Chapter 1: Introduction to Managerial Decision Modeling Jason C. H. Chen, Ph.D. Professor of MIS School of Business Administration Gonzaga University Spokane, WA

Dr. Chen, Decision Support Systems 2 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

Dr. Chen, Decision Support Systems 3 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

Dr. Chen, Decision Support Systems 4 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

Dr. Chen, Decision Support Systems 5 Spreadsheets in Decision Making Computers are used to create and solve models Spreadsheets are a convenient alternative to specialized software Microsoft Excel has extensive modeling capability via the use “add-ins”

Dr. Chen, Decision Support Systems 6 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

Dr. Chen, Decision Support Systems 7 Steps in Modeling

Dr. Chen, Decision Support Systems 8 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

Dr. Chen, Decision Support Systems 9 Tax Brackets Percent of Taxable IncomeTaxable Income up to $14,60010% $14,601 to $59,40015% $59,401 to $119,95025% Go to file 1-1.xls

Dr. Chen, Decision Support Systems 10 Millers' Tax Computation Known Parameters Retirement Savings %0.05 Maximum savings4000 Personal exemption3200per person Standard deduction10000 Tax rates0.1$1 to $14,601 to $59,401 to Variables Sue's estimated income Rob's estimated income Tax Computation Total income=B13+B14 Retirement savings=MIN(B4*B17,B5) Personal exemptions=2*B6 Standard deduction=B7 Taxable income=MAX(0,B17-SUM(B18:B20)) 10% rate=B8*MIN(B21,D8) 15% rate=IF(B21>D8,B9*(MIN(B21,D9)-D8),0) 25% rate=IF(B21>D9,B10*(MIN(B21,D10)-D9),0) Total tax=SUM(B22:B24) Estimated tax per quarter=B25/4 file 1-1.xls Tax Computation Total income$85, Retirement savings$4, Personal exemptions$6, Standard deduction$10, Taxable income$64, % rate$1, % rate$6, % rate$1, Total tax$9, Estimated tax per quarter$2, Variables Sue's estimated income$45, Rob's estimated income$40,000.00

Dr. Chen, Decision Support Systems 11 Example Model: Break-Even Analysis Profit = Revenue – Costs Revenue = (Selling price) x (Num. units) Costs = (Fixed cost) + (Cost per unit) x (Num. units)

Dr. Chen, Decision Support Systems 12 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

Dr. Chen, Decision Support Systems 13 Bill Pritchett's Shop Known Parameters Selling price per unit 10 Fixed cost 1000 Variable cost per unit 5 Variables Number of units, X Results Total revenue =B4*B9 Fixed cost =B5 Total variable cost =B6*B9 Total cost =B13+B14 Profit =B12-B15 Bill Pritchett's Shop Known Parameters Selling price per unit$10.00 Fixed cost$1, Variable cost per unit$5.00 Variables Number of units, X1000 Results Total revenue$10, Fixed cost$1, Total variable cost$5, Total cost$6, Profit$4, Bill Pritchett's Shop Known Parameters Selling price per unit$10.00 Fixed cost$1, Variable cost per unit$5.00 Variables Number of units, X200 Results Total revenue$2, Fixed cost$1, Total variable cost$1, Total cost$2, Profit$0.00 Go to file 1-2.xls

Dr. Chen, Decision Support Systems 14 Possible Problems in Developing Decision Models  Defining the Problem Conflicting viewpoints Impact on other departments Beginning assumptions Solution outdated

Dr. Chen, Decision Support Systems 15 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

Dr. Chen, Decision Support Systems 16 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