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Chapter 1Chapter 1Introduction to Managerial Decision

Modeling

Management Science - BMGT 555Management Science - BMGT 555

Professor AhmadiProfessor Ahmadi

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Learning ObjectivesLearning Objectives

Define decision model and describe its Define decision model and describe its importance.importance.

Understand two types of decision models: Understand two types of decision models: deterministic and probabilistic models.deterministic and probabilistic models.

Understand steps involved in developing Understand steps involved in developing decision models in practice.decision models in practice.

Understand use of spreadsheets in Understand use of spreadsheets in developing decision models. developing decision models.

Discuss possible problems in developing Discuss possible problems in developing decision models. decision models.

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IntroductionIntroduction

Quantitative approaches to decision making are Quantitative approaches to decision making are based on the scientific method.based on the scientific method.

Names for this body of knowledge include: Names for this body of knowledge include: Management Science, Operations Research, and Management Science, Operations Research, and Decision ScienceDecision Science..

It had its early roots in World War II and is It had its early roots in World War II and is flourishing in business and industry with the aid of flourishing in business and industry with the aid of computers in general and the microcomputer in computers in general and the microcomputer in particular.particular.

Some of the primary Some of the primary applications areasapplications areas of this of this body of knowledge are management, marketing, body of knowledge are management, marketing, production scheduling, capital budgeting, and production scheduling, capital budgeting, and transportation.transportation.

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Types of Problem InformationTypes of Problem Information

Quantitative data - Quantitative data - numeric values numeric values that indicate how much or how many.that indicate how much or how many.

• Production quantityProduction quantity

• Rate of returnRate of return

• Financial ratiosFinancial ratios

• Cash flowsCash flows

Qualitative data - Qualitative data - labels or names labels or names used to identify an attribute - used to identify an attribute -

• Pending state or federal legislationPending state or federal legislation

• New technological breakthroughNew technological breakthrough

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Role of Spreadsheets in Decision ModelingRole of Spreadsheets in Decision Modeling

Computers are an integral part of decision Computers are an integral part of decision making.making.

Spreadsheet packages are capable of handling Spreadsheet packages are capable of handling management decision modeling techniques. management decision modeling techniques. Have Have built-in built-in functions and procedures, such as:functions and procedures, such as:

• Goal SeekGoal Seek

• Data TableData Table

• SolverSolver

• Chart Wizard, and others.Chart Wizard, and others.

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ModelsModels

ModelsModels are representations of real objects or are representations of real objects or situations.situations.

Three forms of models are iconic, analog, and Three forms of models are iconic, analog, and mathematical. mathematical. • Iconic modelsIconic models are physical replicas (scalar are physical replicas (scalar

representations) of real objects. representations) of real objects. • Analog modelsAnalog models are physical in form, but do are physical in form, but do

not physically resemble the object being not physically resemble the object being modeled.modeled.

• Mathematical modelsMathematical models represent real world represent real world problems through a system of mathematical problems through a system of mathematical formulas and expressions based on key formulas and expressions based on key assumptions, estimates, or statistical assumptions, estimates, or statistical analyses.analyses.

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Mathematical ModelsMathematical Models

Cost/benefit considerationsCost/benefit considerations must be made in must be made in selecting an appropriate mathematical model.selecting an appropriate mathematical model.

Frequently a less complicated (and perhaps Frequently a less complicated (and perhaps less precise) model is more appropriate than a less precise) model is more appropriate than a more complex and accurate one due to cost more complex and accurate one due to cost and ease of solution considerations.and ease of solution considerations.

Mathematical models relate Mathematical models relate decision variablesdecision variables with fixed or variable parameters. with fixed or variable parameters.

Frequently mathematical models seek to Frequently mathematical models seek to maximize or minimize some maximize or minimize some objective functionobjective function subject to constraints.subject to constraints.

The values of the decision variables that The values of the decision variables that provide the mathematically-best output are provide the mathematically-best output are referred to as the referred to as the optimal solutionoptimal solution for the for the model.model.

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Types of Decision ModelsTypes of Decision Models

DecisionModels

Deterministic Models

Stochastic Models

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Transforming Model Inputs into OutputTransforming Model Inputs into Output

Uncontrollable InputsUncontrollable InputsUncontrollable InputsUncontrollable Inputs

ControllableControllableInputsInputs

(Decision(DecisionVariables)Variables)

ControllableControllableInputsInputs

(Decision(DecisionVariables)Variables)

OutputOutput(Projected(ProjectedResults)Results)

OutputOutput(Projected(ProjectedResults)Results)

MathematicalMathematicalModelModel

MathematicalMathematicalModelModel

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Steps Involved in Decision ModelingSteps Involved in Decision Modeling

1. Formulation.1. Formulation.

2. Solution.2. Solution.

3. Interpretation.3. Interpretation.

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Step 1: FormulationStep 1: Formulation

Defining the problem.Defining the problem.

• Develop clear and concise problem Develop clear and concise problem

statement.statement.

Developing a model.Developing a model.

• Select and develop a decision model.Select and develop a decision model.

• Select appropriate problem variables.Select appropriate problem variables.

• Develop relevant mathematical relation for Develop relevant mathematical relation for

consideration and evaluation.consideration and evaluation.

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Step 1: Formulation Step 1: Formulation (Continued )(Continued )

Acquiring input data.Acquiring input data.

• Collect accurate data for use in the model.Collect accurate data for use in the model.

• Possible data sources are: Possible data sources are:

Official company reports. Official company reports.

Accounting, operating, and financial Accounting, operating, and financial

information.information.

Views, and opinions from Views, and opinions from

knowledgeable individuals.knowledgeable individuals.

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Step 2: SolutionStep 2: Solution

Developing a solution involves:Developing a solution involves:

• Manipulating model to arrive at the best Manipulating model to arrive at the best

(optimal) solution.(optimal) solution.

• Solution of a set of mathematical Solution of a set of mathematical

expressions.expressions.

• Alternative trial and error iterations.Alternative trial and error iterations.

• Complete enumeration of all possibilities Complete enumeration of all possibilities

or utilization of an or utilization of an algorithmalgorithm.. Series of steps repeated until best Series of steps repeated until best

solution is attained.solution is attained.

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Step 2: Solution Step 2: Solution (Continued )(Continued )

Testing a solution involves:Testing a solution involves:

• Prior to implementation of model Prior to implementation of model

solution, testing the solution.solution, testing the solution.

• Testing of solution is accomplished by Testing of solution is accomplished by

examining and evaluating: examining and evaluating:

Data Data utilized in the model and utilized in the model and

On the On the model model itself.itself.

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Step 3: InterpretationStep 3: Interpretation

InterpretationInterpretation and and What-if AnalysisWhat-if Analysis..

Analyzing the results and Analyzing the results and sensitivity analysissensitivity analysis..

1.1. Vary data input values and examine Vary data input values and examine

differences in various optimal solutions.differences in various optimal solutions.

2.2. Make changes in the model parameters Make changes in the model parameters

and examine differences in various and examine differences in various

optimal solutions.optimal solutions.

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Example: Iron Works, Inc.Example: Iron Works, Inc.Iron Works, Inc. (IWI) manufactures two Iron Works, Inc. (IWI) manufactures two products made from steel and just received this products made from steel and just received this month's allocation of month's allocation of bb pounds of steel. It takes pounds of steel. It takes aa11 pounds of steel to make a unit of product 1 pounds of steel to make a unit of product 1 and it takes and it takes aa22 pounds of steel to make a unit of pounds of steel to make a unit of product 2. product 2.

Let Let xx11 and and xx22 denote this month's production denote this month's production level of product 1 and product 2, respectively. level of product 1 and product 2, respectively. Denote by Denote by pp11 and and pp22 the unit profits for the unit profits for products 1 and 2, respectively. products 1 and 2, respectively.

The manufacturer has a contract calling for at The manufacturer has a contract calling for at least least mm units of product 1 this month. The units of product 1 this month. The firm's facilities are such that at most firm's facilities are such that at most uu units of units of product 2 may be produced monthly. Develop product 2 may be produced monthly. Develop a mathematical model for the above.a mathematical model for the above.

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The ModelThe Model

Mathematical Model SummaryMathematical Model Summary

Max Max pp11xx11 + + pp22xx22

s.t. s.t. aa11xx11 + + aa22xx22 << bb xx11 >> mm

xx22 << uu

xx11 & & xx22 >> 0 0

Suppose Suppose bb = 2000, = 2000, aa11 = 2, = 2, aa22 = 3, = 3, mm = 60, = 60, uu = 720, = 720, pp11 = 100,= 100,

pp22 = 200. Rewrite the model with these specific values. = 200. Rewrite the model with these specific values.

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Transforming Model Inputs into OutputTransforming Model Inputs into Output

Uncontrollable Inputs:Uncontrollable Inputs:

100, 200, 2, 3, 2000, 60, 720100, 200, 2, 3, 2000, 60, 720Uncontrollable Inputs:Uncontrollable Inputs:

100, 200, 2, 3, 2000, 60, 720100, 200, 2, 3, 2000, 60, 720

Controllable Inputs:Controllable Inputs:xx11 , , xx22

Controllable Inputs:Controllable Inputs:xx11 , , xx22

Output:Output:Profit ZProfit ZOutput:Output:Profit ZProfit Z

The Model:The Model:Max Z = 100xMax Z = 100x11 + 200x + 200x22

2 x2 x11 + 3 x + 3 x22 << 2000 2000xx11 >> 60 60xx22 << 720 720

The Model:The Model:Max Z = 100xMax Z = 100x11 + 200x + 200x22

2 x2 x11 + 3 x + 3 x22 << 2000 2000xx11 >> 60 60xx22 << 720 720

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Possible Problems in Developing Possible Problems in Developing Decision ModelsDecision Models

Defining the Problem.Defining the Problem.

Conflicting Viewpoints.Conflicting Viewpoints.

Impact on Other Departments.Impact on Other Departments.

Beginning Assumptions.Beginning Assumptions.

Solution Outdated.Solution Outdated.

Developing a Model.Developing a Model.

Fitting the Textbook Models.Fitting the Textbook Models.

Understanding the Model.Understanding the Model.

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Possible Problems in Developing Possible Problems in Developing Decision Models -continuedDecision Models -continued

Acquiring Input Data.Acquiring Input Data.

Validity of Data.Validity of Data.

Developing a Solution.Developing a Solution.

Hard-to-Understand Mathematics.Hard-to-Understand Mathematics.

Only One Answer is Limiting.Only One Answer is Limiting.

Testing the Solution.Testing the Solution.

Analyzing the Results.Analyzing the Results.

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Implementation – Not Just The Final StepImplementation – Not Just The Final Step

Decision models assist decision maker by Decision models assist decision maker by

providing scientific method, model, and providing scientific method, model, and

process which is defensible and reliable.process which is defensible and reliable.

Overcome sole reliance upon intuition, Overcome sole reliance upon intuition,

hunches, and experience.hunches, and experience.

Mathematical models are the primary forms Mathematical models are the primary forms

of models used in Management Science.of models used in Management Science.

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SummarySummary

Decision Models and Modeling -Decision Models and Modeling - The three types of models are The three types of models are Iconic, Analog, Iconic, Analog,

and Mathematical modelsand Mathematical models.. Mathematical Decision models are classified Mathematical Decision models are classified

into two categories:into two categories:

• Deterministic models.Deterministic models.

• Stochastic (Probabilistic) models.Stochastic (Probabilistic) models. Approach includes three primary steps:Approach includes three primary steps:

• Formulation.Formulation.

• Solution.Solution.

• Implementation.Implementation.

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The End of Chapter 1The End of Chapter 1