LP Explorer 1.0: User Guide

This is an introduction to the Java applet LP Explorer. It is not an introduction to Linear Programming or to the Simplex method, for which a textbook on optimization should be consulted.

Starting the applet

LP Explorer is written in the Java programming language and is technically referred to as an applet. It appears on a WWW page as a button with "LP Explorer" written on it, for example

Clicking on a given "LP Explorer" button starts the applet for a particular LP problem. Here are some further examples. Documentation for the parameter list used by the applet is available. However, it is also possible to enter the problem data via a sequence of two forms

The applet display

At the top of the applet is a statement of the LP problem to be solved. Below this is an area where messages are displayed. The current tableau and the previous tableau are displayed below the message bar. The applet starts the simplex method at the origin so, in the initial tableau, the original variables are nonbasic and the slack variables are basic. Since no iterations have been performed, the previous tableau is blank.

For problems with two original variables, a graphical representation of the feasible region is displayed on the left of the tableaux. The constraint lines are displayed in red with their intercepts indexed by constraint number. The current vertex is indicated by a cyan dot and a magenta objective line is drawn through it.

Controlling the applet

The action of the applet is controlled by clicking on the following buttons.

The Zoom In and Zoom Out buttons may be used to scale the graph.
A column selection is made by clicking on the box containing the variable at the top of the column.
A row selection is made by clicking on the box containing the row number at the left end of the row. If a row selection is made without a column having been selected then that row selection is disallowed.
The Update button is used to move to the next vertex and determine the updated tableau.
Once an iteration has been performed, the Back button may be clicked to step back to the previous tableau. If this is done then different column and row selections may be made.
When the back button has been clicked, the Forward button may be clicked to step forwards to the tableau corresponding to the subsequent iteration.
Once an optimal solution has been found, the Sensitivity button may be clicked to explore the sensitivity of the optimal solution with respect to coefficients in the LP problem.

Highlighting

Whenever a valid column or row selection is made, the corresponding values in the tableau are highlighted by switching the text from black to red. red a column selection is made, the ratios are displayed. For problems in two variables, the vertices corresponding to these ratios are indicated by red and green dots. The green dot corresponds to the correct row selection and the red dot(s) correspond(s) to row selections which would result in a move outside the feasible region.

Incorrect/alternative row/column selections

In order to allow the results of incorrect or alternative row and column selections to be observed, the applet allows (limited) abuse of the simplex method.

If a column is selected which does not correspond to that defined by the simplex method then, so long as the corresponding variable is nonbasic, the applet allows the selection to stand and a row selection may be made. If the cost row coefficient is of the wrong sign then a `downhill' step may be made but the Back button must then be clicked to return to the previous vertex. Similarly, the tableau may be updated following an invalid row selection but Back button must then be clicked to return to the previous vertex.

Last modified:
since 16/1/98.
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