The LP/IP Solver add-in provides an algorithm that solves Linear Programming problems. It can be used instead of the Excel solver for the linear programming models created by the Mathematical Programming add-in. It also works when some or all of the variables are required to be integer. When it is installed, a new item appears on the OR_MM menu, LP/IP Solver. Subroutines provided by the algorithm are called when the user clicks on the Solve button on the linear, integer, or mixed integer model sheets. The LP/IP Solver menu item will show a dialog only when a mathematical programming model constructed with the Math Programming add-in is present on the active worksheet. Otherwise the message below indicates that it is not available.

"This is not a valid worksheet for the LP/IP Solver"

When a valid worksheet is active, choosing the LP/IP Solver menu item presents the dialog below. These options only affect the Jensen LP/IP Solver, and do not affect the Excel Solver.

Solution Display Options

These options create a separate worksheet for algorithm details that shows iteration information from the solution algorithms. The reports are useful for the student who is learning about the solution methods used.

Simplex Iterations

This option creates a new worksheet with the suffix Details. Information about the iterations of the primal simplex are printed on this worksheet. The number field to the left on the dialog holds the number of iterations to be displayed. Since some problems may require thousands of iterations, this number should be set to a reasonable value or the memory requirement for Excel will be excessive.

The figure below shows the detail worksheet for the Production problem described earlier. The display shows the slack variables added for the four constraints. No artificial variables are required. Five simplex iterations are required to find a solution. The display shows details about the iterations.

Enumeration Tree

When the production variables are required to be integer, the LP_IP add-in can be used to show the details of the enumeration process. Using the LP/IP Solver dialog we click the Show Enumeration Tree checkbox. The number field to the left on the dialog is the number of enumeration tree vertices to be displayed.

While the problem is solved a record is kept of the enumeration process and displayed on the Details worksheet. The example requires an enumeration tree with 42 vertices.

Clicking both display checkboxes will show both the enumeration tree and subsequent steps of the simplex the simplex method used by the bounding procedure.

Algorithm Control Options

Initial Variable Values

Two different starting strategies are available. The first option starts with all variables values equal to 0. The second strategy gathers the initial variable values from the values shown on the worksheet.. The algorithm starts with these values. This advanced start option reduces the number of iterations required when only slight modifications are made to the model.

MIP Tolerance

When solving all integer or mixed integer programming problems, vertices of the enumeration tree are fathomed when the relaxed solution objective is less than (for a maximization problem) than the incumbent solution. This tolerance makes the fathoming test a little easier by fathoming the vertex if its relaxed objective is within x% of the incumbent solution, where x is the number entered in this field. The solution may be found with fewer iterations and less time when this value is greater than 0. When the tolerance is other than 0, however, there is no guarantee that the optimum solution is obtained. It is a guaranteed that the solution is with x% of the optimum. The Excel Solver has a similar tolerance specified in the Options dialog of the Solver.

Time Limit

When solving all integer or mixed integer programming problems, the process may take a long time. The program will stop when this time limit is reached. The user may give up at this point or continue the optimization. The Excel Solver has a similar time limit specified in the Options dialog of the Solver.

Update Incumbent on the Screen

When solving all integer or mixed integer programming problems, the algorithm may find feasible solutions during the enumeration process. The feasible solution with the best value is called the incumbent solution. Although intermediate steps are not displayed on the model worksheet while the process continues, when this checkbox is selected, the display will be changed whenever a new incumbent is discovered.