Linear/Integer Programming

To enter the model for this situation, select the Linear/Integer item from the OR_MS menu. The dialog defining the structure of the linear model is presented. Fields are available to define the Name, number of variables and number of constraints for the model. Buttons determine whether the problem is a maximization or a minimization, and the integer character of the variables of the problem. The variables may be specified as no integer, all integer, or mixed. In the latter case the field to the right of the buttons determines the number of leading integer variables. We will discuss the specification of integer variables later.

One important point concerns the Problem Name. The entry here is used to provide Excel names to many ranges on the worksheet as well as provide a name for the worksheet on which the model resides. The name must satisfy Excel's restrictions for naming ranges, that is: the names must not contain spaces, they must start with a letter and they may not include punctuation marks. If an error occurs when this dialog occurs, try providing a different name for the problem. The program provides automatic names like LP1, LP2 and so on. The student may provide a more descriptive name. Once the problem is placed on the worksheet, the worksheet name

may not bechangedwithout causing failures in subsequent operations.The checkboxes in the middle of the dialog provides instructions to the add-in about the features of the model that are to be included. The boxes "Include Minimums" and "Include Maximums" determine respectively whether ranges are provided for lower and upper bounds for the decision variables. The "Sensitivity Analysis" button tells the solver add-ins whether to provide a sensitivity analysis for the optimum solution. When checked, the "Random Problem" option generates random numbers for the objective function coefficients, constraint limits and constraint coefficients. This makes it easy to experiment with the different sized models and the different solver models. Random problems have all (<=) constraints and positive coefficients. Feasible solutions are guaranteed.

The grouping labeled Constraint Bounds holds two possibilities, one or two. These buttons determine if the model has one limit per constraint or two limits per constraint. For this example we illustrate the first option where each constraint is a less than or equal to constraint (<=), so we choose the "One" option.

The grouping labeled Solver Option holds buttons for the selection of either the Excel Solver or the LP Solver provided in the collection. Both can solve problems in the linear form, with or without the integer requirement. We have chosen the Excel Solver for the example. The add-in provides automatic loading and calling of the Excel Solver. To take advantage of the automatic feature you must open the Solver dialog before defining a model. For more information see the Excel Solver page at this site.

The Default Button on the worksheet brings up another dialog that specifies default values for model parameters. The dialog is shown below with the initial values for the defaults. These values may be changed.

All variables and constraints constructed on the worksheet will have the defaults specified on this dialog. Although values for all parameters can be entered directly on the worksheet, sometimes it is easier to specify them here. For example, many integer problems allow only values of 0 or 1 for the variables. The upper bound of 1 is most easily entered here. Since models can be constructed in several calls to the problem definition dialog, different parts model can have different default values.

Updated 1/16/01

Operations Research Models and Methods

by Paul A. Jensen and Jon Bard, University of Texas, Copyright by the Authors