Problem

You've performed an optimization problem where several variables were real valued, but realistically, certain values should only be integers. For example, in the previous recipe, the number of optimum lab technicians for a given month was 5.62. Obviously hiring 0.62 of a person would be hard (unless you're assuming the number represents part-time employment, in which case you could assume that 0.62 represents 62% of a regular 40-hour work week). Therefore, you want to constrain certain variables to be whole integers like 5 or 6.

Solution

Use Solver as discussed in the previous recipes, along with integer constraints on certain variables.

Discussion

Let's pick up where we left off with the resource allocation example from the previous recipe. What you need to do now is add several integer constraints. In fact, you want to require every value contained in cells D19 to I22 and D26 to I27 to assume only integer values. Real numbers will not be allowed.

You can add an integer constraint in Solver just as you would an ordinary constraint (see Recipe 9.4 for a discussion of constraints). After opening the Solver window, click the Add button to open the Add Constraint window. Select the cell you want to constrain and then select "int" from the drop-down list in the middle of the window, as shown in Figure 13-7.

Figure 13-7. Adding an integer constraint

Solver will automatically enter "integer" in the Constraint field. Press Add for each constraint you want to add. A faster approach involves selecting an entire cell range in the Cell Reference field. For example, you could select the range D19:I22 to constrain all of the cells within that range to integer values. This approach avoids the tedium of having to add constraints one at a time for each cell in the range.

After you've added integer constraints, you can rerun Solver for this problem. Be prepared to wait, though. Adding integer constraints results in far greater computation time for this model. Whereas the first example (without integer constraints) converged on a solution in a matter of seconds, this second example (with integer constraints) took several hours to find a solution. In fact, it was taking so long on my computer that I left it running overnight, since I couldn't stay awake waiting for Solver to finish.

When Solver did finish, it yielded the results presented in Figure 13-8.

Figure 13-8. Resource allocation results with integer constraints

In this case, the minimum total cost comes to $251,966. This is a little higher than the earlier results discussed in the previous recipe. The reason is that Solver had to round up the number of employees hired or fired, and so on. Therefore, you end up with a little excess labor capacity. The production numbers reflect this excess capacity, where you can see that production will exceed demand by a little bit each month.

A further refinement of this problem would involve carrying over the excess production from one month to the next and factoring it in the required labor optimization each month. I'll leave that exercise to you.

Using Excel

- Introduction
- Navigating the Interface
- Entering Data
- Setting Cell Data Types
- Selecting More Than a Single Cell
- Entering Formulas
- Exploring the R1C1 Cell Reference Style
- Referring to More Than a Single Cell
- Understanding Operator Precedence
- Using Exponents in Formulas
- Exploring Functions
- Formatting Your Spreadsheets
- Defining Custom Format Styles
- Leveraging Copy, Cut, Paste, and Paste Special
- Using Cell Names (Like Programming Variables)
- Validating Data
- Taking Advantage of Macros
- Adding Comments and Equation Notes
- Getting Help

Getting Acquainted with Visual Basic for Applications

- Introduction
- Navigating the VBA Editor
- Writing Functions and Subroutines
- Working with Data Types
- Defining Variables
- Defining Constants
- Using Arrays
- Commenting Code
- Spanning Long Statements over Multiple Lines
- Using Conditional Statements
- Using Loops
- Debugging VBA Code
- Exploring VBAs Built-in Functions
- Exploring Excel Objects
- Creating Your Own Objects in VBA
- VBA Help

Collecting and Cleaning Up Data

- Introduction
- Importing Data from Text Files
- Importing Data from Delimited Text Files
- Importing Data Using Drag-and-Drop
- Importing Data from Access Databases
- Importing Data from Web Pages
- Parsing Data
- Removing Weird Characters from Imported Text
- Converting Units
- Sorting Data
- Filtering Data
- Looking Up Values in Tables
- Retrieving Data from XML Files

Charting

- Introduction
- Creating Simple Charts
- Exploring Chart Styles
- Formatting Charts
- Customizing Chart Axes
- Setting Log or Semilog Scales
- Using Multiple Axes
- Changing the Type of an Existing Chart
- Combining Chart Types
- Building 3D Surface Plots
- Preparing Contour Plots
- Annotating Charts
- Saving Custom Chart Types
- Copying Charts to Word
- Recipe 4-14. Displaying Error Bars

Statistical Analysis

- Introduction
- Computing Summary Statistics
- Plotting Frequency Distributions
- Calculating Confidence Intervals
- Correlating Data
- Ranking and Percentiles
- Performing Statistical Tests
- Conducting ANOVA
- Generating Random Numbers
- Sampling Data

Time Series Analysis

- Introduction
- Plotting Time Series Data
- Adding Trendlines
- Computing Moving Averages
- Smoothing Data Using Weighted Averages
- Centering Data
- Detrending a Time Series
- Estimating Seasonal Indices
- Deseasonalization of a Time Series
- Forecasting
- Applying Discrete Fourier Transforms

Mathematical Functions

- Introduction
- Using Summation Functions
- Delving into Division
- Mastering Multiplication
- Exploring Exponential and Logarithmic Functions
- Using Trigonometry Functions
- Seeing Signs
- Getting to the Root of Things
- Rounding and Truncating Numbers
- Converting Between Number Systems
- Manipulating Matrices
- Building Support for Vectors
- Using Spreadsheet Functions in VBA Code
- Dealing with Complex Numbers

Curve Fitting and Regression

- Introduction
- Performing Linear Curve Fitting Using Excel Charts
- Constructing Your Own Linear Fit Using Spreadsheet Functions
- Using a Single Spreadsheet Function for Linear Curve Fitting
- Performing Multiple Linear Regression
- Generating Nonlinear Curve Fits Using Excel Charts
- Fitting Nonlinear Curves Using Solver
- Assessing Goodness of Fit
- Computing Confidence Intervals

Solving Equations

- Introduction
- Finding Roots Graphically
- Solving Nonlinear Equations Iteratively
- Automating Tedious Problems with VBA
- Solving Linear Systems
- Tackling Nonlinear Systems of Equations
- Using Classical Methods for Solving Equations

Numerical Integration and Differentiation

- Introduction
- Integrating a Definite Integral
- Implementing the Trapezoidal Rule in VBA
- Computing the Center of an Area Using Numerical Integration
- Calculating the Second Moment of an Area
- Dealing with Double Integrals
- Numerical Differentiation

Solving Ordinary Differential Equations

- Introduction
- Solving First-Order Initial Value Problems
- Applying the Runge-Kutta Method to Second-Order Initial Value Problems
- Tackling Coupled Equations
- Shooting Boundary Value Problems

Solving Partial Differential Equations

- Introduction
- Leveraging Excel to Directly Solve Finite Difference Equations
- Recruiting Solver to Iteratively Solve Finite Difference Equations
- Solving Initial Value Problems
- Using Excel to Help Solve Problems Formulated Using the Finite Element Method

Performing Optimization Analyses in Excel

- Introduction
- Using Excel for Traditional Linear Programming
- Exploring Resource Allocation Optimization Problems
- Getting More Realistic Results with Integer Constraints
- Tackling Troublesome Problems
- Optimizing Engineering Design Problems
- Understanding Solver Reports
- Programming a Genetic Algorithm for Optimization

Introduction to Financial Calculations

- Introduction
- Computing Present Value
- Calculating Future Value
- Figuring Out Required Rate of Return
- Doubling Your Money
- Determining Monthly Payments
- Considering Cash Flow Alternatives
- Achieving a Certain Future Value
- Assessing Net Present Worth
- Estimating Rate of Return
- Solving Inverse Problems
- Figuring a Break-Even Point

Index

Excel Scientific and Engineering Cookbook (Cookbooks (OReilly))

ISBN: 0596008791

EAN: 2147483647

EAN: 2147483647

Year: N/A

Pages: 206

Pages: 206

Authors: David M Bourg

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