values in the text box to respective variables.
2) Append slack variables to each equation.
3) Take column of largest coefficient and divide b by the