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Introduction to Modeling & Problem Solving Introduction We face numerous decisions in life & business. We can use computers to create models and analyze the potential outcomes of decision alternatives. Spreadsheets are the tool of choice for today’s managers. What is Management Science? A field of study that uses computers, statistics, and mathematics to solve business problems. Also known as: – Operations research – Decision science Home Runs in Management Science Waste Management – Leading waste collection company in North America – 26,000 vehicles service 20 million residential & 2 million commercial customers – Developed vehicle routing optimization system – Benefits: Eliminated 1,000 routes Annual savings of $44 million Models Changing the real truck routes just to see what happens would be foolish. Instead, they used a model Models are just representations of real things Groups: think of 5 models The Modeling Approach to Decision Making Everyone uses models to exams Homew ork GBS220 Quantitative Methods in Business make decisions. 0 8/22/2006 10:43 Types of models: Homework and projects (100 possible) Watch out. Homew ork not turned in w hen I call for it in class w ill not usually be accepted. Points avail Points earned to date to date Linear programming 20 Probability 20 Decision analysis 20 – Mental (arranging furniture) Project management 20 Inventories 20 – Visual (blueprints, road Totals 100 0 maps) Exams (400 possible) Points avail Points earned to date to date 1 100 2 100 – Physical/Scale 3 100 4 100 Totals 400 0 Grades Total points earned to date (est.) 0.00 A 90% 450.00 Total points avail to date (est) 500.00 (aerodynamics, buildings) B C D 80% 70% 60% 400.00 350.00 300.00 Grade to date (est) 0.00% F – Mathematical (what we’ll be studying: net income, dow jones stock average) Spreadsheets What is a “Computer Model”? A set of mathematical relationships called “functions,” which are based on logical assumptions and programmed into a computer as a representation of a real- world object or phenomenon. Characteristics of Models Models are usually simplified versions of the things they represent A valid model accurately represents the relevant characteristics of the object or decision being studied Benefits of Modeling Economy - It is often less costly to analyze decision problems using models. Timeliness - Models often deliver needed information more quickly than their real-world counterparts. Feasibility - Models can be used to do things that would be impossible. Models give us insight & understanding that improves decision making. Spreadsheets and Functions In pairs, create a spreadsheet that calculates profit, based on revenues and expenses, that is: Profit = Revenue - Expenses Spreadsheets and functions Your spreadsheet is a mathematical model and the spreadsheet is the tool business people usually use. Business people like spreadsheets because they are a lot like accounting worksheets. However, mathematicians have a different approach. Instead of spreadsheets, they specify mathematical models as functions and use mathematical notation. Moving from spreadsheets to mathematical function notation C1 = A1 * B1 or Profit = Revenue - Expenses or Profit = f(Revenue, Expenses) or Y= f(X1, X2) A Generic Mathematical Model Y = f(X1, X2, …, Xn) Where: Y = dependent variable (aka bottom-line performance measure) Xi = independent variables (inputs having an impact on Y) f(.) = function defining the relationship between the Xi & Y Mathematical Models & Spreadsheets Most spreadsheet models are very similar to our generic mathematical model: Y = f(X1, X2, …, Xn) Most spreadsheets have input cells (representing Xi) to which mathematical functions ( f(.)) are applied to compute a bottom-line performance measure (or Y). The Problem Solving Process Identify Formulate & Problem Implement Analyze Test Implement Model Model Results Solution unsatisfactory results Good Decisions vs. Good Outcomes Good decisions do not always lead to good outcomes... A structured, modeling approach to decision making helps us make good decisions, but can’t guarantee good outcomes.
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