### chap1 - Gonzaga University

```Chapter 1:
Introduction to Managerial
Decision Modeling
Jason C. H. Chen, Ph.D.
Professor of MIS
Gonzaga University
Spokane, WA 99223
[email protected]
What is Decision Modeling?
A scientific approach to managerial
decision making
• The development of a (mathematical) model
of a real-world scenario
• The model provides insight into the solution of
the managerial problem
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Types of Decision Models
• Deterministic Models
Where all the input data value are known with
complete certainty
• Probabilistic Models
Where some input data values are uncertain
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Quantitative vs. Qualitative Data
The modeling process begins with data
• Quantitative Data
Numerical factors such as costs and revenues
• Qualitative Data
Factors that effect the environment which are
difficult to quantify
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• Computers are used to create and solve
models
• Spreadsheets are a convenient alternative
to specialized software
• Microsoft Excel has extensive modeling
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Steps in Decision Modeling
1. Formulation
Translating a problem scenario from
words to a mathematical model
2. Solution
Solving the model to obtain the optimal
solution
3. Interpretation and Sensitivity Analysis
Analyzing results and implementing a
solution
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Steps in
Modeling
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Example Model: Tax Computation
Self employed couple must estimate and
pay quarterly income tax (joint return)
• Income amount is uncertain
• 5% of income to retirement account, up to
\$4000 max
• Personal exemption = 2 x \$3200 = \$6400
• Standard deduction = \$10,000
• No other deductions
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Tax Brackets
Taxable Income
up to \$14,600
\$14,601 to \$59,400
\$59,401 to \$119,950
Percent of
Taxable Income
10%
15%
25%
Go to file 1-1.xls
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Millers' Tax Computation
Known Parameters
Retirement Savings %
0.05
Maximum savings
4000
Personal exemption
3200
Standard deduction
10000
Tax rates
per person
0.1
\$1 to
14600
0.15
\$14,601 to
59400
0.25
\$59,401 to
119950
Variables
Variables
Sue's estimated income
Sue's estimated income
\$45,000.00
Rob's estimated income
Rob's estimated income
\$40,000.00
Tax Computation
Tax Computation
Total income
=B13+B14
Total income
Retirement savings
=MIN(B4*B17,B5)
Retirement savings
\$4,000.00
Personal exemptions
=2*B6
Personal exemptions
\$6,400.00
Standard deduction
=B7
Standard deduction
\$10,000.00
Taxable income
=MAX(0,B17-SUM(B18:B20))
Taxable income
\$64,600.00
Tax @ 10% rate
=B8*MIN(B21,D8)
Tax @ 10% rate
\$1,460.00
Tax @ 15% rate
=IF(B21>D8,B9*(MIN(B21,D9)-D8),0)
Tax @ 15% rate
\$6,720.00
Tax @ 25% rate
=IF(B21>D9,B10*(MIN(B21,D10)-D9),0)
Tax @ 25% rate
\$1,300.00
Total tax
=SUM(B22:B24)
Total tax
\$9,480.00
Estimated tax per quarter
=B25/4
Estimated tax per quarter
\$2,370.00
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file 1-1.xls
\$85,000.00
10
Example Model: Break-Even Analysis
Profit = Revenue – Costs
Revenue = (Selling price) x (Num. units)
Costs = (Fixed cost) +
(Cost per unit) x (Num. units)
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The Break Even Point (BEP) is the
number of units where;
Profit = 0, so
Revenue = Costs
BEP
=
Fixed cost
(Selling price) – (Cost per unit)
Go to file 1-2.xls
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Bill Pritchett's Shop
Known
Parameters
Bill Pritchett's Shop
Bill Pritchett's Shop
Known Parameters
Known Parameters
Selling price per unit
10
Selling price per unit
Fixed cost
1000
Fixed cost
Variable cost per unit
5
Variable cost per unit
Variables
Variables
Number of units, X
Number of units, X
Results
Results
Total revenue
=B4*B9
Total revenue
Fixed cost
=B5
Fixed cost
Total variable cost
=B6*B9
Total cost
Profit
\$10.00
\$1,000.00
\$5.00
Selling price per unit
Fixed cost
Variable cost per unit
\$10.00
\$1,000.00
\$5.00
Variables
1000
Number of units, X
200
Results
\$10,000.00
Total revenue
\$2,000.00
\$1,000.00
Fixed cost
\$1,000.00
Total variable cost
\$5,000.00
Total variable cost
\$1,000.00
=B13+B14
Total cost
\$6,000.00
Total cost
\$2,000.00
=B12-B15
Profit
\$4,000.00
Profit
\$0.00
Go to file 1-2.xls
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Possible Problems in
Developing Decision Models
Defining the Problem
• Conflicting viewpoints
• Impact on other departments
• Beginning assumptions
• Solution outdated
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Possible Problems in
Developing Decision Models
Developing a Model
• Fitting the textbook models
• Understanding the model
Acquiring Input Data
• Using accounting data
• Validity of data
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Possible Problems in
Developing Decision Models
Developing a Solution
• Hard to understand mathematics
• Limitations of only one answer
Testing the Solution
Analyzing the Results
Implementation
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