     Constructing the Worksheet Solving the Problem Download Linear/Integer Programming - Solving the Problem The problem is Solved by clicking on the Solve button. When using the Excel Solver, the model is created, loaded into the Solver program and the algorithmic portion of Solver is called to obtain a solution. The solution for the example is shown below. The optimum decision variable values are in the range H8:L8. The objective function value is in F4. The constraint values give the evaluation of the constraint expressions for the optimum solution. The change button is used to change the structure of the problem by changing the numbers of variables and/or constraints or by changing the integer nature of the variables. The solver option, the Goal (max or min) and the Sensitivity choice can also be changed. All changes are automatically incorporated into the Solver model. Jensen Solver The Jensen LP/IP Solver is called automatically when the Solve button is clicked. Jensen solvers are available for linear programming problems and network flow programming problems with or without integer variables. Generally, it takes much longer to solve problems when some or all the variables are required to be integer. The network solver can also solve some nonlinear problems. Excel Solver When using the Excel Solver, you must establish connection to the Solver by selecting the Solver option from the Tools menu. This opens a dialog. Just close the dialog. The add-in will control subsequent activities with regard to the Excel Solver. After the Math Programming add-in has created a model that uses the Excel Solver, the student can interact with the Solver via the Tools menu. The Solver dialog for the example problem is below. The fields refer to named ranges on the worksheet. Clicking the Solver button initiates the Solver algorithm. The Options button provides access to Solver options that control the solution procedure. The most important option for linear programming is the Assume Linear Model button. When checked, the solution algorithm is a simplex procedure, otherwise a nonlinear programming algorithm is used even when the model is linear. Generally, the simplex procedure is faster and more accurate than nonlinear programming for linear problems. When Solver has found the optimum, the Results dialog appears. Several optional reports may be selected. The Sensitivity report provides reduced costs and sensitivity ranges for the variables and dual values and sensitivity ranges for the constraint bounds. If the add-in has called the Solver, this dialog is skipped. A sensitivity report is generated if that option had been selected during the problem definition. It is usually only necessary to load a particular model only once. If the characteristics of the model such as coefficients, bounds, number of variables and number of constraints are changed, the model is automatically adjusted and need not be reloaded. To solve a modified problem, simply click on the Solve button in the Solver dialog. On the other hand if the integrality restrictions for some variables or the direction of the objective function is changed (from max to min or from min to max) then the model must be reloaded into solver. The add-in does all this automatically, however, the changes can also be accomplished by interacting directly with the Excel Solver.  Operations Research Models and Methods
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by Paul A. Jensen
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