Concepts & Techniques

**Tell me and I'll forget.Show me and I might remember.But involve me and I will understand.**

Computer-assisted learning is to convey a vast amount of information in a very short period of time. It is a powerful method of reinforcing concepts and topics first introduced to you through your textbook, and discussion in the classroom. Computer-assessed learning enables you in a powerful way to comprehend complex concepts.

**To search the site**, try __E__dit | __F__ind in page [Ctrl + f]. Enter a word or phrase in the dialogue box, e.g. "`parameter " `or "`linear " `If the first appearance of the word/phrase is not what you are looking for, try `F``ind Next`.

- Introduction
- Computer Package: WinQSB
- Linear Programming (LP) implementations with the WinQSB
- Managerial Interpretation of the WinQSB Report for LP
- How to Use LINDO and Interpret Its Output
- Solving Unrestricted Variables by LINDO
- Integer LP Programs by LINDO
- Shadow Price Might Have Wrong Sign
- Solving LP Problems by Excel
- Network Models Implementations with the WinQSB
- NonLinear Programming Implementations with the WinQSB
- Decision Analysis Implementation with the WinQSB
- Business Forecasting Implementation with the WinQSB
- How to Import/Export Data from WinQSB to Other Applications
- Linear Programming by Excel Solver
- Linear Programming Software Survey

- Forecasting Software Survey

- Decision Analysis Software Survey

**Companion Sites:**

- Linear Optimization Solvers to Download
- Success Science
- Leadership Decision Making
- Linear Programming (LP) and Goal-Seeking Strategy
- Artificial-variable Free LP Solution Algorithms
- Integer Optimization and the Network Models
- Tools for LP Modeling Validation
- The Classical Simplex Method
- Zero-Sum Games with Applications
- Linear Algebra and LP Connections
- From Linear to Nonlinear Optimization with Business Applications
- Sensitivity Region for LP Models
- Zero Sagas in Four Dimensions
- Probabilistic Modeling
- Systems Simulation
- Keywords and Phrases
- Compendium of Web Site Review
- Collection of JavaScript E-labs Learning Objects
- Decision Science Resources

The Value of Performing Experiment: If the learning environment is focused on background information, knowledge of terms and new concepts, the learner is likely to learn that basic information successfully. However, this basic knowledge may not be sufficient to enable the learner to carry out successfully the on-the-job tasks that require more than basic knowledge. Thus, the probability of making real errors in the business environment is high. On the other hand, if the learning environment allows the learner to experience and learn from failures within a variety of situations similar to what they would experience in the "real world" of their job, the probability of having similar failures in their business environment is low. This is the realm of simulations-a safe place to fail.

The appearance of management science software is one of the most important events in decision making process. OR/MS software systems are used to construct examples, to understand the existing concepts, and to discover useful managerial concepts. On the other hand, new developments in decision making process often motivate developments of new solution algorithms and revision of the existing software systems. OR/MS software systems rely on a cooperation of OR/MS practitioners, designers of algorithms, and software developers.

The major change in learning this course over the last few years is to have less emphasis on strategic solution algorithms and more on the modeling process, applications, and use of software. This trend will continue as more students with diverse backgrounds seek MBA degrees without too much theory and mathematics. Our approach is middle-of-the-road. It does not have an excess of mathematics nor too much of software orientation. For example, we lean how to formulate problems prior to software usage. What you need to know is how to model a decision problem, first by hand and then using the software to solve it. The software should be used for two different purposes.

Personal computers, spreadsheets, professional decision making packages and other information technologies are now ubiquitous in management. Most management decision-making now involves some form of computer output. Moreover, we need caveats to question our thinking and show why we must learn by instrument. In this course, the instrument is your computer software package. Every student taking courses in Physics and Chemistry does experimentation in the labs to have a good feeling of the topics in these fields of study. You must also perform managerial experimentation to understand the Management Science concepts and techniques.

Learning Objects: My teaching style deprecates the 'plug the numbers into the software and let the magic box work it out' approach.

Computer-assisted learning is similar to the experiential model of learning. The adherents of experiential learning are fairly adamant about how we learn. Learning seldom takes place by rote. Learning occurs because we immerse ourselves in a situation in which we are forced to perform. You get feedback from the computer output and then adjust your thinking-process if needed. Unfortunately, most classroom courses are not learning systems. The way the instructors attempt to help their students acquire skills and knowledge has absolutely nothing to do with the way students actually learn. Many instructors rely on lectures and tests, and memorization. All too often, they rely on "telling." No one remembers much that's taught by telling, and what's told doesn't translate into usable skills. Certainly, we learn by doing, failing, and practicing until we do it right. The computer assisted learning serve this purpose.

- Computer assisted learning is a collection of experimentation (as in Physics lab to learn Physics) on the course software package to understand the concepts and techniques. Before using the software, you will be asked to do a simple problem by hand without the aid of software. Then use the software to see in what format the software provides the solution. We also use the software as a learning tool. For example, in order to understand linear programming sensitivity analysis concepts, you will be given several managerial scenarios to think about and then use the software to check the accuracy of your answers.
- To solving larger problems which are hard to do by hand.

Unfortunately, the first objective is missing in all management science/operations research textbooks.

What is critical and challenges for you is to lean the new technology, mainly the use of software within a reasonable portion of your time. The learning curve of the software we will be using is very sharp.

We need caveats to question our thinking and show why we must learn-to by instrument that in this course is your computer package. Every student taking courses in Physics and Chemistry does experimentation in the labs to have a good feeling of the topics in these fields of study. You must also perform experimentation to understand the Management Science concepts. For example, you must use your computer packages to perform the "what if" analysis. Your computer software allows you observe the effects of varying the "givens".

You will be engaged in thinking process of building models rather than how to use the software to model some specific problems. Software is a tool, it cannot substitute for your the thinking process. We will not put too much focus on the software at the expense of leaning the concepts. We will lean step-by-step problem formulation, and managerial interpretation of the software output.

Managerial Interpretations: The decision problem is stated by the decision maker often in some non-technical terms. When you think over the problem, and finding out what module of the software to use, you will use the software to get the solution. The strategic solution should also be presented to the decision maker in the same style of language which is understandable by the decision maker. Therefore, just do not give me the printout of the software. You must also provide managerial interpretation of the strategic solution in some non-technical terms.

The QSB (Quantitative Systems for Business) is developed and maintains by Yih-Long Chang. This software package contains the most widely used problem-solving algorithms in Operations Research and Management Science (OR/MS). The WinQSB is the Windows version of the QSB software package runs under the CD-ROM Windows. There is no learning-curve for this package, you just need a few minutes to master its useful features.

The *WinQSB Decision Support Software for MS/OM* is available from the John Wiley & Sons publisher, ISBN 0-471-40672-4, 2003.

**Further Reading:**

Chang Y-L., *QSB+: Quantitative Systems for Business Plus*, Prentice Hall, 1994.

This course uses a professional software called WinQSB, available at: WinQSB Software.

- Create a folder (directory) named WinQSB
- Open the CD-ROM files, and save this file to the folder created in step 1.
- Run the WinQSB.exe program first (You must execute these programs in the proper sequence). Go to the file location (where you saved it step 2) and double click (or click on file-open) to execute the file. Follow the prompts and extract the files to the WinQSB folder that you created in step 1.
- Reboot your system.
- You will now have a list of files (both executable and support files) in the WinQSB folder that you created in step 1. To use the Linear Program model, for example, click (or double-click) on the file called LP-ILP.exe.

If you have no access to any computer outside, you may use the university computer network. The QSB is available on the the University NT server. To reach the system you need an NT account. To obtain your NT account see the Technical Assistance (TA) at the lower level of Business Center. After obtaining your username and a password then you can access the NT system. To reach the QSB, click on Start, choose the Business School Applications, then click on the Shortcut to QSB, or QSB. Then, pick-up the application you wish. All QSB applications are therein.

Computer always solves real world linear programs mostly using the simplex method. The coefficients of the objective function are known as cost coefficients (because historically during World War II, the first LP problem was a cost minimization problem), technological coefficients, and the RHS values. This is a perfect way to learn the concepts of sensitivity analysis. As a user, you have the luxury of viewing numerical results and comparing them with what you expect to see.

The widely used software for LP problems is the Lindo package. A free Windows version can be downloaded right from LINDO's Home page at LINDO, http://www.lindo.com.

Caution! Before using any software, it is a good idea to check to see if you can trust the package.

Here is an LP Software Guide for your review.

Lindo is a popular software package, which solves linear programs. The LP/ILP application of WinQSB does the same operations as Lindo does, but in a much easier to use fashion.

The name LINDO is an abbreviation of __L__inear __IN__teractive __D__iscrete __O__ptimization. Here the word "discrete" means jumping from one basic feasible solution (BFS) to the next one rather than crawling around the entire feasible region in search of the optimal BFS (if it exists).

Like almost all LP packages, including WinQSB, Lindo uses the simplex method. Along with the solution to the problem, the program will also provide ordinary sensitivity analysis of the Objective Function Coefficients (called Cost Coefficients) and the Right-hand-side (RHS) of the constraints. Below is an explanation of the output from the LINDO package.

Suppose you wish to run the Carpenter's Problem. Bring up the LINDO (or your WinQSB) package. Type in the current window as follow:

MAX 5X1 + 3X2

S.T. 2X1 + X2 < 40

X1 + 2X2 < 50

End

- The objective function should not contain any constant. For example, Max 2X1 + 5 is not allowed.
- All variables must appear in the left side of the constraints, while the numerical values must appear on the right side of the constraints (that is why these numbers are called the RHS values).
- All variables are assumed to be nonnegative. Therefore, do not type in the non-negativity conditions.

If you wish to get all Simplex Tableaux, then

- Click on "Reports" and then choose "Tableau", then click on "Solve" and choose "Pivot" then choose "OK", "Close", "Cancel", continue in this manner until you get the message "Do? Range (Sensitivity) Analysis". Select "Yes", if you wish. After minimizing the current window, you will see the output that you may print for your managerial analysis.
- Otherwise, click on "Solve", then choose "Solve".

On the top of the page is the initial tableau, and across the top of tableau are the variables. The first row in the tableau is the objective function. The second row is the first constraint. The third row is the second constraint, and so on until all constraints are listed in the tableau.

Following the initial tableau is a statement that indicates the entering variable and the exiting variable. The exiting variable is expressed as which row the entering variable will be placed. The first iteration tableau is printed next. Entering statements and iterations of the tableau continue until the optimum solution is reached.

The next statement, `LP OPTIMUM FOUND AT STEP 2' indicates that the optimum solution was found in iteration 2 of the initial tableau. Immediately below this is the optimum of the objective function value. This is the most important piece of information that every manager is interested in.

In many cases you will get a very surprising message: "LP OPTIMUM FOUND AT STEP 0." How could it be step 0. Doesn't first have to move in order to find out a result.....? This message is very misleading. Lindo keeps a record of any previous activities performed prior to solving any problem you submit in its memory. Therefore it does not show exactly how many iterations it took to solve your specific problem. Here is a detailed explanation and remedy for finding the exact number of iterations: Suppose you run the problem more than once, or solve a similar problem. To find out how many iterations it really takes to solve any specific problem, you must quit Lindo and then re-enter, retype, and resubmit the problem. The exact number of vertices (excluding the origin) visited to reach the optimal solution (if it exists) will be shown correctly.

Following this is the solution to the problem. That is, the strategy to set the decision variables in order to achieve the above optimal value. This is stated with a variable column and a value column. The value column contains the solution to the problem. The cost reduction associated with each variable is printed to the right of the value column. These values are taken directly from the final simplex tableau. The value column comes from the RHS. The reduced cost column comes directly from the indicator row.

Below the solution is the `SLACK OR SURPLUS' column providing the slack/surplus variable value. The related shadow prices for the RHS's are found to the right of this. Remember: Slack is the leftover of a resource and a Surplus is the excess of production.

The binding constraint can be found by finding the slack/surplus variable with the value of zero. Then examine each constraint for the one which has only this variable specified in it. Another way to express this is to find the constraint that expresses equality with the final solution.

Below this is the sensitivity analysis of the cost coefficients (i.e., the coefficients of the objective function). Each cost coefficient parameter can change without affecting the current optimal solution. The current value of the coefficient is printed along with the allowable increase increment and decrease decrement.

Below this is the sensitivity analysis for the RHS. The row column prints the row number from the initial problem. For example the first row printed will be row two. This is because row one is the objective function. The first constraint is row two. The RHS of the first constraint is represented by row two. To the right of this are the values for which the RHS value can change while maintaining the validity of shadow prices.

Note that in the final simplex tableau, the coefficients of the slack/surplus variables in the objective row give the unit worth of the resource. These numbers are called shadow prices or dual prices. We must be careful when applying these numbers. They are only good for "small" changes in the amounts of resources (i.e., within the RHS sensitivity ranges).

Creating the Non-negativity Conditions (free variables): By default, almost all LP solvers (such as LINDO) assume that all variables are non-negative.

To achieve this requirement, convert any unrestricted variable Xj to two non-negative variables by substituting y - Xj for **every** Xj. This increases the dimensionality of the problem by only one (introduce one y variable) regardless of how many variables are unrestricted.

If any Xj variable is restricted to be non-positive, substitute - Xj for every Xj. This reduces the complexity of the problem.

Solve the converted problem, and then substitute these changes back to get the values for the original variables and optimal value.

**Numerical Examples**

Maximize -X1

subject to:

X1 + X2 Â³ 0,

X1 + 3X2 Â£ 3.

The converted problem is:

Maximize -y + X1

subject to:

-X1 - X2 + 2y Â³ 0,

-X1 - 3X2 + 4y Â£ 3,

X1 Â³ 0,

X2 Â³ 0,

and y Â³ 0.

The optimal solution for the original variables is: X1 = 3/2 - 3 = -3/2, X2 = 3/2 - 0 = 3/2, with optimal value of 3/2.

Maximize X1

Subject To:X1 + X2 > 0

2X1 + X2 < 2

X1 > 0

X2 < 0

The LINDI input is:

Maximize X1

S.T.X1 + X2 > 0

2X1 + X2 < 2

X1 > 0

X2 < 0

End

free X1

free X2

Solution is (X1 = 2, X2 = -2) with optimal value of 2.

For details on the solution algorithms, visit the Web site Artificial-Free Solution Algorithms, example N0. 7 therein.

Suppose in the Carpenterâs Problem ever table needs four chairs; then the LP formulation is:

Max 5X1+3X2

S.T.

2X1+X2 Â£ 40

X1 + 2X2 Â£50

4X1 - X2 = 0

X1 Â³0

X2 Â³0

End

GIN X1

GIN X2

GIN stands for general integer variable.

The optimal solution is (X1 = 5, X2 = 20) with optimal value of 85.

Special case of binary variables (X= 0 or 1) is also permitted in LINDO, the command to make the variable X a binary variable is INT X1.

**Variable Type:** Select the variable type from the "Problem Specification" screen (the first screen you see when introducing a new problem); for linear programming use the default "Continuous" option.

**Input Data Format:** Select the input data format from the "Problem Specification" screen. Usually, it is preferred to use the Matrix format to input the data. In the Normal format the model appears typed in. This format may be found more convenient when solving a large problem with many variables.
You can go back and forth between the formats, selecting the "Switch to theâ¦" from the Format menu.

**Variable/Constraint Identification:** It is a good idea to rename variables and constraints to help identify the context they represent. Changing the names of variables and constraints is done in the Edit menu.

**Best Fit:** Using the best fit from the Format menu lets each column have its own width.

**Solving for the Optimal Solution (if it exists):** Select Solve the problem from the Solve and analyze menu, or use the "solve" icon at the top of the screen. The run returns a "Combined Report" that gives the solution and additional output results (reduced costs, ranges of optimality, slack/surplus, ranges of feasibility, and shadow prices).

**Solving by the Graphic Method:** Select the Graphic method from the Solve and Analyze menu (can only be used for a two-variable problem.) You can also click the graph icon at the top the screen. You can re-scale the X-Y ranges after the problem has been solved and the graph is shown. Choose the Option menu and select the new ranges from the drop down list.

**Alternate Optimal Solutions (if they exist):** After solving the problem, if you are notified that "Alternate solution exists!!", you can see all the extreme point optimal solutions by choosing the Results menu and then select Obtain alternate optimal. Also visit Multiple Solutions section on this Web site for some warnings.

**Notes:**

Use the "Help" file in WinQSB package to learn how to work with it.

For entering problem into the QSB software; for a constraint such as X1 + X2 Â³ 50, the coefficient is 1 and should be entered that way in the software. For any variables that are not used in that particular constraint (for example if there was X3 in the problem but it was not part of the above constraint), just leave the cell blank for that constraint.

You can change the direction of a constraint easily by clicking on Â£ (or Â³) cell.

To construct the dual of a given problem click on Format, then select Switch to the Dual Form.

If you are not careful you may have difficulty with entering LP problem in WinQSB. For example, in a given problem a few of your constraints may have variable on the right hand side (RHS). You cannot enter variable name on the RHS cell otherwise you keep getting an infeasibility response. Only numbers can be entered on the RHS. For example, for the constraint X2 + X4 Â£ .5X5 one must write it first in the form of X2 + X4 - .5X5 Â£ 0, then using any LP package including your QSB.

Unfortunately, in some browsers the Graphical Methods of WinQSB may not be available. However, one may, e.g., use the following JavaScript instead.

- The objective function criterion (Max or Min).
- The type of each constraint.
- The actual coefficients for the problem.

The combine report is a solution report consists of both the solution to the primal (original) problem and it Dual.

The typical output generated from linear programming software includes:

- The optimal values of the objective function.
- The optimal values of decision variables. That is, optimal solution.
- Reduced cost for objective function value.
- Range of optimality for objective function coefficients. Each cost coefficient parameter can change within this range without affecting the current optimal solution.
- The amount of slack or surplus on each constraint depending on whether the constraint is a resource or a production constraint.
- Shadow (or dual) prices for the RHS constraints. We must be careful when applying these numbers. They are only good for "small" changes in the amounts of resources (i.e., within the RHS sensitivity ranges).
- Ranges of feasibility for right-hand side values. Each RHS coefficient parameter can change within this range without affecting the shadow price for that RHS.

The following are detailed descriptions and the meaning of each box in the WinQSB output beginning in the upper left-hand corner, proceeding one row at a time. The first box contains the decision variables. This symbol (often denoted by X1, X2, etc.) represents the object being produced. The next box entitled "solution value" represents the optimal value for the decision variables, that is, the number of units to be produced when the optimal solution is used. The next box entitled "unit costs" represents the profit per unit and is the cost coefficient of the objective function variables.

The next box "total contribution", is the dollar amount that will be contributed to the profit of the project, when the total number of units in the optimal solution is followed. This will produce the optimal value. The next bow is the "Reduced Cost", which is really the increase in profit that would need to happen if one were to begin producing that item, in other words the product, which is currently is not produce becomes profitable to produce.

The next box over is the "allowable minimum" and "allowable maximum", which shows the allowable change in the cost coefficients of that particular item that can happen and still the current the optimal solution remains optimal. However, the optimal value may change if any cost coefficient is changed but the optimal solution will stay the same if the change is within this range. Remember that these results are valid for one-change-at-a-time only and may not be valid for simultaneous changes in cost coefficients.

The next line is the optimal value, i.e., and the value of objective function evaluated at optimal solution strategy. This line shows the maximum (or minimum) value that can be derived under the given the optimal strategy.

The next line down contains the constraints; often C1, C2, etc. denote the constraints. Starting on the left-hand side the first box contains the symbol C1 that represents the first constraint. The next box is the constraint value. That is, the left-hand-side (LHS) of each C1 evaluated ate the optimal solution. The next box over is the "direction box", which is either greater than or equal to / less than or equal to, which are the direction of the each constraint. The next box is the right hand side value, which states the value that is on the right hand side of each constraint.

The next box is the difference between RHS and LHS numerical values called the slack or surplus box. If it is slack, it will have a less than or equal to sign associated with it, which means there is leftover of resources/raw material. If there is a surplus it will have a greater than or equal to sign associated with it, which means that there are over production. Next box over is the shadow price. If any slack or surplus is not zero then its shadow price is zero, however the opposite statement may not be correct. A shadow price is the additional dollar amount that will be earned if the right hand side constraint is increased by one unit while remaining within the sensitivity limits for that RHS.

The next two boxes show the minimum and maximum allowable for the right hand side constraints. The first box (minimum box) shows the minimum value that the RHS constraint can be moved to and still have the same current shadow price. The second box shows the maximum number that the constraint can be moved to and still have the same current shadow price. Recall that the shadow prices are the solution to the dual problem. Therefore, the allowable change in the RHS suggest how far each RHS can go-up or down while maintaining the same solution to the dual problem. In both cases the optimal solution to the primal problem and the optimal value may change.

For example, considering the following LP with a unique optimum solution:

Minimize 18X_{1} + 10X_{2}

Subject to:

12X_{1} + 10X_{2} Â³ 120000

10X_{1} + 15X_{2} Â£ 150000

X_{1}, X_{2} Â³ 0

Running this problem by LINDO, the final report gives the shadow prices U_{1} = -2.125, and U_{2} = 0.75, while the correct ones are U_{1} = 2.125, and U_{1} = - 0.75.

Another example:

Min 3X1 - 5x2s.t.

2x1 + x2 Â£ 40

x1 + 2x2 Â£ 50

X

end

Soling the problem by lindo, we get (X1 = 0, X2 = 25), with optimal value of -125, and shadow prices (0. 2.5). The correct shadow prices are (0. -2.5).

Arsham H., Foundation of Linear Programming: A Managerial Perspective From Solving System of Inequalities to Software Implementation,

- Before you begin using Solver, you should first enter the problem's parameters.
- Click Tools, then click Solver.
- In the Set Target Cell box, enter the cell you want to maximize, minimize or set to a specific value (Point to cell E18.) $E$18 should now appear in the box (Note: cell references should always be absolute).
- Click the Max option button to indicate that you want Solver to maximize the Total Profit.
- In the By Changing Cells box, enter the cell or range of cells that Excel can change to arrive at the solution (Highlight cells C15:D15).
- Click the Subject to the Constraints box, then click the Add... button to add the constraints: For exanple E17<=40 and E19<=50 and C15:D15>=C14:D14.
- Click the OK button.
- Click the Solve button.
- Click the OK button.

**Details:** One can also us Excel to solve linear programming problems using the **Solver tool**. Before we can use the solver tool, we need to set up our spreadsheet. One needs to include three different things for solver to run:

- Cells that contain values of the decision variables.
- A cell which will contain the value of the objective function.
- Cells which contain the value of all of the functional constraints in the problem.

The only thing left to do is to setup the constraints for the problem. Click the Add button to include a new constraint.

Let us begin by including the non-negativity constraints. Under Cell Reference select a cell which contains a value of a decision variable. Next, select the option ">=" then in the constraint box type 0. Select OK, you will now see the first non-negativity constraint included in the box labeled "Subject to the Constraints". Repeat this process for all non-negativity constraints.

Let us turn to the functional constraints. Click the add button again. Now Under the cell reference, select a cell which contains the value of one of the function constraints. Select the appropriate sign and type in the desired value. Click Ok. Repeat this for all of the functional constraints.

Once you have finished inputting the constraints, simply hit the solve button. The next thing you should see is another pop-up which tells you that Solver has found a solution. Simply hit OK. You should also notice that optimal solution will be reported in the cells which store the value of the decision rules, and the maximized value will be in the cell which contains the value of the objective function.

- Prepare a network model for the problem. (Note: you don't have to have a formal model for the data entry. You may modify it along with the process.)
- Select the command New Problem to start a new problem. The program will display a form to specify the problem. Click the problem type, objection function criterion, and the matrix form for the data entry. Also enter the number of nodes and the problem name. Press OK button when specification is done. A spreadsheet will appear for entering the network connection.
- Enter the arc or connection parameter/coefficient on the spreadsheet (matrix). Here are some tips:
- If there is no connection between two nodes, you may leave the corresponding cell empty or enter "M" for infinite cost.
- Use Tab or arrow keys to navigate in the spreadsheet.
- You may click or double click a data cell to select it. Double clicking the light blue entry area above the spreadsheet will high-light the data entry.
- Click the vertical or horizontal scroll bar, if it is shown, to scroll the spreadsheet.
- (Optional) Use the commands from Edit Menu to change the problem name, node names, problem type, objective function criterion, and to add or delete nodes. You may also change the flow bounds from Edit Menu if the problem is a network flow problem.
- (Optional) Use the commands from Format Menu to change the numeric format, font, color, alignment, row heights, and column widths. You may also switch to the graphic model from the Format Menu.
- (Optional, but important) After the problem is entered, choose the command Save Problem As to save the problem.

This program, NonLinear Programming (NLP), solves nonlinear objective functions with or without constraints. Constraints may also be nonlinear. Specific capabilities include:

- Solve the single and multiple variable unconstrained problems by line search method
- Solve the constrained problems by penalty function method
- Allow to analyze an assigned solution
- Analyze constraint violation for the constrained problems
- Perform the constraint function analysis with graph and table
- Perform the objective function analysis with graph and table
- Enter the objective function and/or constraints in algebraic functions
- Enter the problem in spreadsheet format

**To specify an NLP problem, here is the procedure:**

- Enter the problem title, which will be part of the heading for the later windows.
- Enter the number of variables.
- Enter the number of constraints. If you enter 0 constraint, the problem is an unconstrained problem.
- Click or choose the objective criterion of either maximization or minimization.
- If the specification is complete, press the OK button for entering the problem model. Otherwise, press the Cancel button. The Help button is for this help message.

The Da.exe "Decision Analysis" module in your WinQSB package is used for two distinct purposes: to solve large problems, and to perform numerical experimentation. Numerical experimentation including what-if analysis of the payoff matrix and the subjective probability assignments to the states of nature.

The following functions are available in the Da.exe module:

**Bayesian Analysis:** Select this option from the Problem Specification screen to input prior probabilities and conditional probabilities (probability of an indicator value given a state of nature). Then, press the 'solve' icon to obtain the posterior probabilities.

**Decision Trees:** You must draw the decision tree first to number all nodes, including the terminal nodes. These numbers become the node IDs, when building the decision tree within the program.

When you are ready to enter the data, select the option 'Decision Tree Analysis' from the 'Problem Specification' screen.

For each node, you will indicate the number of nodes immediately connected to it (type <node number>,â¦, <node number>).

Mistakes may be corrected by directly typing the changes into the proper cells.

**To enter a forecasting problem, here is the general procedure:**

- For a time series problem, prepare the historical data; for a linear regression problem, prepare the data for multiple factors.
- Select the command New Problem to specify the problem. Choose the appropriate problem type and enter the scope of the data. See Problem Specification.
- Enter the historical data (time series) or factor data (regression) on the spreadsheet. If it is a regression problem, you may want to change the factor or variable name before entering the data. Use the command Variable Name from the Edit Menu to change the variable names.
- (Optional) Use the commands from Format to change the numeric format, font, color, alignment, row heights, and column widths.
- (Optional, but important) After the problem is entered, choose the command Save Problem As to save the problem.

**To perform forecasting for a time series data, here is the general procedure:**

- If the problem is not entered, use the procedure How to Enter a Problem to enter the problem.
- For a general good practice, you may want to save the problem by choosing the command Save Problem As before solving it.
- Select the command Perform Forecasting. The program will bring up a form for setting up the forecasting. See Perform Forecasting for detail.
- After the forecasting is done, the result will be shown. You may choose the command Show Forecasting in Graph from the Results Menu to display graphical result.

**To show time series forecasting in graph, here is the general procedure:**

- Use the procedure How to Perform Time Series Forecasting to perform forecasting. Note that you may specify to retain the previous forecasting result for comparison.
- After the forecasting is done, the result will be shown. Choose the command Show Forecasting in Graph from the Results Menu to display graphical result. Note that you may change the graph range by using the command Change Range.

**To perform a linear regression, here is the general procedure: **

- If the problem is not entered, use the procedure How to Enter a Problem to enter the problem.
- For a general good practice, you may want to save the problem by choosing the command Save Problem As before solve it.
- Select the command Perform Linear Regression. The program will bring up a form for setting up the regression. See Perform Linear Regression for selecting dependent and independent variables.
- After the regression is done, the summarized result will be shown. You may choose the commands from the Results Menu to display other related result.

**To perform estimation or prediction in linear regression, here is the general procedure:**

- Use the procedure How to Perform Linear Regression to perform regression.
- After the regression is done, the result will be shown. Choose the command Perform Estimation and Prediction. The program will bring up a form for specifying the significance level and entering the values for independent variables. See Perform Estimation and Prediction for detail.

**To show a regression line in linear regression, here is the general procedure:**

- Use the procedure How to Perform Linear Regression to perform regression.
- After the regression is done, the result will be shown. Choose the command Show Regression Line from the Results Menu. The program will bring up a form for specifying the x-axis independent variable and entering the values for other independent variables. See Show Regression Line for detail. Note that after the line is shown, you may change the graph range by using the command Change Range.

**Create a Graph/Chart From A Spreadsheet Data:**

- Select an area of data from the current spreadsheet. See Select Area for how to select a data area.
- Select the command Chart/Graph. The program creates a 3D column chart for the selected data.
- Using the Gallery Menu, you can change to different types of charts.
- Using the Data Menu, you can change to titles and data for the chart.

**Create a Graph/Chart From Other Data:**

- Select the command Chart/Graph. The program creates a 3D column chart with random data.
- Using the Gallery Menu, you can change to different types of charts.
- Using the Data Menu, you can change to titles and data for the chart.

- For input data select the copy the data from Word.Doc, block the data area in QSB and then paste therein.
- Save solution (or problem) as file.llp in WinQSB. Open file.llp, in directory, using Notepad. Copy the text and paste it into Excel. Select the area and add grid in "Print Preview". Again, select the area and paste it into Word.
- Use "Print Screen" button on the keyboard. Paste it into Word.

**II) Guideline from WinQSB's help menu**

How to Export Data to Other Applications

You may export the LP-ILP problem data to other applications. The following two methods can achieve the task.

Through Clipboard

1. Click the left-top cell of the LP-ILP problem (which selects the whole problem).

2. Choose the command Copy or its icon to copy the whole problem to the Clipboard.

3. Switch to the target application and use its Paste command to paste the problem to the target application.

Through File

1. Choose the command Save Problem As or its icon to save the problem to a file.

2. Switch to the target application and open the saved data file with the text format.

**III) Export NET (i.e. transportation) problems**

You may export the NET problem data to other applications. The following two methods can achieve the task.

Through Clipboard

1. Click the left-top cell of the NET problem (which selects the whole problem).

2. Choose the command Copy or its icon to copy the whole problem to the Clipboard.

3. Switch to the target application and use its Paste command to paste the problem to the target application.

Through File

1. Choose the command Save Problem As or its icon to save the problem to a file.

2. Switch to the target application and open the saved data file with the text format.

Run the program module for "Decision Analysis" of WinQSB. Select "New problem" from the pull down menu of "File" in the menu bar.

Change the name of decisions and state of the nature to fit this problem. You can do so by selecting appropriate options ("State of the Nature Name", and "Decision Alternative Name") of the pull down menu of "Edit" in the menu bar. Then enter the problem data. Save the problem.

Select the "Solve and Analysis" option in the menu bar. A window will appear, accept all the default selections, and then click on OK. The software will solve the problem and provides a summary of all decisions made using different criterion.

You can select three more options from the pull down menu of "Results" in the menu bar. These selections will provide you with details of payoff analysis using different criteria (Display 4), regret table calculations, and a decision tree graph. Notice that if you select decision tree, a window (Decision Tree Setup) will appear that provides you options for how you would like the tree to look like (Display 6). Make sure you play around with it for different configurations, then you can print it out.

Draw the decision tree to match the requirements for WinQSB. Notice the triangles are used to indicate an end point.

Run the program module for "Decision Analysis" of WinQSB. Select "New problem" from the pull down menu of "File" in the menu bar.

Change the name of nodes to fit this problem. You can do so by selecting each cell and typing in. Then enter the problem data. Save the problem.

Select the "Solve and Analysis" option in the menu bar. The software will solve the problem and provides a detailed solution.

You can select one more options, decision tree graph, from the pull down menu of "Results" in the menu bar. Notice that if you select decision tree, a window (Decision Tree Setup) will appear that provides you options for how you would like the tree to look like. Make sure you play around with it for different configurations.

To perform analysis of a queuing system, select the "Queuing Analysis" option of the WinQSB. You may follow the steps below to input data for each queuing system. Here, entering the cost information is not discussed. As output you can obtain a table that summarizes the system performance and another table that lists the probability of having different number of people in the system.

M/M/1/GD/inf/inf:

Select "New Problem" from the pull down menu of "File" in menu bar.
Select "M/M System". Enter information on number of server
(1), service rate, and arrival rate.

D/D/1:

Select "New Problem" from the pull down menu of "File" in menu bar.
Select radio button for "General Queuing System" then click on "OK".
Type in 1 for "Number of servers". Double click on "service time
distribution". Click on "Constant" and click on "OK". Type
in a value for average service time (not service rate) for "Constant value".
Similarly, select constant for "interarrival time distribution" and enter
a value.

M/M/1/GD/C/inf:

Similar to M/M/1, you just type in the value of "queue capacity", C-1,
to replace for "M".

M/M/S/GD/inf/inf:

Similar to M/M/1, you just type in the value for number of server (S).

M/M/R/GD/K/K:

Similar to M/M/1, you will type in the value of "R" for "Number of
servers", the value of "K-R" for "Queue capacity", and the value of "K"
for "Customer population" (to replace for "M").

Excel 2002/2003:

Start Excel, then click Tools and look for Data Analysis and for Solver. If both are there, press Esc (escape) and continue with the respective assignment. Otherwise click Tools, Add-Ins, and check the boxes for Analysis ToolPak and for Solver, then click OK. Click Tools again, and both tools should be there.

Excel 2007:

Start Excel 2007 and click the Data tab at the top. Look to see if Data Analysis and Solver show in the Analysis section at the far right. If both are there, continue with the respective assignment. Otherwise, do the following steps exactly as indicated:

-click the âOffice Buttonâ at top left

-click the Excel Options button near the bottom of the resulting window

-click the Add-ins button on the left of the next screen

-near the bottom at Manage Excel Add-ins, click Go

-check the boxes for Analysis ToolPak and Solver Add-in if they are not already checked, then click OK

-click the Data tab as above and verify that the add-ins show.

Excel 2010:

Start Excel 2010 and click the Data tab at the top. Look to see if Data Analysis and Solver show in the Analysis section at the far right. If both are there, continue with the respective assignment. Otherwise, do the following steps exactly as indicated:

-click the File tab at top left

-click the Options button near the bottom of the left side

-click the Add-ins button near the bottom left of the next screen

-near the bottom at Manage Excel Add-ins, click Go

-check the boxes for Analysis ToolPak and Solver Add-in if they are not already checked, then click OK

-click the Data tab as above and verify that the add-ins show.

Some of these examples can be modified for other types problems

- Excel Add-Ins
- Excel LP Solver
- Excel Tutorial (Recommended)
- Carpenter I
- Carpenter II
- Carpenter III
- Wilson Problem I
- Wilson Problem II
- Wilson Sensitivity
- Wilson Formulation
- Wilson Problem with New Product
- LP: Non-Standard-Form
- Shadow Prices
- Shadow Prices 3-Constraint
- Degenerate LP

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