sda 3e chapter 9

8/4/2019 SDA 3E Chapter 9

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2007 Pearson Education

Chapter 9: Building and UsingDecision Models


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Models Amodelis an abstraction or representation of

a real system, idea, or object.

Picture Spreadsheet

Mathematical relationships


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Types of Decision Models Descriptive - describe relationships and

provide information for evaluation

Prescriptive (optimization models) -determine an optimal policy, that is, the bestcourse of action that a decision maker shouldtake to maximize or minimize some objective


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New Store Financial Analysis

Model Spreadsheet


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Net Present Value Measures the worth of a stream of cash

flows, taking into account the time value of

money. A cash flow ofFdollars ttime periods in the

future is worth F/(1 + i)tdollars today, whereiis the discount rate.


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Building Decision Models on

Spreadsheets Organize information into a logical framework

that will make the spreadsheet easier to

develop and reduce errors Sketch a logical design of the spreadsheet

Separate the model inputs from the modelitself and to reference the input cells in themodel formulas


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Example Profit = Revenue - Cost

Revenue depends on the unit price and

quantity sold. Total cost depends on the unit cost,

quantity produced, and relevant fixedcosts.

Profit = (Unit price)(Quantity sold) - Cost Profit = (Unit price)(Quantity sold) - [Fixed

cost + (Unit cost)(Quantity produced)]


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Profit Model Spreadsheet


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Elements in Models Constant data

Uncontrollable inputs, quantities that can

change, but cannot be directly controlled bythe decision-maker.

Controllable inputs, often called decisionvariables.


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Spreadsheet Quality Improve the design and format of the

spreadsheet itself.

Improve the process used to develop aspreadsheet.

Inspect your results carefully and useappropriate tools available in Excel.

Use cell and range names Use the Data Validation tool

Inspect and audit formulas


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Model Assumptions All models reflect assumptions used by the

modeler.

Assumptions simplify models and make themeasier to manipulate and solve

Assumptions should be as realistic asnecessary to make models useful but not

overly complex Assumptions should be clearly stated and

documented


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Optimization Models Sales = -2.6556 Price + 3016.2

Revenue = Price (-2.6556 Price + 3016.2) = -

2.6556(Price)

2

+ 3016.2 Price Find the best value of price to maximize revenue


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Models Involving Uncertainty Uncontrollable inputs often exhibit random

behavior, which must be incorporated intomodels

Specify probability distributions for theappropriate uncontrollable inputs. Example: assume that demand is normally

distributed with a mean of 50,000 and a standarddeviation of 10,000 units.

Models that include randomness are calledprobabilistic, or stochastic, models.


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Distribution Fitting

For clues: Examine descriptive statistics Examine histogram


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Normal Probability Plot


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PHStatNormal Probability Plot


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Distribution Fitting With

Crystal Ball

DefineAssumption

button


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Crystal Ball Distribution Gallery


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Fit Distribution Dialog


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Distribution Fitting

Comparison Chart


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Goodness of Fit Statistics


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Model Analysis Scenario evaluation evaluate specific

combinations of model inputs that reflect key

model assumptions. Sensitivity analysis (what if analysis) - the

process of changing key model inputs todetermine their effect on the outputs


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Data Tables Used for sensitivity analyses on variables of a

decision model

Excel tools One-way data tables

Two-way data tables


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One Way Data Table


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Two Way Data Table


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Tornado Chart Graphically shows the impact that variation in

one model input has on some output while

holding all other inputs constant


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Spider Chart Shows the sensitivity that percentage

changesin inputs have on a model output.


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Solving Optimization Models Analytical solutions closed-form

mathematical formulas

Algorithm - a systematic procedure that findsa solution to a problem

Heuristics - solution procedures that generallyfind good solutions without guarantees offinding an optimal solution


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Practical Issues Managers may not always need exact optimal

solutions

Inexact or limited data used to estimate uncontrollablequantities in models may contain more error than that of anon-optimal solution.

The assumptions used in a model make it an inaccuraterepresentation of the real problem, making having the "best"solution pointless.

Managers may not need the very best solution; anythingbetter than the present one will often suffice, so long as itcan be obtained at a reasonable cost and in a reasonableamount of time.


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Excel Solver Maximize Revenue = -2.6556(Price)2 + 3016.2 Price

Spreadsheet Model Solver Model

Solution:

Price = $567.89

Revenue = $856,441.34

sda 3e chapter 9

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