US Army Logistics University
OPERATIONS RESEARCH SYSTEMS
ANALYSIS TECHNOLOGIES AND
APPLICATIONS COURSE (ORSA TAC)
Course Director: John Zauner
(804) 765-4256, DSN 539
john.zauner@us.army.mil
US Army Logistics University (ALU)
College of Professional & Continuing Education
Department of Systems Engineering (DSE)
Fort Lee, VA
ORSA Courses offered by ALU/CPCE/DSE
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ORSA TAC Course Objectives
…to provide previously trained ORSA
analysts with an exposure to some of
the emerging technologies and
applications of operations research
related to military problem solving
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Why focus on spreadsheet technology?
• Availability
• General knowledge by most analysts
• Greater understanding by decision makers
• Enhanced capability with add-in packages
• Great for quick analysis/small to mid-size
models
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Course Materials
• Course based on material from textbooks Practical
Management Science and Managerial Statistics
(Winston, Albright, Zappe)
– Example based learning
– EXCEL workbooks included
– Covers more than we can cover in a one week class
• Use of Decision Tools Suite software
– @Risk, Stat Tools, PrecisionTree, TopRank plus others
– http://www.palisade.com/decisiontools_suite/default.asp
• Student CD contains:
– All course slides and spreadsheet examples used in class
– StatPro and Solver Table add-in packages plus others
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ORSA TAC Schedule
• Contains daily schedule
• Contains instructor contact information
• Contains subject breakout, textbook reference
and examples
• Contains links to all slides and spreadsheet
examples
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ORSA PROCESS
“Strategy for a successful study”
Define the problem
Develop the analysis plan
Gather / review data
Crunch the numbers
Analyze the results
Prove the answer
Package the results
STUDY
PLANNING
(40%)
ORSA TOOLS
(20%)
STUDY
EXECUTION
(40%)
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Spreadsheet Modeling
Fundamentals
Finding a Breakeven Point
at Great Threads
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Background Information
Breakeven Analysis at Great Threads
• The Great Threads Company sells hand-knit sweaters. They want
to print a product brochure for a direct mail campaign.
• The costs of printing, mailing, and materials are provided. The
average size of a customer order is $40, and the company’s
variable cost per order averages around 80% of the order’s value.
• The company plans to mail 100,000 catalogs. It wants to develop a
spreadsheet model to answer the following questions:
– How does a change in the response rate affect profit? (answer)
– For what response rate does a company break even? (answer)
– If the company estimates a response rate of 3%, should it
proceed with the mailing? (answer)
– How does the presence of uncertainty affect the usefulness of
the model? (answer)
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Basic Modeling Tenants
Breakeven Analysis at Great Threads
• Note the clear layout of the model
– The input cells are outlined and shaded and separated
from the outputs
– Headings clearly define cells (bold, indented)
– Formulas use cell or range name reference (very few
numbers in formulas)
– Appropriate numeric formats
– Range names listed in text boxes to the right
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Creating the Model
Breakeven Analysis at Great Threads
• To create this model, proceed through the
following steps:
– Enter heading and range names
– Enter input values
– Model the responses (enter an estimate in the
Response Rate cell – we’ll use 8%)
– Model the revenues, costs and profits
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Answering the Questions
Breakeven Analysis at Great Threads
• Now that a basic model has been created, we can
answer the questions posed by the company.
• For question 1, we form a data table to show how
profit varies with the response rate. The table is
shown here.
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Creating a Data Table
Breakeven Analysis at Great Threads
• Enter a series of response rates (1% to 10%) in col A,
and “link” them to the profit in cell B18 (=Profit)
• Highlight the entire range (A18:B28) and select the
Data Table option from the What If Analysis Icon
(Data Tools Group on Data Ribbon)
• Put cell $E$4 (ResponseRate) as the column input
cell
• The data table reports the change in profit as the
response rate changes
• Create a scatterplot (XY chart) of the values in the
data table to provide a visual of the results
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Answering the Questions
Breakeven Analysis at Great Threads
• Profit increases in a linear manner as response
rate varies. A 1% increase in the response rate
always increased profit by $7800.
• Profit goes from negative to positive when the
response rate is between 5% and 6%.
• Use GoalSeek to answer Question 2 about the
exact breakeven point
• Goal Seek is useful for solving a single equation
in a single unknown
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Answering the Questions
Breakeven Analysis at Great Threads
• To implement Goal Seek, select Goal Seek from the What If
Analysis Icon (set Profit to 0 by changing the Response Rate)
• If the response rate is 5.77%, Great Threads breaks even
• Question 3 asks if the company should proceed with the
mailing if the response rate is only 3%. The short term view
says “no”, but we may want to go ahead anyways.
– Many customers who respond to direct mail will reorder in the
future. If each of the respondents ordered two more times, the
company would earn (3000)($7.80)(2) = $46,800 more than
appears in the model, and profit would then be positive.
– The moral is to look at the long-term impact of our decisions
(which means a more complex model)
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Answering the Questions
Breakeven Analysis at Great Threads
• Finally, question 4 asks about the impact of
uncertainty in the model (all inputs are not known
with certainty)
• For example, a high degree of uncertainty about
model inputs makes it difficult to talk about the profit
level or the breakeven response rate.
• It makes more sense to talk about the probability that
profit will have a certain value or the probability that
the company will break even.
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Cleaning Input Data
Cleaning Customer Data
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Data Cleaning
Cleaning Customer Data
• Lists data on 1500 customers of a company
• How much of this data set is usable? How much
needs to be cleaned?
• It is the analyst’s responsibility to correct data
problems before doing any serious analysis
(data cleaning)
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Cleaning the Data
Cleaning Customer Data
• All of the problems in this data are typical of real
world data sets.
• In cleaning this data we will look at the following
variables:
– Social Security Number(SSN)
– Birthdate/Age
– Region
– CredCardUser
– Income
– Purchases and AmtSpent
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Finding Duplicate Entries
Cleaning Customer Data
• For SSN, all 1500 customers are distinct people, so all
1500 SSNs should be different.
• One of the simplest ways to check this is to sort on
the SSN column
• To check whether two adjacent SSN are identical, add
formula IF(B5=B4,1,0) in cell J5 and copy down
• Then enter the formula =SUM(J5:J1503) in cell J4
(you should find two duplicates)
• Use Edit/Find menu item (set Look in: to “Values”) to
find the exact records with duplicate SSNs
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Cleaning Up Dates
Cleaning Customer Data
• Sorting on birth date finds that the first 18 customers all
have birthdate 05/17/27
• Excel’s dates are stored internally as integers
• Select the 18 birth dates and use the Format/Cells
menu item with the number option(and zero decimals)
• The dates format to 9999, the “code” many analysts
use for missing values
• If the birth date is important for further analysis, these
18 customers should probably be deleted form the data
set.
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Cleaning Up Dates
Cleaning Customer Data
• Sorting on age shows the first twelve customers with
negative ages (all were born before 1930)
• EXCEL assumes that any two-digit year from 00 to 29
is the 21st century; years from 30 to 99 are the 20th
century
• Fix by selecting the 12 birth dates , select
Edit/Replace, set find what: to /202, set replace with:
to /192 , click on “Replace All”
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Fixing Text Labels
Cleaning Customer Data
• Sort on Region does not seem to work correctly
• After a close look we will find that the top labels in
these cells begin with a space (Fix with Edit/Replace)
• For the CredCard user column (1 means user, 0 is
non-user), taking an average gives a #DIV/0! Error
• The problem is that the numbers were somehow input
or transformed into text labels
• Two ways to convert to numbers:
• Put a 1 in an empty cell (make sure entered as number),
select Edit/Copy, select cells to convert, select Edit/Paste
Special and choose multiply operation (prior to Excel 2002)
• Highlight range, click on Error Indicator (exclamation point in
upper left corner of range), select convert to number
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Examining Numeric Data
Cleaning Customer Data
• Sorting the Income column shows most values from
$20,000 to $160,000
• Some values are much smaller (may have entered
without 000)
• Some values are 9999 (many times a code for a
missing value)
• Sorting by Purchases also shows 9999 for the
records at the bottom for Purchases and Amount
Spent (again probably a missing value code)
• Put a blank row between records where 9999 starts
for Purchases to separate from other records
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Examining Data Relationships
Cleaning Customer Data
• Presumably there is a relationship between Purchases
and Amount Spent
• A scatterplot shows an upward trend with some outliers
at the bottom of the plot
• The outliers could represent the average amount spent
per purchase instead of the total amount spent
• If this is true, sort on AmtSpent and Purchases and
multiply the AmtSpent by the number of purchases for
the outlier values
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Using EXCEL’s AutoFilter
and Advanced Filter
Querying Customer Records
at Hytex
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Background Information
Querying Customer Records at HyTex
• 1000 customers records of HyTex (direct marketing firm)
• Data collected:
–
–
–
–
–
–
–
–
Age: (1 = 30 or younger, 2 = 31 to 55, 3 = 56 and older)
Gender: (1= males, 2 = females)
OwnHome: (1 = customer owns a home, 2 = don’t own home)
Married: (1 = customer currently married, 2 = not married)
Close: (1 = lives near shops that sells similar items, 2 = not close)
Salary: combined annual salary of customer and spouse (if any)
Children: number of children living with customer
History: (“NA” = no dealings with company in prior years, 1 = low
spending customer, 2 = medium-spending, 3 = high-spending)
– Catalogs: Number of catalogs sent to the customer this year
– AmountSpent: Total amount of purchases by customer this year
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Excel’s AutoFilter Tool
• Excel’s autofilter tool performs simple queries on
an existing Excel database easily
• Terms that we will be used:
- Database: a set of related data (each column is a
field, each row is a record)
- Top row contains field names
- No empty rows
- Query: a command that asks for the subset of a
database that satisfies specified conditions
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Using AutoFilter
Querying Customer Records at HyTex
• To use the autofilter tool, make sure the cursor is
anywhere within the database, and select the Filter Icon
(on Data and Home Ribbons)
• Click on the dropdown arrows next to a field name to
view a list of choices
• Choices are available to sort and filter (text or number)
• Click on any value in any fields’ dropdown list to see
only the records where that field equals the selected
value
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Using Autofilter
Querying Customer Records at HyTex
• Records are temporarily hidden (not deleted)
• Setting filter on multiple lists implies “and” condition
• Select “All” from list to remove filter for that field
• Select “Top Ten” to see top/bottom of items or
top/bottom percent
• To see the entire database: select clear option in Sort
and Filter group
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Complex Queries with Autofilter
Querying Customer Records at HyTex
• The “Custom” item allows us to enter up to two
conditions for any field (can be “and” or “or” conditions)
• Choose from a number of types of conditions such as
“greater than some value,” “contains some value,”
“does not equal some value,” and others.
• Use “wildcard” characters ? and * (useful for text data)
- ? stands for any single character
- * stands for a series of characters
• Example: perform a query where Salary must be
between $40,000 and $80,000, History must not be
“NA” and Catalogs can either be 6 or 24
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Performing Analysis on Query Results
Querying Customer Records at HyTex
• Once we obtain the results of a query we might want
to summarize these results in some way.
• If you use functions/add-ins, when you select the
result cells from a query, all hidden rows are included
• The trick is to copy and paste the results of the query
to a new location.
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Excel’s Advanced Filter Tool
• Excel’s advanced filter tool can be used only after
creating a “criteria range”
• The “criteria range” consists of a top row of field
names and one or more rows of conditions.
• To use the advanced filter tool:
- Copy the row of field names to any unused area (this is the
top row of the criteria range)
- Manually enter conditions in the cells just below those field
names
- Conditions in a given row are “and” conditions
- Conditions across rows are treated in an “or” manner
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Advanced Filter Example
Querying Customer Records at HyTex
• First row: all customers who are married and
have salary at least $80,000 and have at least 2
children.
• Second row: all customers who have salary
$100,000 and received at least 12 catalogs.
• Return all records that meet the first row or
second row conditions
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Advanced Filter Example
Querying Customer Records at HyTex
• Once the criteria range is created, we run the query
by using the Data/Filter/Advanced Filter menu item.
• The associated dialog box is completed as follows.
Works like
Autofilter
Entire
database
Include field
names and
all conditions
Can specify
upper left corner
of range
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Another Advanced Filter Example
Querying Customer Records at HyTex
• Suppose we want the customers who are either
(1) male with salary between $40,000 and
$50,000, or (2) female with salary over $70,000
• How should this condition be entered in the
criteria range? It is tempting to enter the label
”>40000,<50000” in a cell under Salary.
However, this doesn’t work.
• One solution is to enter two Salary fields in the
criteria range as shown on the next slide
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Another Example
Querying Customer Records at HyTex
• There is no rule in Excel that every field name must
be included in the criteria range. Only those involved
in the query are required.
• Also the same field name can be included more than
once, evidently to deal with the situation we have
posed.
• The criteria range above will return exactly the
records we seek.
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Importing External
Data from Access
Importing customer orders from a database
for the Fine Shirt Company
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Background Information
Customer Orders for the Fine Shirt Company
• The Fine Shirt Company has a database of historical
customer retail shirt sales information that we want to
analyze
• There are three related tables in this database:
Customers, Orders, and Products
– Customer table (info on seven customers): CustomerNum,
Name, Street, City, State, Zip, Phone
– Products table (info on ten shirt types): ProductNum,
Description, Gender, UnitPrice
– Orders table (info on 2245 orders): OrderNum, CustomerNum,
ProductNum, OrderDate, UnitsOrdered, Discount
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Introduction to Relational Databases
• Excel “databases” are flat files or lists
• They are also called single-table databases, where table is
the usual database terminology for a rectangular range of
data
• Flat files are fine for relatively simple database applications,
but are not powerful enough for more complex applications
• A relational database is a set of tables, where each table is
a rectangular arrangement of fields and records, and the
tables are linked explicitly.
• Microsoft Query (EXCEL add-in) allows import of data from
many database packages with very little work
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Single Table Query Example
Customer Orders for the Fine Shirt Company
• Find all of the records from the Orders Table in the
Shirtorders database that meet the following conditions:
– Order date is during the years 1997 or 1998
– Product number is 3 or 5
– Number of units ordered is at least 100
• Return to Excel all fields in the Orders Table for these
records
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Importing Data with Microsoft Query
Customer Orders for the Fine Shirt Company
• Import is a three step process done in Excel and Query,
not Access
• Step 1: Define a “data source”
– Select Data/Import External Data/New Database Query menu
item, then select “<New Data Source>” from Database tab of
Data Source dialog box
– In the Create New Data Source dialog box, give a name to the
data source, select appropriate driver (Microsoft Access), click
Connect, then Select and choose the database file & click OK a
couple of times to get back to the Data Source dialog box
– Make sure that the data source you defined is highlighted in the
Data Source dialog box, then click OK (should see Add Tables
dialog box)
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Importing Data with Microsoft Query
Customer Orders for the Fine Shirt Company
• Step 2: Specify the data you want
– Select the appropriate table and click Add (click Close when
completed)
– The table should appear in the top part of the window
– Double click on fields you want returned to EXCEL (click on * to
return all fields)
– The data should appear on the bottom part of the window
– Click on the “Show/Hide Criteria” button on the toolbar to view
the criteria section in the middle of the window
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Importing Data with Microsoft Query
Customer Orders for the Fine Shirt Company
• Step 3: Specify criteria and return data to EXCEL
– Entering criteria is similar to the Advanced Filter Tool
– Can type in criteria or use Criteria/Add Criteria menu item
– For Add Criteria dialog box, use pull-downs to select field and
operator, click on Values to select values from records (or can
type in values box)
– If you type anything in, be careful with syntax
– Can select more than one value in value box
– Records in bottom part of window are filtered each time a new
criteria is added
– Select File/Return Data to Microsoft Excel and select location of
data
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Working with Imported Data
Customer Orders for the Fine Shirt Company
• You can now analyze the data using any EXCEL
features
• The imported data are still linked to the query
– With the cursor anywhere in the data, select the Data/Get
External Data/Edit Query menu item
– This takes you back into Microsoft Query, with your criteria
showing
– Any changes in criteria will be reflected in the Excel data
• You can also select File/Save in Microsoft Query to
save the query for later use (select Data/Get External
Data/Run Saved Query)
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Creating a Complex Query
Customer Orders for the Fine Shirt Company
• Find all records that meet the following conditions:
– All orders for at least 80 units
– Order made by the customer “Shirts R Us” (customer
number 3)
– Product is Long sleeve Tunic (product number 6)
– Return the order date and units ordered for these orders.
• The main difference is that we now have to base the
query on all three tables in the database
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Creating a Complex Query
Customer Orders for the Fine Shirt Company
• The trick is to use the links between the tables
• Create a new query by clicking on the data source
created from the previous example
• Inside the Query screen, first add all three tables by
using the Tables/Add Table menu item
• Double click the fields you want to return to EXCEL
• Create the appropriate criteria (fields will be
displayed as table.field)
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Exploring Data with
Pivot Tables
Examining effects on elevator rail
diameters for Otis Elevator
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Background Information
Rail diameters for Otis Elevator
• Spreadsheet contains the diameters (in inches) of
elevator rails produced by Otis Elevator’s two
machines and two operators
• Each diameter corresponds to a particular machine/
operator combination.
• What effects, if any, do the operator and machine
have on elevator rail diameters?
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Pivot Tables
• Pivot tables provide an incredible amount of of
useful information about a data set
• Pivot tables allow us to break the data down into
subpopulations
• Statisticians often refer to the resulting tables as
contingency tables or crosstabs
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Creating a Pivot Table
•
Position the cursor in the data range
•
Select PivotTable from Insert Ribbon
•
Select the data source and type of report (table or
chart/table)
•
Specify the range of the data set (should be set
properly if you placed the cursor in the data range)
•
Drag appropriate fields to the PivotTable Field List on
right side of workbook
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Creating a Pivot Table
•
Click on any of the variable buttons and drag into the
appropriate areas
•
Row: shows field items as row labels
•
Column: shows field items as column labels
•
Report Filter: shows field items one at a time in the table
•
Values: summarizes values/statistics in the body of the
table
•
Double click on variables in data area to set
appropriate statistical calculation
•
Specify the location of the pivot table
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Pivot Table and Chart Output
Rail diameters for Otis Elevator
Average of Diameter Machine
Operator
1
2 Grand Total
1
0.5190
0.5286
0.5231
2
0.5291
0.5412
0.5347
Drop
Page Fields Here
Grand Total
0.5243
0.5358
0.5294
Average of Diameter
0.60
0.55
0.50
0.45
0.40
0.35
Mac hine
0.30
1
2
0.25
0.20
0.15
0.10
0.05
0.00
1
2
Operator
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Additional Pivot Table Options
• Can import data from an external database
• Can drag multiple field to any of the areas
• Can drag fields without going back to the wizard (table
updates automatically)
• Double click on any pivot table entry to see the source
data
• Use pull downs on table or chart to select/deselect
specific field values
• if the original data changes, the pivot table recalculates
automatically (click the exclamation point on the Pivot
Table toolbar to refresh the data)
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Spreadsheet Modeling
and Analysis
Ordering with quantity discounts
at Sam’s Bookstore
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Background Information
Ordering Books With Quantity Discounts
• Sam’s Bookstore needs a model to help it order the
appropriate number of hardback books of any title
• The unit costs for books depends on the quantity ordered
• The demand for books is uncertain (best estimate is a
range)
• Any hardback books not sold before the paperback book
comes out will be sold for $10
• Determine the company’s profit for a book’s sales for a
fixed demand and order quantity, then analyze the
demand uncertainty to choose an order quantity that
maximizes expected profit
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Modeling Process
Ordering Books With Quantity Discounts
• Develop a model that will determine the profit
for any order quantity and any possible demand
• Perform a sensitivity analysis to see how profit
changes as order quantity and demand changes
• Estimate probabilities and determine the
expected profit for different order quantities
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Building the model
Ordering Books With Quantity Discounts
• Use the MIN function with order quantity (Q) & demand
(D) to determine books sold at regular price (cell B15)
• Use the IF function to determine books sold at leftover
price (cell B16): IF(Q > D, Q – D, 0)
• Revenue = price * units sold (cell B17)
• Use VLOOKUP function to determine unit cost:
VLOOKUP(Q,CostLookup,2)*Q (cell B18)
• Profit = Revenue – Cost (cell B19)
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Sensitivity Analysis
Ordering Books With Quantity Discounts
• Develop a two way data table to determine profit as the
demand and order quantity changes
– Create a demand row in row 22 (500 to 4500 in increments of
500)
– Create an order quantity column in column A (500 to 4500 in
increments of 500)
– Link cell A22 to the profit cell (=A19)
– Highlight table and Select Data Table from menu
» Row Input Cell: B12
» Column Input Cell: B9
• Table shows profit for varying levels of demand and order
quantity
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Expected Profit
Ordering Books With Quantity Discounts
• Use probabilities of demand (row 35) to calculate
expected profit for different order quantities
• Use SUMPRODUCT function to calculate expected profit
– First range: profits for order quantity 500 (B23:J23)
– Second range: probabilities (B$35:J$35)
• Select order quantity with largest expected profit
(what does that number represent?)
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