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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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*$E6(copied to B18:D24)
B25: =SUM(B18:B24)(copied right)
B27: =MAX(B25:D25)
B28: =INDEX(B17:D17,MATCH(B27,B25:D25,0))
A17: =A5
SUMPRODUCT Function SUMPRODUCT function a handy way to
computed weighted sums, such as in this example.
=SUMPRODUCT (range1, range2) Range1 and range2 must be the same size. SUMPRODUCT multiplies corresponding elements of
range1 and range2, and then sums these products. Example: =SUMPRODUCT(A1:A3,B1:B3) is equivalent
to =A1*B1 + A2*B2 + A3*B3. However, with large ranges, SUMPRODUCT is much
easier and less error-prone!
Example 2 with SUMPRODUCT
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Example A.2 (Same as Example 9.3 in Textbook)Factor Rating for Antonio's Italian Restaurant
Factor Location 1 Location 2 Location 3Factor Weight
Appearance 5 3 2 20Ease of expansion 4 4 2 10Proximity to market 2 3 5 20Customer parking 5 3 3 15Access 5 2 3 15Competition 2 4 5 10Labor supply 3 3 4 10
Total 100
Compute Overall Scores for Each Location
Location 1 Location 2 Location 3
Overall Score 380 305 340
Best Total Score 380Best Location Location 1
Factor Scores (1-5 scale)
E13: =SUM(E6:E12)
B17: =SUMPRODUCT($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.
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