Chapter 11Spreadsheet Modeling and Analysis

Predictive modeling is the heart and soul of business decisions.

Building decision models is more of an art than a science.

Creating good decision models requires: - solid understanding of business functional areas - knowledge of business practice and research - logical skills It is best to start simple and enrich models as

necessary.

Predictive Decision Modeling

Simple mathematics◦ “Back-of-the-envelope” calculations can provide the

basis for a more formal model Influence diagrams◦ Introduced in Chapter 1, an influence diagram is a logical

and visual representation of key model relationships

Strategies for Predictive Decision Modeling

A restaurant customer dines 6 times a year and spends an average of $50 per visit.

The restaurant realizes a 40% margin on the average bill for food and drinks.

Annual gross profit on a customer = $50(6)(0.40) = $120 30% of customers do not return each year.

Average lifetime of a customer = 1/0.3 = 3.33 years Average gross profit during a customer’s lifetime =

$120(3.33) = $400

Example 11.1: The Economic Value of a Customer

V = value of a loyal customer R = revenue per purchase F = purchase frequency (number of visits per year) M = gross profit margin (expressed as a fraction) D = defection rate (fraction of customers not returning each year)

Developing a General Model for Example 11.1

Example 11.2: Developing a Decision Model Using an Influence Diagram

P = profitR = revenueC = cost

p = unit pricec = unit costF = fixed costS = quantity soldD = demandQ = quantity

produced

Cost = fixed cost + variable cost

C = F + cQ Revenue = price times quantity sold

R = pS Quantity sold = Minimum{demand, quantity sold}

S = min{D, Q} Profit = Revenue − Cost

P = p*min{D, Q} − (F + cQ) (11.2)

Principles of good spreadsheet design:◦Separate the data, model calculations, and model

outputs clearly in designing a spreadsheet. ◦Do not use input data in model formulas, but reference

the spreadsheet cells that contain the data. In this way, if the data change or you want to experiment with the model, you need not change any of the formulas, which can easily result in errors.

Implementing Models on Spreadsheets

(Example 1.8 in Chapter 1) The scenario involves a manufacturer who can produce

a part for $125/unit with a fixed cost of $50,000. The alternative is to outsource production to a supplier at a unit cost of $175.

Models for total cost:

Example 11.3: A Spreadsheet Model for the Outsourcing Decision

Excel spreadsheet

Example 11.3 Continued

A firm wishes to determine the best pricing for one of its products to maximize revenue.◦ Sales = -2.9485 × price + 3,240.9◦ Total revenue = price × sales

= price × (-2.9485 × price + 3,240.9)= -2.9485 × price2 + 3,240.9 × price

Example 11.4: Pricing Decision Spreadsheet Model

Example 11.5: Spreadsheet Implementation of the Profit Model

Assume that unit price = $40, unit cost = $24, fixed cost = $400,000, and demand = 50,000.

The decision variable is the quantity produced; assume a value of 40,000 units.

Building spreadsheet models (called spreadsheet engineering) is part art and part science.

Spreadsheets need to be ◦ accurate, ◦ understandable, and ◦ user friendly.

Verification is the process of ensuring that a model is accurate and free from logical errors.

Spreadsheet Quality

Improve the design and format of the spreadsheet itself.◦ Sketch a logical design of the spreadsheet.◦ Break complex formulas into smaller pieces◦ Design the spreadsheet in a form that the end user can easily

interpret and understand Improve the process used to develop a spreadsheet.◦ Work on one part at a time◦ Check formula results with simple numbers

Inspect your results carefully and use appropriate tools available in Excel.◦ Use Excel auditing tools

Improving Spreadsheet Quality

Gross profit = sales – cost of goods sold Operating expenses = administrative expenses + selling expenses + depreciation expenses Net operating income = gross profit – operating expenses Earnings before taxes = net operating income – interest expense Net income = earnings before taxes – taxes

Example 11.6: Modeling Net Income on a Spreadsheet

Example 11.6 Continued

Simple model: ◦ net income = sales - cost of goods sold - administrative expenses

- selling expenses – depreciation expenses - interest expense - taxes

Data-model format

Example 11.6 Continued

Pro forma income statement

Example 11.6 Continued

A wide variety of practical problems in business analytics can be modeled using spreadsheets.

A useful spreadsheet model need not be complex; often, simple models can provide managers with the information they need to make good decisions.

Spreadsheet Applications in Business Analytics

The manager of a loan processing department wants to know how many employees will be needed over the next several months to process a certain number of loan files per month so she can better plan capacity.

Different types of products, such as a 30-year fixed rate mortgage, 7/1 ARM, FHA loan, or a construction loan, each varying in complexity and time to complete.

Data:◦ Forecasts: 700 loan applications in May, 750 in June, 800

in July, and 825 in August. ◦ Each employee works productively for 6.5 hours each

day, and there are 22 working days in May, 20 in June, 22 in July, and 22 in August.

Example 11.7: A Predictive Model for Staffing

Predict the number of full time equivalent (FTE) staff needed each month to ensure that all loans can be processed.

Spreadsheet Model

Example 11.7 Continued

Many practical models incorporate multiple time periods that are logically linked together.

Taking a systematic approach to putting the pieces together logically can often make a seemingly difficult problem much easier.

Models Involving Multiple Time Periods

Moore Pharmaceuticals needs to decide whether to conduct clinical trials and seek FDA approval for a newly developed drug. R&D cost = $700 million Clinical trials cost = $150 million Market size = 2 million people Market size growth = 3% per year Market share = 8% Market share growth = 20% per year Monthly revenue/prescription = $130 Monthly variable cost/prescription = $40 Discount rate = 9%

Example 11.8: New-Product Development

Example 11.8 Continued Spreadsheet Model

Example 11.8 Continued Spreadsheet Formulas

One-time purchase decisions often must be made in the face of uncertain demand.

Newsvendor Problem: How many newspapers to purchase each day? C = cost to purchase a newspaper Q = number of newspapers the vendor purchases D = number of newspapers demanded R = revenue from selling a newspaper S = salvage value of unsold newspapers

Net profit = R × quantity sold + S × surplus quantity – C ×Q= R(min{Q,D}) + S(max{0,Q−D}) − CQ

Single-Period Purchase Decisions

A small candy store makes Valentine’s Day gift boxes that cost $12 and sell for $18.

In the past, at least 40 boxes have sold by Valentine’s Day but the actual amount is unknown.

After the holiday, boxes are discounted 50%. C = $12, R = $18, S = $9 Net profit = R(min{Q,D}) + S(max{0,Q−D}) − CQ =18(min{Q,D}) + 9(max{0,Q−D}) − 12Q ◦ Note that D is actually uncertain and can be modeled using a

probability distribution.

Example 11.9: A Single-Period Purchase Decision Model

Spreadsheet model

Example 11.9 Continued

Find the number of reservations to accept to effectively fill capacity knowing that some customers may not use their reservations.

A common practice in these industries is to overbook reservations.◦ When more customers arrive than can be handled, the business

usually incurs some cost to satisfy them. ◦ Therefore, the decision becomes how much to overbook to

balance the costs of overbooking against the lost revenue for underuse.

Overbooking Decisions

A popular resort hotel has 300 rooms. The room rate is $120 per night. Reservations can be cancelled by 6:00 p.m. Cost of overbooking is $100 per occurrence. Decision variable = number of reservations to accept. Customer demand and cancellations are actually random variables.

Example 11.10: A Hotel Overbooking Model

Models cannot capture every detail of the real problem, and managers must understand the limitations of models and their underlying assumptions.

Validity refers to how well a model represents reality. Judging validity:◦ Identify and examine the assumptions made in a model to see

how they agree with our perception of the real world◦ Compare model results to observed results

Model Assumptions, Complexity, and Realism

Start work at age 22, earning $50,000 per year. Expect a salary increase of 3% per year. Required to contribute 8% to retirement. Employer contributes 35% of that amount. Expect an annual return of 8% on the portfolio.

Example 11.11: A Retirement-Planning Model

Validity issues:◦Whether the assumptions of the annual salary increase

and return on investment are reasonable ◦Whether they should be assumed to be the same each

year◦How the model calculates the return on investment –

Current year balance only? End-of-year balance plus current-year contributions? Monthly?

Example 11.11 Continued

Sources of data◦Subjective judgment◦Existing databases◦Analysis of historical data◦Surveys, experiments, or other methods of data

collection

Data and Models

Many predictive models in business analytics use empirical data in conjunction with logical model development. ◦ In other words, we observe some phenomenon and then

try to develop a model that best reflects the data that we observe.

Using Empirical Data in Models

In the spring, a department store introduces a new line of bathing suits that sell for $70.

The store purchases 1000 of these bathing suits. During the prime selling season (50 days), the store sells an

average of 7 units per day at full price. Around July 4th, the price is marked down 70% to sell off remaining

inventory. During a special sale, the price was reduced to $49 and sales

increased to 32.2 units per day. If the stored decides to sell at full retail price for x days and then

discounts the price by y% for the remainder of the selling season, followed by the clearance sale, what total revenue could they predict?

Example 11.12: Modeling Retail Markdown Pricing Decisions

Modeling daily sales as a function of price◦ Assume a linear trend model between sales and price:

Example 11.12 Continued

daily sales = a – b × price 7 = a – b × 70 32.2 = a – b × 49

Daily sales = 91 – 1.2 × price

Modeling total revenue

1. Sell at full retail price for x days:◦ Full retail price revenue = 7 units/day × x days ×$70.00 = $490.00x

2. Markdown revenue = units sold x markdown price◦ Markdown price = $70(100% - y%)◦ Daily sales = a - b x markdown price = 91 - 1.2 x $70 x (100% - y%)◦ Units sold at markdown = daily sales x (50 - x), as long as this is less than or

equal to the number of units remaining in inventory from full retail sales.

3. Clearance revenue◦ Clearance inventory = 1000 - units sold at full retail - units sold at markdown =

1,000 - 7x - [91 - 1.2 × $70.00 × (100% - y%)] × (50 - x)

◦ Clearance price revenue = [1,000 - 7x - [91 - 1.2 × $70.00 × (100% - y%)] × (50 – x)] × $21.00

Total revenue = sum of full retail, markdown, and clearance revenues

Example 11.12 Continued

Spreadsheet model

Example 11.12 Continued

Useful Excel tools◦Data validation◦Range Names◦ Form Controls

Developing User-Friendly Applications

Outsourcing Decision Model◦ Suppose that we know that the unit cost of any item is at least $10 but no

more than $100. If a cost is $47.50, for instance, a misplaced decimal would result in either $4.75 or $475, which would clearly be out of range.

Data > Data Tools > Data Validation

Example 11.13 Using Data Validation

Error alert message

Suppose that the unit price is stored in cell B13 and quantity sold is in cell B14.

Suppose you wish to calculate revenue in cell C15. ◦ Instead of writing the formula =B13*B14, you could

define the name of cell B13 as “UnitPrice” and the name of cell B14 as “QuantitySold.”

◦ Then in cell C15, write the formula =UnitPrice*QuantitySold.

Range Names

Form controls are buttons, boxes, and other mechanisms for inputting or changing data on spreadsheets easily that can be used to design user-friendly spreadsheets.

Activate the Developer tab on the Excel ribbon: File > Options > Customize Ribbon and check the box for Developer.

Form Controls

Button Combo box Check box Spin button List box Option button Group box Label Scroll bar

Types of Form Controls

Spin button for the supplier unit cost (which we will assume might vary between $150 and $200 in increments of $5)

Scroll bar for the production volume (in unit increments between 500 and 3000 units)

Developer > Controls > Insert; then click in the spreadsheet. Right click and set Format Control options.

Example 11.14 Using Form Controls for the Outsourcing Decision Model

Predictive analytical models are based on assumptions about the future and incorporate variables that most likely will not be known with certainty.

It is usually important to investigate how these assumptions and uncertainty affect the model outputs.

Analyzing Uncertainty and Model Assumptions

Spreadsheet models allow you to easily evaluate what-if questions by changing input values and recalculating model outputs.

Systematic approaches to what-if analysis that are available in Excel make the process easier and more useful.◦Data tables◦Scenario Manager◦Goal Seek

What-If Analysis

Uncertain demand in the Profit Model. Excel table using formulas:

Example 11.15: Using Excel for What-If Analysis

Visualization of profit:

Data Tables summarize the impact of one or two inputs on a specified output.◦A one-way data table evaluates an output variable

over a range of values for a single input variable. ◦Two-way data tables evaluate an output variable over

a range of values for two different input variables.

Data Tables

Create a range of values for some input cell in your model that you wish to vary.

Enter the cell reference for the output variable in your model that you wish to evaluate in the row above the first value and one cell to the right of the column of input values.

Select the range of cells that contains both the formulas and values you want to substitute.

Data > What-If Analysis > Data Table Type the cell reference for the input cell in your model in the

Column input cell box.

Creating (Column) Data Tables in Excel

1. Create a column of demand values (column E).

2. Enter =C22 in cell F3 (to reference the output cell).

3. Highlight the range E3:F11.

4. Data > What-If Analysis > Data Table

5. Enter B8 for Column input cell in the Data Table dialog (tells Excel that column E refers to demand)

Example 11.16: A One-Way Data Table for Uncertain Demand

5

1 2

3

Create a second output column for revenue.

Enter =C15 in cell G3. Highlight E3:G11. Data > What-If Analysis > Data

Table Enter B8 for Column input cell in

the Data Table dialog

Example 11.17: One-Way Data Tables with Multiple Outputs

Type a list of values for one input variable in a column and a list of input values for the second input variable in a row, starting one row above and one column to the right of the column list.

In the cell in the upper left-hand corner immediately above the column list and to the left of the row list, enter the cell reference of the output variable you wish to evaluate.

Select the range of cells that contain this cell reference and both the row and column of values.

In the Row input cell of the dialog box, enter the reference for the input cell in the model that corresponds to the input values in the row.

In the Column input cell box, enter the reference for the input cell in the model that corresponds to the input values in the column.

Two-Way Data Tables

Evaluate the impact of both unit price and unit cost

Create a column of unit prices.

Create a row of unit costs. Enter =C22 in upper left

corner. Select range of data (not

including headings). In Data Table dialog

◦ Enter B6 for Row input cell. ◦ Enter B5 for Column input cell.

Example 11.18: A Two-Way Data Table for the Profit Model

Allows creation of scenarios – sets of values that are saved and can be substituted in worksheets.

Data > What-If Analysis > Scenario Manager

Click Add button to open Add Scenario dialog

Enter a Scenario Name In Changing Cells box, enter cell

references to include in scenario. In the Scenario Values dialog enter values

for each of the changing cells. Click Show button to display the results

Scenario Manager

Evaluate 4 strategies for pricing and discounts on the bathing suits in the Markdown Pricing Model.

Example 11.19: Using the Scenario Manager for the Markdown Pricing Model

If you know the result that you want from a formula but are not sure what input value the formula needs to get that result, use the Goal Seek feature in Excel.

Data > What-If Analysis > Goal Seek Set cell contains the cell reference for the formula you want to

resolve To value is the target value you want the formula to return. By changing cell is the reference of the input value that you

want to change to achieve the set cell value.

Goal Seek

Find the value of demand for which manufacturing

cost equals purchased cost◦ Set cell: B19◦ To value: 0◦ By changing cell: B12.

Example 11.20: Finding the Break-Even Point in the Outsourcing Model

Break-even volume

Parametric sensitivity analysis is the term used by Analytic Solver Platform for systematic methods of what-if analysis. ◦A parameter is simply a piece of input data in a model.

You can create data tables and tornado charts.

Parametric Sensitivity Analysis Using Analytic Solver Platform

Create a one-way data table to evaluate the profit as the unit price in cell B5 is varied between $35 and $45 in the profit model.

Define cell B5 as a parameter by selecting B5, click Parameters and select Sensitivity.

In the Function Arguments dialog, specify the range of values.

Example 11.21: Creating Data Tables with Analytic Solver Platform

Click the Reports button and click on Parameter Analysis from the Sensitivity menu. This displays a Sensitivity Report dialog; use the arrows to move cells into the panes on the right.

Example 11.21 Continued

One-way data table result

Example 11.21 Continued To create a two-way data table, define both inputs as parameters

and in the Sensitivity Report dialog, be sure to check the box Vary Parameters Independently near the bottom.

To create charts to visualize the data tables, click the Charts button, and then click Parameter Analysis from the Sensitivity menu.◦ Replace the cell references ($B$5, $B$6, and $C$22) by descriptive names to

facilitate understanding the results.

A tornado chart shows the impact that variation in a model input has on some output while holding all other inputs constant.◦ Shows which inputs are the least and most influential on the

output.◦ Helps you select the inputs that you would want to further

analyze. Analytic Solver Platform automatically identifies all the

data input cells on which the output cell depends and creates the chart.

Tornado Charts

In the Profit Model spreadsheet, select cell C22; then click the Parameters button and choose Identify.

Example 11.22: Creating a Tornado Chart in Analytic Solver Platform