sda 3e chapter 14

8/4/2019 SDA 3E Chapter 14

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2007 Pearson Education

Chapter 14: Solving andAnalyzing Optimization Models


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Excel Solver Standard Solver (packaged with Excel)

Premium Solver (available on CD-ROM)

Can toggle between both versions


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Premium Solver Solution procedures

Standard GRG Nonlinear used for solving nonlinear optimizationproblems

Standard Simplex LP used for solving linear and linear integeroptimization problems

Standard Evolutionary used for solving complex nonlinear andnonlinear integer problems


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Differences in Options Dialog

Standard Premium


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Click hereto addconstraints

Set cell references forobjective function and

decision variables

Product

Mix Model

ClickSolve


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Add Constraint Dialog


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Solver Results Dialog

Select reports to save


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Possible Outcomes Unique optimal solution

Alternate optimal solution

Unbounded problem

Infeasible problem


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Product Mix Model Solution


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Slack and Binding Constraints Slackis the difference between the left- and right-

hand sides of a constraint when the optimal solution issubstituted for the variables.

A constraint is binding if the slack is zero. Example:

Amount of Component Used Amount Available Amount of Component Used + Amount of

Component Unused = Amount Available Slack = Amount of Component Unused

= Amount Available - Amount of Component Used


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Answer Report


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Sensitivity Report


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Interpreting the Sensitivity

Report Reduced cost how much the objective

coefficient needs to change for a variable tobecome positive in the optimal solution

Allowable Increase/Decrease how much anindividual objective coefficient can changebefore the optimal values of the decision

variables will change Shadow price how much the value of theobjective function will change as the right-hand-side of a constraint is increased by 1.


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Solver Limits Report Shows the lower limit and upper limit that each variable

can assume while satisfying all constraints and holding allof the other variables constant.


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How Solver Creates Names in

Reports How you design your spreadsheet model will affect on

how Solver creates the names used in the outputreports.

Poor spreadsheet design can make it difficult orconfusing to interpret the Answer and Sensitivityreports.

Solver assigns names to target cells, changing cells,and constraint function cells by concatenating the textin the first cell containing text to the left of the cellwith the first cell containing text above it.


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Example


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Models With Lower and Upper

Bounds Bounded variables are listed in theAdjustable Cells section.

Reduced costs may be interpreted asshadow prices.


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ExampleAdd constraint: G 400


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Modeling Trick Using reduced costs as shadow

prices can be a bit confusing.

In your spreadsheet model,define a new set of cells for anydecision variables that haveupper or lower bound constraintsby referencing (not copying) theoriginal changing cells.

In the Solver model, use thisauxiliary variable cell to definethe bound constraint; that is,B18 B8.


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Solver Results Using Auxiliary

Variable


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Difficulties With Solver A poorly scaled modelone in which the parameters of the

objective and constraint functions differ by several orders ofmagnitude may cause round-off errors in internalcomputations or error messages such as The conditions for

Assume Linear Model are not satisfied. The values of thecoefficients in the objective function and constraints, as well asthe right hand sides, should not differ from each other by afactor of more than 1,000 or 10,000.

Remedies

Keep the solution that Solverfound and run Solveragainstarting from that solution. Solver also has a checkbox for Use Automatic Scaling that

can be used, especially if solver gives an error message thatlinearity is not satisfied.


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Solving Integer Models Define decision variables as either int or bin in

the Add Constraint dialog

Set tolerance toZero in Integer

Options


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Solving Nonlinear Models Select Standard GRG Nonlinear in Premium

Solver as the solution procedure

Sensitivity report is different for nonlinearmodels Reduced gradient is analogous to reduced

cost, but more difficult to interpret

Lagrange multipliers are similar to shadowprices, but give only approximate rates ofchange


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Hotel Pricing Example

Sensitivity Report


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Metaheuristics Used for difficult nonlinear problems

Premium Solver Standard Evolutionary

solution procedure Evolutionary Solver produces an Answer

Report a Population Report, which providesstatistics on the solutions encountered during

the search process, showing the best value,mean, standard deviation, maximum, andminimum values for each variable andconstraint function (excluding upper andlower bounds).


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Example Population Report


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Risk Analysis and Optimization Crystal Ballmay be used to conduct

post-optimality risk analysis to

understand the impact of uncertainty ofoptimization model parameters.


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OptQuest: Combining

Optimization and Simulation OptQuestsearches for optimal solutions

within Crystal Ballsimulation model

spreadsheets. OptQuestis also designed to find

solutions that satisfy a wide variety of

constraints or a set of goals that youmay define.


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OptQuest Procedure1. Create a Crystal Ballmodel of the decision problem.

2. Define the decision variables within Crystal Ball.

3. Invoke OptQuestfrom the Crystal Balltoolbar or the

corresponding menu.4. Create a new optimization file.

5. Select decision variables.

6. Specify constraints.

7. Select the forecast.

8. Modify OptQuestoptions.9. Solve the optimization problem.

10. Save the optimization files.

11. Exit OptQuest.

sda 3e chapter 14

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