Understanding Solver Results messages Understanding Solver Results messages

If Solver stops with a solution (set of values for the decision variables) that is different from what you expect, or what you believe is correct, please follow the suggestions below. You can usually narrow down the problem to one of a few possibilities.

 Be sure to read the message in the Solver Results dialog, and check the explanation of the message in this Help topic.

 Consider the possibility that the solution found by Solver is correct, and that your expectation is wrong. This may mean that what your model actually says is different from what you intended.

 If you receive the message “Solver could not find a feasible solution,” read the topic Understanding the Feasibility Report. Understanding the Feasibility Report

The purpose of the Feasibility Report is to help you isolate the source of infeasibilities in your model. Most often, an infeasible result simply means that you’ve made a mistake in formulating your model, such as specifying a <= relation when you meant to use >=. However, if your model contains hundreds of constraints, it can be quite challenging to locate an error of this type. By isolating the infeasibility to a small subset of the constraints, the Feasibility Report can show you where to look, and hence save you a good deal of time.

To produce the Feasibility Report, Solver may test many different variations of your model, each one with different combinations of your original constraints. This process ultimately leads to a so-called “Irreducibly Infeasible System” (IIS) of constraints and variable bounds which, taken together, make the problem infeasible, but with the property that if any one of the constraints or bounds is removed from the IIS, the problem becomes feasible.

In a model with many constraints that “interact” with each other in complex ways, there may be many possible subsets of the constraints and bounds that constitute an IIS. Often, some of these subsets have many fewer constraints than others. Solver attempts to find an IIS containing as few constraints as possible, trying first to eliminate “formula” constraints and then to eliminate simple variable bounds – since it is usually easier to understand the effects of variable bounds on the infeasibility of the resulting IIS.

The Feasibility Report performs a complete analysis of your model, including bounds on the variables, to find the smallest possible subset of these constraints that is still infeasible. This can sometimes take a great deal of computing time (if necessary, you can interrupt the analysis and production of the report by pressing the ESC key). The Feasibility-Bounds alternative performs a similar analysis of the constraints, but does not attempt to eliminate bounds on the variables, to save computing time.

 If you receive the message “The linearity conditions required by this LP Solver are not satisfied,” read the topic Understanding the Linearity Report.

Understanding the Linearity Report

The purpose of the Linearity Report is to help you pinpoint nonlinear formulas in your model. The format of the Linearity Report is similar to that of the Answer Report: It lists each decision variable and constraint on a separate row, with its cell reference, a “name” as described for the Answer Report, the cell’s original and final values, and a column containing “Yes” (the objective or constraint is a linear function, or the variable occurs linearly throughout the model) or “No” (the function is nonlinear, or the variable occurs nonlinearly). Since you are normally interested in the nonlinearities, any “No” entries appear in boldface.

If your objective or constraints are computed through a chain of formulas in different cells that ultimately depend on the decision variable cells, you may want to use Excel’s auditing features to trace the dependents of your formula cells and find the point where you’ve introduced a nonlinear dependence. If you multiply or divide two quantities that both depend on decision variables, the result is nonlinear. Excel functions other than SUM, SUMPRODUCT and selected other cases will compute a nonlinear or non-smooth function of the variables. For more information, see the topic Linear Functions.

Once you identify specific formulas that are nonlinear, you should determine whether they are correct for your problem, and decide whether they can be rewritten as linear functions, or whether there is an alternative, linear formulation of your problem. If you can formulate the model as a linear programming problem, you’ll have the benefit of faster and more reliable solutions – especially if you also have integer restrictions on decision variables. Otherwise, you’ll have to select the GRG Nonlinear or Evolutionary Solving method to solve your problem.

 If your model includes integer, binary or alldifferent constraints, read the topic Integer Constraints and the Integer Optimality Tolerance.