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Download your day FREE trial now from Parallels Desktop Windows on Mac Parallels Desktop Windows on Mac lets you seamlessly run Windows and Mac OS X side-by-side, drag-and-drop your files between operating systems, and run Windows software on your Apple computer without rebooting. What's new in this version: Windows 7 Menu Icons If you are a developer or a UI designer in a company that releases several applications or websites a month, you most definitely use stock icon sets to save time and maintain the same quality level throughout many projects. If you are looking for a new collection of interface Icons for Windows 7 and Vista Larger and more colorful icons, new styles, transparency - all of this became a must have for any icon that was used in Vista and its successor, Windows 7.

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This Windows Live Mail Converter is made with easy user interface and the tool doesn't demand much effort from users to handle it and to import windows live mail The costs consist of two types - fixed costs and variable costs, but there may be several individual costs that comprise the fixed costs or the variable costs. In the example that follows, there are five different individual costs and two options. Data Cost type. Each type of cost must be identified as either a fixed cost or a variable cost.

The default is that the first cost in the list is fixed and that all other costs are variable. These values can be changed by using the drop-down box in that cell. The specific costs for each option are listed in the two right columns in the table. If a volume analysis is desired, enter the volume at which this analysis should be performed. The volume analysis will compute the total cost revenue at the chosen volume. If the volume is 0, no volume analysis will be performed other than for the breakeven point. Volume analysis is at units.

Modules Solution The solution screen is very straightforward. In the preceding screen there are five costs with some fixed and some variable. The program displays the following results: Total fixed costs. For each of the two options, the program takes the fixed costs, sums them, and lists them in the table. Total variable costs.

The program identifies the variable costs, sums them, and lists them. Breakeven point in units. The breakeven point is the difference between the fixed costs divided by the difference between the variable costs, and this is displayed in units. In the example, it is units. Breakeven point in dollars. The breakeven point can also be expressed in dollars. A volume analysis has been performed for a volume of units. The total fixed costs and total variable costs have been computed for each option and these have been summed to yield the total cost for each option.

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A graph is available, as follows. Breakeven analysis One standard type of breakeven analysis involves revenue versus costs. Data entry for this option is slightly different in that the program creates a column for costs and a column for revenues. The fixed and variable costs get entered in the cost column and the revenue per unit is placed in the revenue column. This model requires exactly three inputs.

This example could also have been solved using the cost-volume submodel. Select two options and let one be the costs and one be the revenues. Place the fixed costs and variable costs in their obvious cells; use no fixed cost for the revenue and use the revenue per unit as a variable cost, displayed as follows.

Breakeven point with more than two options The breakeven module can perform a breakeven analysis for up to five options. The following screen demonstrates the output for a three-option breakeven. The screen indicates that there are three breakeven points as it makes comparisons for Computer 1 versus Computer 2, Computer 1 versus Computer 3, and Computer 2 versus Computer 3. Of course, even though there are three breakeven points, only two of them are relevant.

This is seen a little more easily by looking at the following breakeven graph. The breakeven point at 40, units does not matter because at 40, units the two computers that break even have higher costs than the Computer 2 option. The data for this example consist of a stream of inflows and a stream of outflows. In addition, for finding the net present value an interest rate must be given. Net Present Value Consider the following example. The company would like to know the net present value using an interest rate of 10 percent. The data screen follows. The screen has two columns for data.

One column is labeled Inflow and the other column is labeled Outflow. At the time of problem creation a six-period problem was created and the data table includes the six periods plus the current period 0. The six savings in the second column are inflows, and they are placed in the inflow column for Periods 1 through 6. The salvage value could be handled two ways, and we have chosen the way that we think gives a better display.

Instead, it is represented as a negative outflow. This keeps the meaning of the numbers clearer. The last item to be entered is the interest rate in the text box above the data. The results appear as follows: Modules A column has been created that gives the present value factors for single payments.

To the right of this, the inflows and outflows are multiplied by these present value factors, and the far right column contains the present values for the net inflow inflow minus outflow on a period-by-period basis. Internal Rate of Return The computation of the internal rate of return is very simple. The data is set up the same way but the method box is changed from net present value to internal rate of return. The results appear as follows. You can see that the internal rate of return for the same data is The Decision Table Model The decision table can be used to find the expected value, the maximin minimax , or the maximax minimin when several decision options are available and there are several scenarios that might occur.

Also, the expected value under certainty, the expected value of perfect information, and the regret opportunity cost can be computed. The general framework for decision tables is given by the number of options or alternatives that are available to the decision maker and the number of scenarios or states of nature that might occur. In addition, the objective can be set to either maximize profits or to minimize costs. Scenario probabilities. For each scenario it is possible but not required to enter a probability.

The expected value measures expected monetary value, expected value under certainty, and expected value of perfect information require probabilities, whereas the maximin minimax and maximax minimin do not. Profits or costs. The profit cost for each combination of options and scenarios is to be given. Hurwicz alpha. The Hurwicz value is used to give a weighted average of the best and worst outcomes for each strategy row. Please note that the Hurwicz value is not in every textbook.

Modules Example 1: A decision table The following example presents three decision options: The possible scenarios states of nature are that demand will be low, normal, or high; or that there will be a strike or a work slowdown. The table contains profits as indicated.

The first row in the table represents the probability that each of these states will occur. The remaining three rows represent the profit that we accrue if we make that decision and the state of nature occurs. For example, if we select to use overtime and there is high demand, the profit will be Solution The results screen that follows contains both the data and the results for this example. Expected values. Row minimum. For each row, the minimum element has been found and listed. This element is used to find the maximin or minimin. For each row, the maximum element in the row has been found and listed.

This number is used for determining the maximax or minimax. These represent 40 percent multiplied by the best outcome plus 60 percent multiplied by the worst outcome for each row. For example, for subcontracting the Hurwicz is. Maximum expected value. Because this is a profit problem finding the maximum values is of importance.

The maximum expected value is the largest number in the expected value column, which in this example is In this example, the maximin is The maximax is the largest value in the table or the largest value in the maximum column. In this example, it is Perfect Information A second screen of results presents the computations for the expected value of perfect information as follows. Perfect information. In this row, the best outcome for each column is listed.

For example, for the low demand scenario the best outcome is the given by using overtime. The expected value under certainty is computed as the sum of the products of the probabilities multiplied by the best outcomes. Expected value of perfect information. The expected value of perfect information EVPI is the difference between the best expected value Table values.

The values in the table are computed for each column as the cell value subtracted from the best value in the column in the data. For example, under low demand the best outcome is The two columns on the right yield two sets of results. There also is a window not displayed in this manual that yields Hurwicz values for alpha ranging from 0 to 1 by.

Decision Trees Decision trees are used when sequences of decisions are to be made. The trees consist of branches that connect either decision points, points representing chance, or final outcomes. All decision tables can be put in the form of a decision tree. The converse is not true. Version 4 of the software includes two different input styles for decision trees. The first model has tabular data entry whereas the second model is easier to use because it has graphical data entry. The first model has been maintained in the software for consistency with previous versions.

A decision tree — Graphical user interface One of the models allows for decision trees to be entered graphically rather than in the table as given previously. This model can be used to examine the same example just completed. After selecting the model, the interface will be displayed as follows. This is the only model in the software that has an input interface that is not the usual data table interface. The graph is displayed in the large area on the left and created using the tools on the right. In the beginning, there is only one node. The next step is to add two event nodes to node 1.

The tool on the right is set to node 1. The default for node 1 is that it is a decision node as needed in this case. A button is available to change the node if this becomes necessary. The new tree appears as follows. Modules Notice that two branches have been added. The current node is node 2, which is indicated by both the fact that the node number in the upper right is node 2 and by the fact that the branch to node 2 is highlighted in a different color.

At this point, two branches need to be added to node 2. The default is to add decision branches to events and vice versa. The type of node can always be changed later. This yields the following diagram. After all data has been entered, click on the Solve button on the toolbar. The data is in black and the solution is in blue as usual.

Notice that branches that should be used are indicated in blue. In the past, an airline has observed a demand for meals that are sold on a plane as given in the following table. How many meals should the airplane stock per flight? Modules Meals Probability The program is requesting three profits as well as the obvious demands and probabilities.

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Profit per unit. This is the normal profit for units bought and sold. Profit per unit excess. This is the profit for units that are overordered. In some cases, where there is a salvage value that exceeds the cost of the unit this will be a profit whereas in other cases this will be a loss. Profit per unit short. This is the profit for units when not enough units are ordered.

It will be a profit if you can purchase units to sell after the fact at a cost less than the selling price. Otherwise it will be a 0 or possibly a loss. If there were no voucher there would be no profit or loss for units for the demands that could not be satisfied. Demands and probabilities. Enter the list of demands and their associated probabilities.

The airline should order 20 meals to maximize its expected profit. Modules Factor Rating In the following screen, a filled-in sample along with its solution is displayed. Notice that the cities and the factors have been named. The output is very straightforward and consists of the following: Total weighted score. For each city, the weights are multiplied by the scores for each factor and summed. The total is printed at the bottom of each column. For example, the score for Philadelphia has been computed as: The first type of model is when past data sales are used to predict the future demand.

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This is termed time series analysis, which includes the naive method, moving averages, weighted moving averages, exponential smoothing, exponential smoothing with trend, trend analysis, linear regression, multiplicative decomposition, and additive decomposition. The second model is for situations where one variable demand is a function of one or more other variables. This is termed multiple regression. There is overlap between the two models in that simple one independent variable linear regression can be performed with either of the two submodels.

In addition, this package contains a third model that enables the creation forecasts given a particular regression model, and a fourth model that enables the computation of errors given demands and forecasts. Time Series The input to time series analysis is a series of numbers representing data over the most recent n time periods.

Although the major result is always the forecast for the next period, additional results presented vary according to the technique that is chosen. When using trend analysis or seasonal decomposition, forecasts can be made for more than one period into the future. The summary measures include the traditional error measures of bias average error , mean squared error, standard error, mean absolute deviation MAD , and mean absolute percent error MAPE.

Different authors compute the standard error in slightly different ways.

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That is, the denominator in the square root is given by n — 2 by some authors and by n — 1 by others. If you have a Pearson textbook the denominator should match the one in your text. If not, POM-QM for Windows uses n — 2 in the denominator for simple cases and always displays the denominator in the output. Modules The Time Series Data Screen Suppose that data is given as in the following table and the forecast for the demand for the week of February 14 and maybe the weeks of February 21, February Week Sales January 3 January 10 January 17 January 24 January 31 February 7 The general framework for time series forecasting is given by indicating the number of past data points.

The preceding example has data for the past six periods weeks , and the forecast for the next period - period 7 February 14 is needed. Forecasting method. The drop-down method box contains the eight methods that were named at the beginning of this module plus a method for users to enter their own forecasts in order to perform an error analysis. Of course, the results depend on the forecasting method chosen. A moving average is shown in the preceding screen. Number of periods in the moving average, n. To use the moving average or weighted moving average, the number of periods in the average must be given.

This is some integer between 1 and the number of time periods of data. In the preceding example, 2 periods were chosen, as seen in the extra data area. Demand y or Values for dependent y variable. These are the most important numbers because they represent the data. The data is in the demand column as , , , , , and Solution The solution screens are all similar, but the exact output depends on the method chosen.

For the smoothing techniques of moving averages weighted or unweighted and single exponential smoothing, there is one set of output, whereas for exponential smoothing with trend, there is a slightly different output display. For the regression models, there is another set of output. The first available method is the naive method which simply uses the data for the most recent period as the forecast for the next period. Begin with the moving averages. The main output is a summary table of results. The computations for all of these results can be seen on the following details window.

Modules Forecasts. The first column of output data is the set of forecasts that would be made when using the technique. Notice that because this is a 2-week moving average, the first forecast cannot be made until the third week. The following three numbers — , Next period forecast. As mentioned in the previous paragraph, the last forecast is below the data and is the forecast for the next period; it is marked as such on the screen. In the example, it is This column begins the error analysis.

The difference between the forecast and the demand appears in this column. The first row to have an entry is the row in which the first forecast takes place. In this example, the first forecast occurs on January 17 row 3 and the forecast was for , which means that the error was 0. In the next week the forecast was for , but the demand was only , so the error was Absolute value of the error. The fifth column contains the absolute value of the error and is used to compute the MAD, or total absolute deviation. Notice that the in the error column has become a plain, unsigned, positive 10 in this column.

Error squared. The sixth column contains the square of each error in order to compute the mean squared error and standard error. The 10 has been squared and is listed as Be aware that when squaring numbers it is quite possible that the numbers will become large and that the display will become a little messy. This is especially true when printing. Absolute percentage error. The seventh column contains the absolute value of the error divided by the demand. If the demand is 0, then the software will issue a warning regarding the MAPE.

The total for the demand and each of the four error columns appears in this row. This row contains the answers to problems in books that rely on the total absolute deviation rather than the mean absolute deviation. Books using total instead of mean should caution students about unfair comparisons when there are different numbers of periods in the error computation.

The averages for each of the four errors appear in this row. The average error is termed the bias and many books neglect this very useful error measure. The average squared error is termed the mean squared error MSE and is typically associated with regression least squares. The average of the absolute percentage errors is termed the mean absolute percentage error MAPE.

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In this example, the bias is 1. Standard error. One more error measure is important. This is the standard error. Different books have different formulas for the standard error. That is, some use n —1 in the denominator, and some use n — 2. The denominator is displayed in the summary output as shown previously. In this example, the standard error is The Normal distribution calculator can be used to find confidence intervals and address other probabilistic questions related to forecasting.

One more screen is available for all of these methods. It is a screen that gives the forecast control tracking signals results. For moving averages there is a summary screen of error measures, versus the n in the moving average. Modules One of the output displays not shown in this manual presents error measures as a function of n.

Also, the moving average graph has a scroll bar that enables you to easily see how the forecasts change as n varies. Weighted moving averages If the weighted moving average method is chosen, two new columns will appear on the data table as shown in the following screen. The far right column is where the weights are to be placed.

The weights may be fractions that sum to 1 as in this example. If they do not, they will be rescaled. In this example, weights of. For example, the forecast for week 7 is. A secondary solution screen follows. As before, the errors and the error measures are computed. Exponential smoothing Alpha for exponential smoothing.

In order to use exponential smoothing, a value for the smoothing constant, alpha, must be entered. This number is between 0 and 1. The smoothing constant alpha is. A starting forecast for exponential smoothing. In order to perform exponential smoothing, a starting forecast is necessary. Underneath will be a blank column. If you want, you may enter one number in this column as the forecast. If you enter no number, the starting forecast is taken as the starting demand.

The results screen has the same columns and appearance as the previous two methods, as shown next. Also, the graph for exponential smoothing has a scrollbar that enables you easily to see how the forecasts change as alpha varies. Exponential smoothing with trend3 Exponential smoothing with trend requires two smoothing constants. A smoothing constant, beta, for the trend is added to the model. Beta, for exponential smoothing. In order to perform exponential smoothing with trend, a smoothing constant must be given in addition to alpha.

If beta is 0, single exponential smoothing is performed. If beta is positive, exponential smoothing with trend is performed as shown. Initial trend. In this model, the trend will be set to 0 unless it is initialized. It should be set for the same time period as the initial forecast. The solution screen for this technique is different from the screens for the previously described techniques. Trend analysis 3 Unfortunately, there are several different exponential smoothing with trend methods. Although they are all similar, the results will vary. This is unfortunate but unavoidable. If you are using a Prentice Hall text, be certain that the software is registered Help, User Information for that text in order to get the matching results.

Modules As mentioned previously, the solution screen for regression differs from the solution screens for the other forecasting techniques. A sample summary output using regression for the same data follows. Values for independent x variable. For time series regression, the default values are set to 1 through n and cannot be changed. For paired regression, the actual values of the dependent variable need to be entered see Example 6. The screen is set up in order that the computations made for finding the slope and the intercept will be apparent.

In order to find these values, it is necessary to compute the sum of the x2 and the sum of the xy. These two columns are presented. Depending on the book, either the sum of these columns or the average of these columns, as well as the first two columns, will be used to generate the regression line. The line is given by the slope and the intercept, which are listed at the bottom left of the screen.

In this example, the line that fits the data best is given by: This is given by inserting one more than the number of periods into the regression line. In the example, we would insert 7 into the preceding equation, yielding The standard error is computed and shown as with all other methods. In this example, it is 8. Also notice that the mean squared error is displayed The bias is, of course, 0, because linear regression is unbiased.

The summary screen is displayed as follows. In the summary are the forecasts for the next several periods, because this was a trend analysis time series regression. The trend analysis graph has scrollbars that make it very easy to modify the slope and intercept of the line. Modules Example 6: Non time series regression Regression can be used on data that is causal. In the next screen, the sales of umbrellas as a function of the number of inches of rain in the last 4 quarters of the year are presented.

Above the data is a textbox that enables you to place in a value for x to enter into the regression equation. The solution appears in the summary table not displayed. Decomposition and Deseasonalization The following screen displays an example with seasonal data. As can be seen in the screen, there are 12 data points.

You must enter the number of seasons, such as 4 quarters or 12 months or 5 or 7 days. In addition, you must enter the basis for smoothing. In addition, you can have the software scale the seasonal factors if you like. The solution screen contains several columns. Centered moving average. The data is smoothed using a moving average that is as long as the time period — 4 seasons. Because the number of seasons is even, the weighted moving average consists of one-half of the end periods and all of the three middle periods.

Demand to moving average ratio. For all of the data points that have moving averages computed, the ratio of the actual data to the moving average is computed. Seasonal factors. The seasonal factors are computed as the average of all of the ratios. For example, the summer seasonal factor is the average of 1.

Seasonal factor scaling. The four seasonal factors are 1. Modules Smoothed data. The original data is divided by its seasonal factor in order to take out the seasonal affects and compute the smoothed data. Unadjusted forecast. After smoothing the data the software finds the trend line for the smoothed data. The trend line itself can be found on the summary results screen.

Adjusted forecast. The final column before the error analysis takes the forecasts from the trend line and then multiplies them by the appropriate seasonal factors. The errors are based on these adjusted forecasts versus the original data. The summary table contains the forecasts for the coming periods. Additive Decomposition The output is not displayed here.

The additive decomposition model uses differences rather than ratios to determine the seasonal factors that are additive rather than multiplicative. User Defined The last method available is user defined. This allows you to enter the forecasts and let the software perform the error analysis. The same module is available as the fourth submodel when New is selected. There are two inputs to the data. The number of periods of data must be given; in addition, the number of independent variables must be given.

In this example, the regression problem in Example 6 is extended. Note that for simple regression one independent variable there are two submodels that can be used to solve the problem. Either time series analysis using the regression method or the regression submodel. Example 8: Multiple Regression In this example, we have used two independent variables and therefore multiple regression must be used.

We have entered 4 for the number of periods and 2 for the number of independent variables. The data is entered and the solution screen appears next. The input has four columns: Did this solve your problem? Yes No. Sorry this didn't help. Skip to main content. Site Feedback. Tell us about your experience with our site. ValChesebro Created on May 28, I have the same question