Modelling and Modelling and Business DecisionsBusiness Decisions

Robert ZimmerRobert Zimmer

Room 6, 25 St JamesRoom 6, 25 St James

This course is about building This course is about building models and making decisionsmodels and making decisions

► It is about organising informationIt is about organising information► It is about being able to ask what-if It is about being able to ask what-if

questionsquestions► It is about applying powerful It is about applying powerful

mathematical models (I might try to mathematical models (I might try to teach you some maths when you teach you some maths when you aren’t looking but that is incidental)aren’t looking but that is incidental)

Example of a decision:Example of a decision:should I have another beer?should I have another beer?

►Organising Information:Organising Information: How much money I haveHow much money I have How much money a beer costsHow much money a beer costs How drunk am I? How drunk am I? Do I have to drive?Do I have to drive? How fat am I?How fat am I? How much do I like the people in the pub?How much do I like the people in the pub? How much do I like the people at home?How much do I like the people at home?

►What-if questionsWhat-if questions What if I can convince the barman to give What if I can convince the barman to give

me a half-price beerme a half-price beer What if I decide that I like these people What if I decide that I like these people

twice as much as I didtwice as much as I did ……

►The Maths here would be difficultThe Maths here would be difficult►Luckily for us, Microsoft has Luckily for us, Microsoft has

implemented a special beer decision implemented a special beer decision function: the famous function: the famous Beer DecisionBeer Decision AlgorithmAlgorithm within excel within excel

►So all we need to do is put all of our So all we need to do is put all of our figures on a spreadsheet, press the = figures on a spreadsheet, press the = button to pull up the formula function button to pull up the formula function and type and type BDA(A1,A2,….) BDA(A1,A2,….)

or whatever or whatever

►Then Bob’s our uncle. We know Then Bob’s our uncle. We know whether to have the drink or notwhether to have the drink or not

►Because we did this on a spreadsheet Because we did this on a spreadsheet it is flexible enough for us to change it is flexible enough for us to change the parameters (that is, inputs) and the parameters (that is, inputs) and find out if we should change our find out if we should change our decisionsdecisions

Another QuestionAnother Question

►What is the most money I am What is the most money I am prepared to pay for this drink? That is prepared to pay for this drink? That is at what price does the pleasure of the at what price does the pleasure of the drink become less than its price?drink become less than its price?

Some more questionsSome more questions

►What is the geometric shape of all the What is the geometric shape of all the points at which the pleasure of the points at which the pleasure of the beer exactly matches the pain of the beer exactly matches the pain of the payment? payment?

►How will my pleasure, my weight, and How will my pleasure, my weight, and my mental state compare if instead of my mental state compare if instead of a beer I have chips? a beer I have chips?

►or do my Java coursework?or do my Java coursework?

After this course you will be able After this course you will be able to answer questions like thisto answer questions like this

►Some names for what we are studying: Some names for what we are studying: operations research, decision science, operations research, decision science, management sciencemanagement science

►Our tool of choice: the humble Our tool of choice: the humble spreadsheet.spreadsheet.

It’s not just beer: example 1It’s not just beer: example 1

►Merril LynchMerril Lynch 5 million customers5 million customers 16,000 financial advisors16,000 financial advisors Developed a model to design product Developed a model to design product

features and pricing options to better features and pricing options to better reflect customer valuereflect customer value

Benefits: Benefits: ►$80 million increase in annual revenue$80 million increase in annual revenue►$22 billion increase in net assets$22 billion increase in net assets

It’s not just beer: example 2It’s not just beer: example 2

► Jan de Wit Co.Jan de Wit Co. Brazil’s largest lily farmerBrazil’s largest lily farmer Annually plants 3.5 million bulbs and Annually plants 3.5 million bulbs and

produces 420,000 pots & 220,000 bundles produces 420,000 pots & 220,000 bundles of lilies in 50 varieties.of lilies in 50 varieties.

Developed model to determine what to Developed model to determine what to plant, when to plant it, and how to sell it.plant, when to plant it, and how to sell it.

Benefits:Benefits:►26% increase in revenue26% increase in revenue►32% increase in contribution margin32% increase in contribution margin

►NBCNBC Must determine program schedulesMust determine program schedules Schedules must meet advertisers Schedules must meet advertisers

demographic and cost requirementsdemographic and cost requirements Developed optimization model to Developed optimization model to

determine optimal timing and pricing of determine optimal timing and pricing of commercialscommercials

Benefits:Benefits:►$50 million increase in annual revenue$50 million increase in annual revenue

Our modus operandiOur modus operandi

1.1. Make a mathematical modelMake a mathematical model

2.2. Implement it in excelImplement it in excel

3.3. Play with it to find out how the answers Play with it to find out how the answers depend on the input variablesdepend on the input variables

4.4. Use the inbuilt mathematical functions Use the inbuilt mathematical functions to do complicated analysesto do complicated analyses

5.5. Use the excel graphic packages to Use the excel graphic packages to make diagramsmake diagrams

How you will learn to do this How you will learn to do this

►Option 1: You will listen to me, go to the Option 1: You will listen to me, go to the labs, and not think about the subject in labs, and not think about the subject in betweenbetween

►Option 2: You will not listen to me and Option 2: You will not listen to me and stay homestay home

►Option 3: You will listen to me and do Option 3: You will listen to me and do everything I tell you toeverything I tell you to

►Option 4: You won’t leave off your Option 4: You won’t leave off your modelling practice, even to listen to memodelling practice, even to listen to me

ModelsModels

• Everyone uses models to make Everyone uses models to make decisions.decisions.

• Types of models:Types of models:– Mental (arranging furniture)Mental (arranging furniture)– Visual (blueprints, road maps)Visual (blueprints, road maps)– Physical/Scale (aerodynamics, buildings)Physical/Scale (aerodynamics, buildings)– Mathematical (what we’ll be studying) Mathematical (what we’ll be studying)

Mathematical ModelsMathematical Models

Profit = Revenue - ExpensesProfit = Revenue - Expenses

or or

Profit = Profit = ff(Revenue, Expenses)(Revenue, Expenses)

oror

Y = Y = ff(X(X11, X, X22))

Characteristics of ModelsCharacteristics of Models

• Models are Models are simplifiedsimplified versions of the versions of the things they representthings they represent

• A A validvalid model accurately represents model accurately represents the the relevantrelevant characteristics of the characteristics of the object or decision being studiedobject or decision being studied

• So a large part of the art: is what is So a large part of the art: is what is relevant and what can be abstracted relevant and what can be abstracted awayaway

Benefits of ModelsBenefits of Models

• EconomyEconomy - it is often less costly to - it is often less costly to analyze decision problems using analyze decision problems using models.models.

• TimelinessTimeliness - models often deliver - models often deliver needed information more quickly than needed information more quickly than their real-world counterparts.their real-world counterparts.

• FeasibilityFeasibility - models can be used to do - models can be used to do things that would be impossible.things that would be impossible.

• Models give us Models give us insightinsight & & understandingunderstanding that improves decision making.that improves decision making.

MathsMaths

Y = f(X1, X2, …, Xn)► 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

Identify Problem

Formulate & Implement

ModelAnalyze Model

Test Results

Implement Solution

unsatisfactoryresults

1.4 Seven-Step Modeling 1.4 Seven-Step Modeling ProcessProcess

Step 1: Problem DefinitionStep 1: Problem Definition - Define the - Define the problem including the objectives and the problem including the objectives and the parts of the organization that must be parts of the organization that must be studied.studied.

Step 2: Data CollectionStep 2: Data Collection – Collect the data – Collect the data to estimate the value of parameters that to estimate the value of parameters that affect the organization’s problem.affect the organization’s problem.

Step 3: Model DevelopmentStep 3: Model Development – Develop – Develop an an analyticalanalytical or or simulation simulation model. model.

Step 4: Model VerificationStep 4: Model Verification – Determine – Determine whether the model is an accurate whether the model is an accurate representation of reality.representation of reality.

Step 5: Optimization and Decision MakingStep 5: Optimization and Decision Making – – Given the model and a set of possible decisions, Given the model and a set of possible decisions, the analyst must choose the decision that best the analyst must choose the decision that best meets the organization’s objectives.meets the organization’s objectives.

Step 6: Model Communication to ManagementStep 6: Model Communication to Management – The analyst presents the model and the – The analyst presents the model and the recommendations to the organization.recommendations to the organization.

Step 7: Model ImplementationStep 7: Model Implementation – If the – If the organization accepts the model then the analysts organization accepts the model then the analysts assists with implementation. Implementation must assists with implementation. Implementation must be monitored constantly to ensure that the model be monitored constantly to ensure that the model enables the organization to meets its objectives.enables the organization to meets its objectives.

►Models can be used for structurable Models can be used for structurable aspects of decision problems.aspects of decision problems.

►Other aspects cannot be structured Other aspects cannot be structured easily and require intuition and easily and require intuition and judgment.judgment.

►CautionCaution: Human judgment and : Human judgment and intuition is not always rational!intuition is not always rational!

Framing EffectsFraming Effects

►Refers to how decision-makers view a Refers to how decision-makers view a problem from a win-loss perspective.problem from a win-loss perspective.

►The way a problem is framed often The way a problem is framed often influences choices in irrational ways…influences choices in irrational ways…

►Suppose you’ve been given $1000 and Suppose you’ve been given $1000 and must choose between:must choose between:

– A. Receive $500 more immediatelyA. Receive $500 more immediately– B. Flip a coin and receive $1000 more if heads B. Flip a coin and receive $1000 more if heads

occurs or $0 more if tails occursoccurs or $0 more if tails occurs

►Now suppose you’ve been given Now suppose you’ve been given $2000 and must choose between:$2000 and must choose between:

– A. Give back $500 immediatelyA. Give back $500 immediately– B. Flip a coin and give back $0 if heads occurs B. Flip a coin and give back $0 if heads occurs

or give back $1000 if tails occursor give back $1000 if tails occurs

Initial state

$1,500

Heads (50%)

Tails (50%)

$2,000

$1,000

Alternative A

Alternative B(Flip coin)

Payoffs

Chapter 2Chapter 2

Introduction to Spreadsheet Introduction to Spreadsheet ModelingModeling

2.1 Introduction2.1 Introduction

►Excel skills are critical. There is an Excel skills are critical. There is an Excel tutorial on the CD-ROM that Excel tutorial on the CD-ROM that accompanies the book. accompanies the book.

►Excel’s features will provide insight Excel’s features will provide insight into solving real business problems.into solving real business problems.

2.2 Basic Spreadsheet Modeling: 2.2 Basic Spreadsheet Modeling: Concepts and Best PracticesConcepts and Best Practices

►Most mathematical models, including Most mathematical models, including spreadsheet models, involve inputs, spreadsheet models, involve inputs, decision variables, and outputs.decision variables, and outputs.

►The model The model inputsinputs are given values are given values that are fixed.that are fixed.

►The The decision variablesdecision variables are values are values that a decision maker has control over.that a decision maker has control over.

►The model The model outputsoutputs are the ultimate are the ultimate values of interest.values of interest.

► Spreadsheet modelingSpreadsheet modeling is the process of is the process of

entering the inputs and decision variables into a entering the inputs and decision variables into a spreadsheet and then relating them spreadsheet and then relating them appropriately, by means of formulas, to obtain the appropriately, by means of formulas, to obtain the outputs.outputs.

►Once a model is created there are several Once a model is created there are several directions in which to proceed.directions in which to proceed. Sensitivity analysis to see how one or more outputs Sensitivity analysis to see how one or more outputs

change as selected inputs or decision variables change.change as selected inputs or decision variables change. Finding the value of a decision variable that maximizes Finding the value of a decision variable that maximizes

or minimizes a particular output.or minimizes a particular output. Create graphs to show graphically how certain Create graphs to show graphically how certain

parameters of the model are related.parameters of the model are related.

►Good spreadsheet modeling practices are Good spreadsheet modeling practices are essential.essential.

► Spreadsheet models should be designed with Spreadsheet models should be designed with readability in mind.readability in mind.

► Several features that improve readability Several features that improve readability include:include:

►A clear logical layout to the overall modelA clear logical layout to the overall model►Separation of different parts of a modelSeparation of different parts of a model►Clear headings for different sections of the model Clear headings for different sections of the model ►Liberal use of range namesLiberal use of range names►Liberal use of formatting featuresLiberal use of formatting features►Liberal use of cell commentsLiberal use of cell comments►Liberal use of text boxes for assumptions, lists or Liberal use of text boxes for assumptions, lists or

explanationsexplanations

Example 2.1 – Building a Example 2.1 – Building a ModelModel

► Randy Kitchell is a NCAA t-shirt vendor. Randy Kitchell is a NCAA t-shirt vendor. The fixed cost of any order is $750, the The fixed cost of any order is $750, the variable cost is $6 per shirt. variable cost is $6 per shirt.

► Randy’s selling price is $10 per shirt, Randy’s selling price is $10 per shirt, until a week after the tournament when until a week after the tournament when it will drop to $4 apiece. The expected it will drop to $4 apiece. The expected demand at full price is 1500 shirts.demand at full price is 1500 shirts.

►He wants to build a spreadsheet model He wants to build a spreadsheet model that will let him experiment with the that will let him experiment with the uncertain demand and his order quantity.uncertain demand and his order quantity.

Ex. 2.1(cont’d) - Building a Ex. 2.1(cont’d) - Building a ModelModel

► The logic behind the model is simple. An The logic behind the model is simple. An Excel IF function will be used.Excel IF function will be used.

►In this model the profit is calculated with the formula

Profit = Revenue – Cost and the Cost = 750 + 6*B4

RevenueRevenue

Case 1: Demand outstrips order (B3 > B4)In that case everything gets sold for 10

dollars Revenue is then simply 10*B4(since B4 is the number ordered)

RevenueRevenue

Case 2:You have ordered too many.That is order (B3) is less than peak

demandThen you can only sell B3 at 10 dollars

and the rest (B4-B3) at 4 dollars

Revenue = 10*B3+4*(B4-B3)

Revenue FormulaRevenue Formula

Revenue = Revenue =

IF(B3>B4,10*B4,10*B3+4*(B4-B3))

Profit FormulaProfit Formula

Profit = Profit =

IF(B3>B4,10*B4,10*B3+4*(B4-B3)) – (750 + 6* B4)

More FlexibilityMore Flexibility

Ex. 2.1(cont’d) - Building a Ex. 2.1(cont’d) - Building a ModelModel

► The formula can be rewritten to be more flexible.The formula can be rewritten to be more flexible.=-B3-B4*B9+IF(B8>B9,10*B8+B6*(B9-B8))=-B3-B4*B9+IF(B8>B9,10*B8+B6*(B9-B8))

► It can be made more readable by using range It can be made more readable by using range names. The formula would then readnames. The formula would then read=-Fixed_order_cost-Variable_cost*Order + =-Fixed_order_cost-Variable_cost*Order + IF(Demand > Order, Selling_price*Order, IF(Demand > Order, Selling_price*Order, 10*Demand+Salvage_value* (Order-Demand)10*Demand+Salvage_value* (Order-Demand)