Supplement ASpreadsheet Modeling: An Introduction

Operations Managementby

R. Dan Reid & Nada R. Sanders2nd Edition © Wiley 2005

PowerPoint Presentation byRoger B. Grinde, University of New Hampshire

Learning Objectives

Explain what models are and why they are used. Identify the main types of models. Describe the different components of mathematical models. Identify the recommended steps in the spreadsheet modeling

process. Explain the importance of model correctness, flexibility and

documentation. Construct spreadsheet models applying sound modeling

principles. Enter key Excel formulas and functions in models. Use the Goal Seek and Data Table features of Excel to perform

meaningful analysis. Develop meaningful charts representing the results of analysis.

Types of Models

Mental Models Visual Models Physical Models Mathematical Models Spreadsheet Models

Model Characteristics

Motivated by a decision Inputs: quantities or factors that

affect a decision Controllable Inputs (decision

variables) Uncontrollable Inputs (parameters)

Outputs: Primary & secondary

Model Definition A model is a purposeful representation

of the key factors in a situation and the relationships among them. Abstraction of real situation Enough detail so results meet current needs Omit unnecessary details

“Everything should be made as simple as possible, but not simpler.” (Albert Einstein)

Model Schematic

Uncontrollable Inputs

(Parameters)

Controllable Inputs (Decision Variables)

Mathematical Model: set of relationships

(spreadsheet formulas)

Outputs

Spreadsheet Modeling Process

1. Turn off the computer. Draw a picture/diagram, identify controllable & uncontrollable inputs, outputs.

2. Sketch out overall plan for spreadsheet model. Determine where inputs, intermediate calculations, and outputs will go.

3. Develop the base case spreadsheet model.4. Test the model using trial values.5. Use the model to perform the needed

analysis.6. Document the model so others can

understand it.

Evaluating Spreadsheet Models

Correct Correct numerical answer for base case (i.e., “given”

information) Flexible

Accurate results if any of the input values are changed. Each input value entered only once in the model. Formulas contain only cell references, not numerical values.

Good: =B1+C1 Bad: =B1+55

Documented Descriptive labels, units of measure, numerical formatting,

cell formatting, cell comments Printouts: include row/column headings, gridlines, footer

Example 1 Sports Feet: New line of footwear Variable Cost: $9.00 Selling Cost: $25.00 Fixed Cost: $52,000/year

Develop flexible spreadsheet model, perform sensitivity analysis, find breakeven point

Example 1: “Black Box” Determine inputs & outputs

Model:

Set of relationships

(formulas) to translate the inputs

into the outputs

Unit Sales Price

Annual Fixed Cost

Unit Variable Cost

Quantity Made and Sold

Annual Revenue

Annual Total Cost

Annual Profit (Loss)

Example 1: Key Relationships Annual Profit = Annual Revenue –

Annual Total Cost Annual Revenue = Unit Selling Price *

Quantity Made and Sold Annual Total Cost = Annual Fixed Cost

+ Annual Variable Cost Annual Variable Cost = Unit Variable

Cost * Quantity Made and Sold

Example 1: Excel Model

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A B C

Example A.1 (Similar to Textbook Example 3.1)Profit/Loss Analysis for Sports Feet Manufacturing

InputsUnit Sales Price $25.00

Annual Fixed Cost $52,000Unit Variable Cost $9.00

Quantity Made and Sold 2500 (user-specified quantity)

Calculations and OutputsAnnual Revenue $62,500

Annual Variable Cost $22,500Annual Fixed Cost $52,000Annual Total Cost $74,500

Annual Profit (Loss) ($12,000) (profit or loss at the user-specified quantity)

B12: =B5*B9

B13: =B9*B7

B14: =B6

B15: =B13+B14

B16: =B12-B15

Trial value entered for “quantity made and sold.” At this trial value, Profit = ($12,000).

Example 1: Find Breakeven Point

What Quantity results in a Profit of $0? We have a flexible model. Can do

“what-if” analysis on cell B9 to determine when the Profit becomes $0.

However, Excel has Goal Seek tool which can automate this what-if analysis.

Excel: Goal Seek Goal Seek works backwards to find the

value of an input quantity that causes an output quantity to have a particular value.

Excel: ToolsGoal Seek Set Cell: Output Cell (cell must contain a

formula) To Value: Specify the numerical value you

want the output cell to have (e.g., 0 for a breakeven analysis).

By Changing Cell: Input Cell (cell must contain a value)

Example 1: Goal Seek

ToolsGoal Seek

After Solving

Goal Seek changes the value of the Quantity Cell (B9) to 3250. This results in the Profit Cell (B16) having a value of $0. Therefore, the breakeven point is 3250 pairs of shoes.

Goal Seek Comments Sometimes critical values (e.g., breakeven points) can be found

using algebraic methods. However, many real-world problems are quite complex and an algebraic approach is difficult, if not impossible. This is where Goal Seek is particularly useful.

There is nothing special about choosing $0 for profit. We used this because it is common to find a breakeven point. However, in a particular situation we may be interested in some other critical value (e.g., How much do we need to sell in order to make a $2000 profit?).

Goal Seek can be used to find a series of critical values for each of the input quantities. For example, we could find the variable cost, the fixed cost, and the selling price for which profit equals $0 (for a specified quantity made and sold).

Excel: Data Table Feature

Spreadsheets are a great “what-if” tool. But, what-if analysis can be tedious.

Excel has a feature called a Data Table Data Table allows one to systematically

vary one or two input quantities, and keep track of a resulting input value.

For example, vary “quantity made and sold” and keep track of “profit.”

Example 1: Data Table

2223242526272829303132333435363738394041

A B CData Table to Show Profit as Function of Quantity

Sales Quantity Profit($12,000)

0 ($52,000)500 ($44,000)

1000 ($36,000)1500 ($28,000)2000 ($20,000)2500 ($12,000)3000 ($4,000)3500 $4,0004000 $12,0004500 $20,0005000 $28,0005500 $36,0006000 $44,0006500 $52,0007000 $60,0007500 $68,0008000 $76,000

B24: =B16

This is a completed Data Table

Excel automatically calculates the profit for each of the sales quantities in the left column.

The results are dynamic. If we change, for example, the variable cost, this data table will be automatically re-calculated.

Powerful tool for sensitivity analysis!

Example 1: Data Table “How To”

1. Enter labels in Rows 22 & 23 as shown in previous slide.

2. Cells A25:A41. Enter 0,500,…,8000 (use EditFill or write a formula to add 500 to the above quantity).

3. Cell B24: Enter “=B16”. This is the “output” that Excel will compute each time.

4. Select A24:B41. Keep this range selected.5. From menu, DataTable. For the “column input cell,”

select Cell B9.6. Click OK. If all the profit values are the same, press

the F9 key (F9 forces Excel to recalculate the spreadsheet).

Example 2: Multi-Criteria Decision Making

Antonio’s Italian Restaurant Three possible locations for new

restaurant. Seven different factors that are

important in the decision. How to decide which location is

“best?”

Multi-Criteria Model: Basic Ideas Develop weights for each factor. Sum of

weights to equal 100. Higher weights imply more important factors.

For each location and factor, assign a score representing how well that location scores with respect to that factor. Here we use a 1-5 scale, with higher values indicating a better score.

Overall score for each location is a weighted sum of the factor weights and the scores for that location.

Example 2: Spreadsheet Model

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10111213

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Example A.2 (Same as Example 9.3 in Textbook)Factor Rating for Antonio's Italian Restaurant

Factor Location 1Location

2Location

3Factor Weight

Appearance 5 3 2 20Ease of expansion 4 4 2 10Proximity to market 2 3 5 20Customer parking 5 3 3 15Access 5 2 3 15Competition 2 4 5 10Labor supply 3 3 4 10

Total 100

Factor Scores (1-5 scale)

E13: =SUM(E6:E12)

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A B C D E F GCompute Weighted Factor Scores and Overall Scores for Each Location

Factor Location 1Location

2Location

3Appearance 100 60 40Ease of expansion 40 40 20Proximity to market 40 60 100Customer parking 75 45 45Access 75 30 45Competition 20 40 50Labor supply 30 30 40Totals 380 305 340

Weighted Factor ScoresB18: =B6*$E6(copied to B18:D24)

B25: =SUM(B18:B24)(copied right)

A17: =A5

Cells B18:B24. Compute weighted scores for each factor/location combination.

Cells B25:D25. Compute overall scores.

Result: Location 1 has highest weighted score.

Example 2: Visualization (Stacked Column Chart)

Weighted Factor and Overall Scores of Alternate Restaurant Locations

0

50

100

150

200

250

300

350

400

Location 1 Location 2 Location 3

Labor supply

Competition

Access

Customer parking

Proximity to market

Ease of expansion

Appearance

Example 2 Enhancement Automatically show best score and best alternative. Uses Excel’s MAX, INDEX, and MATCH functions. See Excel

Help system for more information.

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A B C D E FCompute Weighted Factor Scores and Overall Scores for Each Location

Factor Location 1Location

2Location

3Appearance 100 60 40Ease of expansion 40 40 20Proximity to market 40 60 100Customer parking 75 45 45Access 75 30 45Competition 20 40 50Labor supply 30 30 40Totals 380 305 340

Best Total Score 380Best Location Location 1

Weighted Factor ScoresB18: =B6*$E6(copied to B18:D24)

B25: =SUM(B18:B24)(copied right)

B27: =MAX(B25:D25)

B28: =INDEX(B17:D17,MATCH(B27,B25:D25,0))

A17: =A5

SUMPRODUCT Function SUMPRODUCT function a handy way to

computed weighted sums, such as in this example.

=SUMPRODUCT (range1, range2) Range1 and range2 must be the same size. SUMPRODUCT multiplies corresponding elements of

range1 and range2, and then sums these products. Example: =SUMPRODUCT(A1:A3,B1:B3) is equivalent

to =A1*B1 + A2*B2 + A3*B3. However, with large ranges, SUMPRODUCT is much

easier and less error-prone!

Example 2 with SUMPRODUCT

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1617181920

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Example A.2 (Same as Example 9.3 in Textbook)Factor Rating for Antonio's Italian Restaurant

Factor Location 1 Location 2 Location 3Factor Weight

Appearance 5 3 2 20Ease of expansion 4 4 2 10Proximity to market 2 3 5 20Customer parking 5 3 3 15Access 5 2 3 15Competition 2 4 5 10Labor supply 3 3 4 10

Total 100

Compute Overall Scores for Each Location

Location 1 Location 2 Location 3

Overall Score 380 305 340

Best Total Score 380Best Location Location 1

Factor Scores (1-5 scale)

E13: =SUM(E6:E12)

B17: =SUMPRODUCT($E6:$E12,B6:B12)

B19: =MAX(B17:D17)

B20: =INDEX(B16:D16,MATCH(B19,B17:D17,0))

When using SUMPRODUCT, the individual weight*score calculations are not needed. They are included as part of the SUMPRODUCT calculation.

Supplement A Highlights A model is a purposeful representation of the key factors in a situation, and

the relationships among them. It abstracts the real situation, incorporating those factors that are important to the decision it was designed to address.

The main types of models are mental models, visual models, physical models, and mathematical models. Spreadsheet models are essentially mathematical models, and are the focus of this supplement.

Mathematical models translate inputs into outputs through a set of relationships. Inputs consist of uncontrollable inputs and controllable inputs, sometimes called decision variables. There can be many outputs of mathematical models, but often we are interested in a relatively small number of primary outputs.

The recommended spreadsheet modeling process consists of understanding the problem, drawing a sketch of the model, developing a base case spreadsheet, testing the spreadsheet, using the model to perform analysis, and documenting the model.

Models should be correct, flexible, and documented. Correctness implies the numerical calculations are correct for the current situation. Being flexible implies that the user can change any of the input values, and the results will be correctly calculated. A well-documented spreadsheet can be understood by someone else without a detailed explanation by the developer.

Supplement A Highlights (continued)

This supplement focused on the construction of models by applying sound modeling principles. You should invest time applying the principles to problems in this supplement as well as other problems in this text.

Key Excel formulas and functions were addressed in this supplement. A critical skill is the correct use of Relative and Absolute References. Mastery allows you to develop a model in a fraction of the time it would take otherwise. Several important functions were shown in Table A-3.

Two useful Excel analysis tools, Goal Seek and Data Table, were illustrated. Goal Seeks allows you to find the value of an input that causes an output to be equal to a value you specify. A Data Table allows you to vary one (or two) inputs, and automatically calculate the value of an output for each of the input values in the range. We covered data tables where one input was varying.

Several different chart types were used to illustrate model results. These were the XY chart, the Column chart, and the Stacked Column chart. Other useful chart types for presentation of model results are Pie charts, Line charts, and Bar charts. Excel has many other chart types.

The EndCopyright © 2005 John Wiley & Sons, Inc. All

rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United State Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.