MSF ExcelProgrammingPrimer

2006-2010 Microsoft Corporation

Microsoft Solver Foundation Solver Foundation for Excel Primer

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2 2006-2010 Microsoft Corporation

Contents Contents ........................................................................................................................................................ 2

Introduction .................................................................................................................................................. 3

What does Solver Foundation for Excel look like?........................................................................................ 4

Basic How-To ................................................................................................................................................. 7

Creating the Model ................................................................................................................................... 7

Binding Data .............................................................................................................................................. 8

Goals, Constraints, and Directives .......................................................................................................... 11

Checking and Solving the Model ............................................................................................................. 15

Sample Projects ........................................................................................................................................... 16

Airline Allocation Sample ..................................................................................................................... 17

Data and data binding ......................................................................................................................... 17

Appendix 1: Directive Options .................................................................................................................... 28

CompactQuasiNewtonDirective ............................................................................................................. 28

ConstraintProgrammingDirective ........................................................................................................... 28

HybridLocalSearchDirective .................................................................................................................... 29

InteriorPointMethodDirective ................................................................................................................ 29

MixedIntegerProgrammingDirective ...................................................................................................... 30

SimplexDirective ..................................................................................................................................... 30

StochasticDirective.................................................................................................................................. 31

Appendix 2: Optimization Modeling Language (OML) ................................................................................ 32

Appendix 2: OMLX File Format ................................................................................................................... 33

Root Element Model ........................................................................................................................ 33

Name Element .................................................................................................................................... 33

ModelText Element ............................................................................................................................. 33

DataBindings Element ......................................................................................................................... 33

BindingSourceInfo Element ................................................................................................................ 34

InputBindingInfo Element ................................................................................................................... 35

OutputBindingInfo Element ................................................................................................................ 36

Directives Element .............................................................................................................................. 36


DirectiveInfo Element ......................................................................................................................... 37

DirectivePropertyInfo Element ........................................................................................................... 37

Introduction Solver Foundation is a pure, managed code runtime for mathematical programming, modeling, and

optimization. This .NET/CLR based framework provides a rich set of tools, services, and engines for

Visual Studio and Office. The Solver Foundation for Excel add-in enables the mathematical modeler to

optimize problems easily and within the comfort of the Excel environment. Key features of this

application include the following:

o Modeling Editor. Simplifies the modeling experience by using a collection of modeling panes

and includes a modeling syntax checker and other similar features exposed through the Solver

Foundation ribbon bar for Excel.

o Excel Cell binding. Binds static or dynamic data in a range to and from the model.

o Automatic Results and Report generation. Displays all results and reports on separate Excel

sheets for easy viewing, saving, or integration into other workflow systems.

o Import/Export capabilities. Supports MPS, QPS, SMPS, and OML formats. You can deploy a

model from Excel directly to C# - avoiding the need for the application developer to re-write any

model code.

o Improved Microsoft Office Integration. Deploy models from Excel to SharePoint using our

OMLX file (model + metadata). This provides a script-safe and secure method to transfer models

between client and a server.

This release of the Solver Foundation for Excel add-in provides several improvements:

Support for 18 new OML operators such as Sin, Cos, If, Max, Min.

Nonlinear optimization support using the Compact Quasi Newton and Hybrid Local Search solvers.

Improved data binding support.

This document covers how you can model, solve, and generate reports by using the Solver Foundation

for Excel add-in. Please direct queries and feature suggestions online at www.solverfoundation.com.


What does Solver Foundation for Excel look like? The Solver Foundation for Excel add-in makes it easier to build and solve models. Analysts, decision

makers, and the academic community can use the add-in as a tool for understanding the basics of

optimization. The following screenshot demonstrates the Solver Foundation for Excel add-in user

interface:

Models are entered in the right-hand pane. Models are built from input parameters, decisions, goals (in

the form of objective functions), constraints, and sets. Constraint and goal expressions are specified

using the Optimization Modeling Language (OML), a type safe declarative modeling language. You can

bind input parameters and output decisions to cell ranges in a worksheet.


To get started, enter the model in the modeling pane, and press the Check button on the Ribbon to

make sure the model is valid. Then, press the Solve button, and view the results on the Solver

Foundation Results sheet.

The Solver Foundation ribbon tab includes many features to help build, solve, and analyze models.

Model. Basic functionality for displaying, importing, exporting, and deploying models.

o Model. Hides or shows the modeling pane window.

o Import. Supports importing OML, MPS and QPS files. The add-in supports file sizes up to 10

MB. Larger files can be processed by the command-line tool MSFCLI, or by writing .NET

code to call Solver Foundation Services.

o Export. Save as MPS, QPS (when appropriate) or OML.

o Deploy. A model can be deployed to SharePoint (via OMLX format) or Visual Studio (via C#).

o Check. Performs syntax checking on the model. Results of this check will be displayed below

the model in the Model Validation text box within the modeling pane.

Report Verbosity. These options enable the user to fine tune what details are generated.

o Clear Log On Solve. The Log tab will clear after each Solve.

o Decisions. Display detailed Decision information when available.

o Directives. Display Directive related information.

o Infeasibility. Include solver specific sensitivity information.

o Sensitivity. Include solver-specific feasibility information when available.

o Solver Details. Include details such as solve time, algorithms used, etc.

Simulation. Solver Foundation supports stochastic programming to perform basic MonteCarlo and

Latin Hypercube simulations.

o Method. The sampling method used to solve stochastic models. Choose between Automatic

(the default), Monte Carlo and Latin Hypercube.

o Count. The number of samples. Larger values lead to improved accuracy but require more

time to solve.

o Seed. The seed used to initialize the random number generator. Using the same seed leads

to more predictable solution behavior.

Solve. The main runtime to invoke a solution.

o Solve. Runs the appropriate solver, and generates results in the Solver Foundation Results

sheet.

o (Solve) Next. Iterate through Constraint Programming problems that have multiple

solutions. Multiple solutions will be shown sequentially in the Solver Foundation Results

sheet.

o Stop. Interrupts the Check, Solve or Summary functions mid-stream.


Summary. Generates a report overview plus any solver execution details.


Basic How-To This section goes through the general process of creating and solving a

model.

Creating the Model A model can be formed several different ways:

Importing an existing model (including MPS, QPS, OML, etc.)

Typing a new model directly within the Model tab.

Typing values through the collection of modeling tabs.

Sets. These are collections of objects that are used as indexes in Parameters or Decisions. For

example, a matrix Parameter takes two Sets as indexes.

Parameters. These are the inputs of the solver data is bound from an Excel sheet to the model.

Parameters can be indexed, or singled-valued constants of type Reals, Integers, or Booleans.

Decisions. These are the outputs or results of the model being solved. Data can be bound to a

specific Excel sheet. Supported types for Decisions can be Reals, Integers, or Booleans.

Goals. This is where you define the business goal or goals you are trying to accomplish. These are

used to specify a quantity or equation that should be maximized or minimized.

Constraints. This is where you can add constraints to the model. These are restrictions placed on

Decisions.

Directives. Ability to provide solver hints and other solver specific attributes.

Model. Shows the model in OML format. Advanced users can manually edit OML directly from this

pane.

Log. Solver output details. This is similar to the command line interface output.


Binding Data Most real world models have an algebraic form but depend on data to be used for a specific problem

instance. For example, a model may use a Demand parameter where product demand values are stored

in a range of cells. Data can be entered manually, or imported from a variety of sources using the Get

External Data button on the Data ribbon tab. Once the sheet contains model data, you can use the

Parameters and Decisions modeling pane tabs to bind the data to and from the model.

Parameters The Parameters tab allows the user to bind data from an Excel sheet to the model. The following

parameter types are available:

- Parameter. These represent real or integer values over a range.

- Random Parameter. These are used in stochastic models and represent a random distribution.

Random parameters are either:

o Scenario Parameter. A random parameter where the possible values are specified by

scenarios. Each scenario has an associated value and probability of occurring.

o Distribution Parameter. A random parameter that represents a discrete or continuous

random distribution.

Parameters can be single-valued or indexed using Sets. A Set is an unordered list of items that define the

valid set of indexes for a Parameter or Decision. Both random and non-random parameters can be

indexed. You can use the Binding Editor to associate Sets with Parameters. Click on the Binding button

for a parameter to display the Binding Editor. The Binding Editor is shown in the following screenshot:


Set the cell range for the data using the control at the top of the dialog. The Binding Editor supports

three different data layouts.

A single row or column. Uncheck the Range Includes Column Headers and select the range

containing the data. In the first Set dropdown, choose the Set that represents the indexes for

the Parameter.

A table (matrix) containing data values. Uncheck the Range Includes Column Headers and

select the range containing the data. In the first Set dropdown select the Set that represents the

first (row) index. In the second Set dropdown select the second (column) index. The Column

Header controls are disabled.

A table containing rows containing indexes and values. The table has headers that describe the

contents of each column. Check the Range Includes Column Headers checkbox. Typically one

or more columns will represent indexes and one column contains the values. For each column

that represents an index, select the appropriate Set and Column Header. In the Value Field

dropdown, select the dropdown that contains the parameter values.

Decisions Similar to the Parameters tab, the Decisions pane allows the user to bind Decisions generated from

Solver Foundation directly into an Excel sheet. The following input Decisions are available.

- Decision. An output value that represents values that the solver should determine.

- Recourse Decision. An output value in a stochastic model that is made in response to the

realization of a random parameter.


Decisions, just like Parameters, can be indexed using Sets. In the airline simulation sample below, there

are two decisions:

A doubly-indexed Decision that represents the number of aircraft of each type assigned to each

route.

A Recourse Decision that represents the number of passengers that will be bumped from each flight.

In this example, the customer demand for each route is random, therefore the number of passengers

that will need to be bumped is not known in advance. Since the number of bumped passengers depends

on the realization of the demand random parameter, it is defined as a recourse decision.


Goals, Constraints, and Directives Parameters and Decisions are the raw materials used to build models using goals, constraints, and

directives. Goals and constraints are specified algebraically using OML. OML provides logical, arithmetic,

iteration and set operations that allow a wide range of goals and constraints to be clearly expressed.

Many real-world models have goals or constraints that apply to a range of input or output values. In

such cases, it is useful to define indexed parameters over sets and use the Foreach and Sum operators.

The following sections show how goals and constraints can be created and manipulated in the Excel add-

in. Then you can learn how Directives can be used to customize Solver Foundations solution behavior.

Goals

A goal combines Parameters and Decisions in order to express how a model is to be optimized. Typically,

goals represent business objectives or preferences such as maximize profit, or minimize waiting

time. In the following example, the goal is to minimize operational cost:


The first step is to specify a unique name for the goal. The Kind of goal is either Maximize or Minimize.

The Expression is text that combines Decisions, Parameters, and constant values using the rich set of

operations provided by OML. This example uses the Sum and Foreach expressions to iterate over the

set of possible routes and airplane types. Goals can contain Recourse Decisions, in which case Solver

Foundation can substitute the expected value over all samples of the random parameters.


Constraints

A constraint is simply an expression that restricts possible values for decisions. Some constraints are

logical in nature for example, the sum of demand over all routes is equal to the total demand.

Others represent business constraints, such as do not allow server load to exceed 90%.

The constraint above is indexed over the Routes set using the Foreach expression. The constraint says

that for each route, the demand is the sum of the products of the passenger capacities and airplane

fleet allocation, minus the number of passengers bumped from the route


Directives

Parameters, decisions, goals and constraints all describe the content of a model, whereas a directive

specifies how a model should be solved. Directives are not required when building a model; however,

these are useful when you want to customize the behavior of a solver.

A Stochastic Directive in used for this model because it contains random parameters. A complete list of

Directive attributes can be found in the appendix.


Checking and Solving the Model After the data binding is complete, you are ready to validate the model by using the Check button. This

functionality validates your model and checks the matching between data and parameters. A valid

model can be solved at any time by simply pressing the Solve button. Solver Foundation automatically

generates results, and if you specify an output binding, any Excel valid action (graphing, charting, etc.)

can be used.

Solver Foundation for Excel provides a detailed summary for additional post optimality analysis. Click the

Summary button to initiate a report that includes an Overview, Solver Execution Details, and if available,

the Stochastic Measures and Sensitivity Details reports.


Sample Projects The Solver Foundation installation includes several samples to help you get started. These samples

demonstrate a variety of solver and application domain types:

Area Domain Samples

Solver Foundation for Excel

XLSX Linear Programming Supply Chain Planning

XLSX Constraint Programming Job Machine Allocation

XLSX Quadratic Programming Quadratic Portfolio

XLSX Simulation Airline Allocation

XLSX Mixed Integer Programming Airline Allocation

XLSX Nonlinear Programming Shipping Route

XLSX Special Ordered Sets (SOS) Purchase

These samples span classical problem domains in mathematical programming and operations research:

linear programming (LP), quadratic programming (QP), constraint programming (CP), nonlinear

programming (NLP) and stochastic programming (SP).


Airline Allocation Sample In the following walkthrough, use the Solver Foundation add-in for Excel to solve an operational

planning problem using stochastic programming and Monte Carlo simulation. An operations planner for

a regional airline needs to determine how to utilize its fleet to minimize operational cost. The airline has

a mixed fleet of planes that operate five routes out of six cities. A demand forecast for each route has

been determined, as well as the capacity and per-mile costs for each type of plane on each route. The

planner wants to determine the allocation of planes to routes that results in the lowest monthly

operational cost.

Data and data binding

The first Excel sheet contains the problem data:


The sheet contains the following data:

The number of aircraft of each type.

The forecasted demand and price for each route.

The carrying capacity per month for each type of plane for each route (in thousands).

The operational cost for a plane on a route, in thousands.

The cost of a refund due to overbooking for each route.

The actions in the Solver Foundation ribbon cover the entire lifecycle of building a model, checking

correctness, solving, and analyzing results. The modeling pane on the right guides the model creation


process. The first step is to create Parameters that bind to the data in the worksheet. In the right-hand

pane, there is defined Parameter called Demand that binds to a range in the worksheet. The decisions

are defined in a similar fashion. The most interesting decision is Allocation: the number of planes of each

type to assign to each route. First define Routes and Aircraft sets by switching to the Sets tab, clicking

New, and entering the name for each Set.

Now create the decision by switching to the Decisions tab and clicking New. Use the Binding Editor to

associate the Routes and Aircraft sets:


The goal is to minimize operational costs. This goal is expressed by combining the inputs and outputs

using OML's expression language. Similarly you can define constraints, such as the constraint that the

sum of the allocations for a plane type over all routes must not exceed inventory.


The model definition is complete. The OML tab shows the complete representation of the model in

OML. Click the Solve button, and Solver Foundation automatically interprets the OML, determines the

underlying type of optimization problem, calls the correct underlying solver, and returns the best

allocation, shown in the results:


The decision values are data bound to the right-hand portion of the worksheet. These values are used in

a pivot table and chart that provide additional insight:


Solver Foundation introduces a simulation framework that extends OML to handle stochastic models. In

this example, the customer demand is an imprecise estimate. Therefore it is more realistic to capture

this uncertainty directly in the model. This is easily done in OML using a random parameter.


The demand is modeled using a NormalDistribution parameter. A normal distribution is defined by its

mean and standard deviation. These values are different for each route, so this example uses data

binding to define the mean and standard deviation. The model can now be modified to use the random

parameter. Since the demand is random, it is necessary to have a fallback plan in case demand for a

route exceeds capacity. If a route is overbooked, it is possible to bump passengers and refund them

money. This is a recourse decision that is made once the actual passenger demand is known. Recourse

decisions are defined in the Output tab, similar to how the Allocation decision was defined earlier.


Click Solve to use sampling to simulate different values for the random parameters and solve the model,

finding the allocation that works best over the range of possible demands.

The average, minimum, and maximum values for the recourse decisions are shown in the log.


Click the Summary button to produce a solution report, which in this case includes additional

information particular to stochastic models, including information about how sampling was performed.

Solver Foundation chooses default values for sampling parameters, but these can be changed in the

Simulation area of the Solver Foundation ribbon. For example, the number of samples can be increased

to 200.

More information about sampling options and stochastic models can be found in the Simulation Primer.


Appendix 1: Directive Options There are seven categories of Solvers with respective Directives available for advanced manipulation via

Directives - essentially a hint to point the solvers to use a specific set of attributes.

Unconstrained Nonlinear Programming. Compact Quasi Newton Directive

Constraint Satisfaction. Constraint Programming Directive

Interior Point Method. Interior Point Method Directive

Mixed Integer Programming. Mixed Integer Programming Directive

Nonlinear Programming. Hybrid Local Search Directive

Simplex. Simplex Directive

Stochastic. Stochastic Directive

CompactQuasiNewtonDirective Int. IterationLimit: The maximum number of iterations.

Int. IterationsToRemember: Number of previous iterations to remember for estimate of Hessian

(default is 17).

Double. Tolerance: The solver tolerance.

ConstraintProgrammingDirective

ConstraintProgrammingAlgorithm. Algorithm: The algorithm to use:

o Default. Use whatever algorithm the solver thinks is best.

o TreeSearch. Use tree search.

o LocalSearch. Use local search.

TreeSearchVariableSelection. VariableSelection: Heuristic for selecting decisions to branch on

o Default. Use whatever heuristic the solver thinks is best

o MinimalDomainFirst. Enumeration that chooses a variable with smallest domain

o DeclarationOrder. Enumeration following the declaration order of the variables

o DynamicWeighting. Weigh variables dynamically according to their dependents and current domain sizes

o ConflictDriven. Enumeration based on conflict analysis following a variant of the VSIDS heuristic used in SAT solvers

o ImpactPrediction. Enumeration based on a forecast of the impact


o DomainOverWeightedDegree. Enumeration based on the "domain over weighted degree"

o TreeSearchValueSelection. ValueSelection: Heuristic for selecting decision value to test first


o SuccessPrediction. Value enumeration based on a prediction of the success

o ForwardOrder. Value enumeration that follows the order of the values

o RandomOrder. Value enumeration that picks uniformly at random

LocalSearchMoveSelection. MoveSelection: Heuristic for selecting local search moves


o Greedy. Violation-guided greedy move

o SimulatedAnnealing. Simulated annealing

o GreedyNoise. Violation-guided greedy with noise

o Tabu. Violation-guided greedy with noise and tabu

o Gradients. Gradient-guided with tabu and escape strategy

Bool. RestartEnabled: Whether to enable the solver to restart from the beginning if it isn't making progress

Int. PrecisionDecimals: Number of decimal digits of precision (0 to 4)

ReadOnlyCollection. UserOrderVariables: A list of decisions to branch on first

HybridLocalSearchDirective Int. PresolveLevel: Presolve level. -1 means automatic, 0 means no presolve.

Bool. RunUntilTimeout: whether to continue to search for improved solutions until aborted.

InteriorPointMethodDirective Double. GapTolerance: The gap tolerance. If set to 0, the solver can choose

InteriorPointMethodAlgorithm. Algorithm: The algorithm

o Default. Use whatever algorithm the solver thinks is best

o PredictorCorrector. Use Predictor Corrector

o HomogeneousSelfDual. Use Homogeneous Self Dual

Int. IterationLimit: Iteration count limit. If negative, no limit


MixedIntegerProgrammingDirective Double. GapTolerance: Gets or sets the tolerance to declare an integer solution optimal

Bool. QuickFeasibility: Whether or not to focus on getting quick feasibility

Bool. CuttingPlaneGeneration: Enable/disable cutting plane

Bool. LocalSearch: Enable/disable local search in Mixed Integer Solvers

SimplexDirective SimplexPricing. Pricing: The pricing strategy to use

o Default. Use whatever pricing the solver thinks is best

o SteepestEdge. Use steepest edge pricing

o ReducedCost. Use reduced cost pricing

o Partial. Use partial pricing

Int. IterationLimit: The limit on number of pivots. If negative, no limit

SimplexAlgorithm. Algorithm: The algorithm to use

o Default. Use whatever algorithm the solver thinks is best

o Primal. Use primal simplex

o Dual. Use dual simplex

SimplexBasis. Basis: The basis to use

o Default. Use whatever basis the solver thinks is best

o Crash. Use crash basis

o Slack. Use slack basis

o Freedom. Use freedom basis

Bool. GetSensitivity: Whether to generate sensitivity information

bool. GetInfeasibility: Whether to generate infeasibility information

Double. PricingTolerance: Numerical tolerance for Simplex pricing

Double. VariableTolerance: Numerical tolerance for variables


StochasticDirective Int. MaximumScenarioCountBeforeSampling: When there are more than

MaximumScenarioCountBeforeSampling scenarios, sampling will be used instead of enumeration.

Use -1 for automatic mode (Default)

DecompositionType. DecompositionType: Whether to use decomposition or the deterministic

equivalent.

Automatic. Let the solver decide whether to use decomposition.

o Disabled. Do not use decomposition. Form the Deterministic Equivalent instead

o Enabled. Use decomposition.


Appendix 2: Optimization Modeling Language (OML) Solver Foundation includes an Optimization Modeling Language (OML) system, designed exclusively for

modeling and solving using the underlining Solver Foundation infrastructure. It is an algebraic modeling

language.

If you use the Automatic Editing Mode in the Modeling Pane, the comments may be removed from the

OML code. To work around this issue, use Annotation to add metadata to a parameter, decision,

constraint, or goal.

Please refer to the Solver Foundation OML Syntax Document for more information.


Appendix 2: OMLX File Format This document defines an XML schema for extended OML model. The schema provides for information

suitable for editing, validating and solving the model with different data sources.

Root Element Model

Every OMLX file must contain single model. A Model root element contains the entire model. The

namespace for OMLX is

...

Name Element

Name element contains the name of the model.

Supply Chain Planning

ModelText Element

ModelText element contains the entire OML model text.

Model[

Parameters[

Sets, Products, Factories, Areas, Promotions

],

...

]

DataBindings Element

DataBindings element contains information for binding to different type of data sources. DataBindings

element can contains 0 to n BindingSourceInfo element. Each BindingSourceInfo element contains

information for setting up input and output data binding when solving a model.

XML

...

SQL

...


BindingSourceInfo Element

In BindingSourceInfo element there are two metadata elements:

Name element contains the name of the binding source. The name should be unique in

DataBindings collection.

Connection element contains the connection information for the data source. For SQL Server it

will be connection string; For XML file it will be the filename; For SharePointSite it will be the Url

to the site collections.

There are two sections for individual Parameter/Decision bindings:

ParameterBindings element contains input binding information for parameters in model.

ParameterBindings element can contain 0 to n InputBindingInfo each represent binding

information to a parameter.

DecisionBindings element contains output binding information for decisions in model.

DecisionBindings element can contain 0 to n OutputBindingInfo each represent binding

information to a decision.

SQL

Data Source=(local);Initial Catalog=SupplyChainPlanning;Integrated Security=SSPI;

manufactureLoads

manufactureLoads

ManufactureLoads

Product

...

Plan

Plan

value

Products,Areas,Promotions,Factories


...

InputBindingInfo Element

InputBidingInfo contains binding information to a parameter:

Name element contains name of the parameter in model.

TableName element contains name of the table data container from data source.

ValueField element contains name of the value field in table.

IndexFields element contains names of index fields separated by commons.

manufactureLoads

manufactureLoads

ManufactureLoads

Product

To define a binding for UniformDistributionParameter following elements can be used:

Name element contains name of the uniform distribution parameter.


LowerBoundField element contains field name for lower bound field.

UpperBoundField element contains field name for upper bound field.


gasDemand

gasDemand

LowerBound

UpperBound

country

To define a binding for NormalDistributionParameter following elements can be used:

Name element contains name of the uniform distribution parameter.


MeanField element contains field name for field contains mean value.

VarianceField element contains field name for field contains variance value.



gasDemand

gasDemand

LowerBound

UpperBound

country

OutputBindingInfo Element

OutputBindingInfo contains information for single decision binding:

Name element contains name of the decision in model.

TableName element contains name of the table data container which output data will write it

to.

ValueField element contains name of the value field in table.


TotalCost

TotalCost

Cost

Products,Areas

Directives Element

Directives element contains all directives will be used to solve the model. Directives element contains 0

to n directives. Each directive represent an instance can be created by SFS. There should be only one

instance per type can exist in directives collection.

Here is an example of Directives element:

SimplexDirective

true

Algorithm

2


Arithmetic

2

Basis

1

GetSensitivity

true

IterationLimit

200

MaximumGoalCount

20

TimeLimit

2000

DirectiveInfo Element

DirectiveInfo element contains all information for a SFS directive object. DirectiveInfo element contains

following elements:

TypeName element contains the type name of SFS directive object.

Enabled element identify if the directive should be used or not.

Properties element contains property values for the SFS directive object.

DirectivePropertyInfo Element

DirectivePropertyInfo contains name value pair for each directive object property. DirectivePropertyInfo

element contains following elements:


Name element contains the name of the property.

Value element contains the value of the property.

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MSF ExcelProgrammingPrimer