Chapter 1 Introduction to Managerial Decision Modeling

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Chapter 1Introduction to Managerial Decision
Modeling

• Management Science - BMGT 555
• Professor Ahmadi

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Learning Objectives

• Define decision model and describe its
  importance.
• Understand two types of decision models
  deterministic and probabilistic models.
• Understand steps involved in developing decision
  models in practice.
• Understand use of spreadsheets in developing
  decision models.
• Discuss possible problems in developing decision
  models.

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Introduction

• Quantitative approaches to decision making are
  based on the scientific method.
• Names for this body of knowledge include
  Management Science, Operations Research, and
  Decision Science.
• It had its early roots in World War II and is
  flourishing in business and industry with the aid
  of computers in general and the microcomputer in
  particular.
• Some of the primary applications areas of this
  body of knowledge are management, marketing,
  production scheduling, capital budgeting, and
  transportation.

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Types of Problem Information

• Quantitative data - numeric values that indicate
  how much or how many.
• Production quantity
• Rate of return
• Financial ratios
• Cash flows
• Qualitative data - labels or names used to
  identify an attribute -
• Pending state or federal legislation
• New technological breakthrough

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Role of Spreadsheets in Decision Modeling

• Computers are an integral part of decision
  making.
• Spreadsheet packages are capable of handling
  management decision modeling techniques. Have
  built-in functions and procedures, such as
• Goal Seek
• Data Table
• Solver
• Chart Wizard, and others.

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Models

• Models are representations of real objects or
  situations.
• Three forms of models are iconic, analog, and
  mathematical.
• Iconic models are physical replicas (scalar
  representations) of real objects.
• Analog models are physical in form, but do not
  physically resemble the object being modeled.
• Mathematical models represent real world problems
  through a system of mathematical formulas and
  expressions based on key assumptions, estimates,
  or statistical analyses.

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Mathematical Models

• Cost/benefit considerations must be made in
  selecting an appropriate mathematical model.
• Frequently a less complicated (and perhaps less
  precise) model is more appropriate than a more
  complex and accurate one due to cost and ease of
  solution considerations.
• Mathematical models relate decision variables
  with fixed or variable parameters.
• Frequently mathematical models seek to maximize
  or minimize some objective function subject to
  constraints.
• The values of the decision variables that provide
  the mathematically-best output are referred to as
  the optimal solution for the model.

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Types of Decision Models
Decision Models
Deterministic Models
Stochastic Models
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Transforming Model Inputs into Output
Uncontrollable Inputs
Output (Projected Results)
Controllable Inputs (Decision Variables)
Mathematical Model
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Steps Involved in Decision Modeling

• 1. Formulation.
• 2. Solution.
• 3. Interpretation.

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Step 1 Formulation

• Defining the problem.
• Develop clear and concise problem statement.
• Developing a model.
• Select and develop a decision model.
• Select appropriate problem variables.
• Develop relevant mathematical relation for
• consideration and evaluation.

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Step 1 Formulation (Continued )

• Acquiring input data.
• Collect accurate data for use in the model.
• Possible data sources are
• Official company reports.
• Accounting, operating, and financial information.
• Views, and opinions from knowledgeable
  individuals.

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Step 2 Solution

• Developing a solution involves
• Manipulating model to arrive at the best
  (optimal) solution.
• Solution of a set of mathematical expressions.
• Alternative trial and error iterations.
• Complete enumeration of all possibilities or
  utilization of an algorithm.
• Series of steps repeated until best solution is
  attained.

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Step 2 Solution (Continued )

• Testing a solution involves
• Prior to implementation of model solution,
  testing the solution.
• Testing of solution is accomplished by examining
  and evaluating
• Data utilized in the model and
• On the model itself.

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Step 3 Interpretation

• Interpretation and What-if Analysis.
• Analyzing the results and sensitivity analysis.
• Vary data input values and examine differences in
  various optimal solutions.
• Make changes in the model parameters and examine
  differences in various optimal solutions.

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Example Iron Works, Inc.

• Iron Works, Inc. (IWI) manufactures two products
  made from steel and just received this month's
  allocation of b pounds of steel. It takes a1
  pounds of steel to make a unit of product 1 and
  it takes a2 pounds of steel to make a unit of
  product 2.
• Let x1 and x2 denote this month's production
  level of product 1 and product 2, respectively.
  Denote by p1 and p2 the unit profits for products
  1 and 2, respectively.
• The manufacturer has a contract calling for at
  least m units of product 1 this month. The
  firm's facilities are such that at most u units
  of product 2 may be produced monthly. Develop a
  mathematical model for the above.

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The Model

• Mathematical Model Summary
• Max p1x1 p2x2
• s.t. a1x1 a2x2 lt
  b
  x1 gt m
  x2 lt u
• x1 x2 gt 0
• Suppose b 2000, a1 2, a2 3, m 60, u
  720, p1 100,
• p2 200. Rewrite the model with these specific
  values.

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Transforming Model Inputs into Output

Uncontrollable Inputs 100, 200, 2, 3, 2000, 60,
720
Output Profit Z
The Model Max Z 100x1 200x2 2 x1 3 x2 lt
2000 x1 gt 60 x2 lt 720
Controllable Inputs x1 , x2
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Possible Problems in Developing Decision Models

• Defining the Problem.
• Conflicting Viewpoints.
• Impact on Other Departments.
• Beginning Assumptions.
• Solution Outdated.
• Developing a Model.
• Fitting the Textbook Models.
• Understanding the Model.

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Possible Problems in Developing Decision Models
-continued

• Acquiring Input Data.
• Validity of Data.
• Developing a Solution.
• Hard-to-Understand Mathematics.
• Only One Answer is Limiting.
• Testing the Solution.
• Analyzing the Results.

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Implementation Not Just The Final Step

• Decision models assist decision maker by
  providing scientific method, model, and process
  which is defensible and reliable.
• Overcome sole reliance upon intuition, hunches,
  and experience.
• Mathematical models are the primary forms of
  models used in Management Science.

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Summary

• Decision Models and Modeling -
• The three types of models are Iconic, Analog, and
  Mathematical models.
• Mathematical Decision models are classified into
  two categories
• Deterministic models.
• Stochastic (Probabilistic) models.
• Approach includes three primary steps
• Formulation.
• Solution.
• Implementation.

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The End of Chapter 1