OPIM 5641 BUSINESS DECISION MODELING SURESH NAIR, Ph.D.
Department of Operations and Information Management, School of
Business Administration 1
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Business Forecasting 2
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A forecast is an estimate of the future level of some variable.
The variable is most often demand, but also can be others Demand
forecasts Supply forecasts Price forecasts Laws of forecasting
Forecasts are almost always wrong (but still useful) Near term
forecasts more accurate that long term Aggregate forecasts more
accurate that individual forecasts If calculated values can be
used, dont use forecasts Forecast end products, not components
(which can be calculated) 3
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Steps in Forecasting Determine the purpose of the forecast
accuracy, granularity and timeliness needed. Establish a time
horizon Select a forecasting technique appropriate for the needs
and the data available. Obtain, clean and analyze data Make the
forecast Monitor the forecast Forecasting Methods Judgmental
forecasts historical data scarce, not available or irrelevant
(e.g.; demand for a new technology) Causal Models variables other
than time (price, capacity, etc.) on the x-axis Time Series Models
time on the x-axis 4
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Judgmental Forecasts Used when judgment is better than data,
when data does not reflect recent decisions, etc. Consumer Surveys
Based of questionnaires submitted to potential customers Executive
and Sales force Opinions Build-up forecast Individuals familiar
with a particular segment estimate the demand for that segment.
These individual forecasts are aggregated. Panel consensus forecast
Brings a panel of experts together to jointly discuss and develop a
forecast. Delphi method Similar to panels, but experts work
individually and their forecasts are shared anonymously with the
rest of the panel. The effect of strong personalities in the panel
is removed. 5
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Causal Forecasting using Simple Linear Regression The objective
of regression is to use data to predict values. We use values of
the independent variable, x, to predict the values of the dependent
variable, y. For example, we may want to predict recruitment as a
function of advertising for recruitment. The relationship between x
and y may be linear or non-linear. We will focus of linear
relationships. The regression may be simple (one independent
variable, x) or multiple (many independent variables, x1, x2, ).
Excel can be used for both simple or multiple regression. The
equation can be represented by y = a + bx where a is the intercept
on the y-axis, that is, value of y when x=0, b is the slope of the
line, that is, the change in y for a unit change in x. 6
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Download file site.txt and gm.txt from website The regression
is done using a method called the Least Squares method. 7
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The R 2 value is a measure of goodness of fit, called
Co-efficient of determination. The closer it is to 1, the better
the fit. Notice from the chart that the fit is very good. It means
that 90.97% of the variation in sales can be explained by the
variation in size of store. 8
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From the output we see that the equation is Sales = 901.25 +
1.69 SqFt This equation can be used to predict the sales for any
other size store not in the data set. For example, the expected
sales for a store with an area of 6000 square feet would be Sales =
901.25 + 1.69(6000) = $11041.25 The standard error of 936.85 in the
output implies that the sales of a stores with an area of 6000
square feet would be normally distributed with a mean of $11041.25
and a standard deviation of 936.85. (You guessed right, it would be
the same no matter what the square footage was). 9
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Time Series Forecasting A time series is a set of data obtained
at regular periods over time. The objective of time series
forecasting is to use the time series data to forecast future
values The components of a time series are Trend Seasonality
Cyclicality (like seasonality, but over more than an year)
Irregular or random The forecast should incorporate all these
components, if present. If no trend seems to be present, we need to
smooth the series to obtain an overall long term impression. This
is done using moving averages or exponential smoothing. If trend is
present, we need to estimate the trend using least squares
technique. 10
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Technique for Seasonality A seasonal relative could be used The
seasonal relative can be found using the following method Fit a
trend line through the data to get a Trend for each period. Divide
the Actual by Trend for each period in the data to get a
seasonality ratio Find the seasonal relative for each of the
periods in the season by taking the average of the seasonality
ratios in Step 2 for each period in the season. You obtain seasonal
relatives for each period in the season. The seasonal relative can
be used to Seasonalize a forecast extrapolate the time series to
the next 7 periods and multiply by the seasonal relatives
Deseasonalize a forecast Take seasonal data and divide by the
seasonal relative to remove the seasonal component Download the
Seasonality_RPM.xlsx file from the website 11
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Using Pivot tables to advantage Download the
AnnualElectricityGen.xlsx file from the website Use the Pivot Table
wizard in Excel Select the data including the headings Choose
\Insert\Pivot Table 12
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Using Pivot tables to advantage Select the Filter, Column and
Row variables, and the body of the matrix (S value) by dragging
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Using Pivot tables to advantage You may choose to display the
data as percentage of row or column 14
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Breakout Exercise (in teams) Download the Natural Gas.xlsx file
from the website Create a de-seasonalized and seasonalized forecast
for each month of 2014 How would you incorporate the changes
brought about by Fracking technologies production is increasing
dramatically and prices are going down. 15
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Forecast Accuracy The following measures of the error in the
forecasting model may be used Mean Absolute Deviation (MAD) MAD is
the average of the absolute deviations between the observed and the
fitted values. Use ABS(.) in Excel to obtain the absolute value.
Mean Square Error (MSE) MSE is the average of the squared
deviations between the observed and the fitted values. 16
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More on Forecasting If there are variables in your control that
increases variability, try to reduce those variabilities first,
before attempting forecasting. For example, to forecast credit card
remittance processing and billing volume, variability could be
reduced by managing accounts in various billing cycles and leveling
the load. Only then do the forecasting. Forecasting models can also
be used to back into rankings and fix issues that will improve
rankings. Download the US News MBA rankings data from the website.
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Modeling What-ifs Monte Carlo Simulation 18
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SIMULATION A Simulation is an experiment in which we attempt to
understand how some process will behave in reality by imitating its
behavior in an artificial environment that approximates reality as
closely as possible. Simulation is typically used when No formulae
or good solution methods exist because assumptions in existing
formulae/methods are violated. Data does not follow standard
probability distributions Most importantly, to evaluate
alternatives (e.g..., designs, systems, methods of providing
service, etc.) Examples include evaluating overbooking policies for
airplanes, inventory policies in stores, deciding on the number and
location of warehouses/emission stations/fire stations, evaluating
work schedules, maintenance policies, emergency room schedules,
financial portfolios, real estate salesperson planning, etc., etc.
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An Example Suppose demand and lead time for procuring a
particular item is Suppose the beginning inventory of the item is
120, and the reorder point is 36. Suppose it costs $0.30 to carry
one unit of the item in inventory per week, it costs $45 to place
orders and get a new consignment, and the penalty for shortages is
$20/unit. What is the best order quantity? DemandFreq.Lead
TimeFreq. 200.310.4 180.430.6 160.3 20 Life is random Give Chance a
Chance iPod Shuffle
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Setting it up It is fairly simple to evaluate different
alternative order quantities quickly using simulation. Step 1
Compute cumulative frequencies and assign random numbers The trick
for assigning random numbers is easy. Compute the cumulative
frequency, start from 00 to 1 less than the cum frequency. For the
next row, start from the next random number to 1 less than the cum
freq., etc. Step 2 For a particular order quantity, say Q=75,
simulate the process DemandFreq.CumFRNsLTimeFreq.CumFRNs 200.3
00-2910.4 00-39 180.40.730-6930.6140-99 160.3170-99 21
Evaluating Alternatives Step 3 Calculate costs for this value
of Q Holding cost = Ending Inv*0.3 = 620*0.3 = $186 Ordering cost=
Orders*45 = 3*45 = $135 Shortage costs= Shortages*20 = 26*20 = $520
TOTAL$841 Choose another Q and repeat steps 2 and 3 Choose the Q
that minimizes total costs This procedure of simulation is called
Monte Carlo Simulation. If the probabilities were 0.1550.3810.464
How many digit random numbers would you choose? 23
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Another Simulation Example Jack sells insurance. His records on
the number of policies sold per week over a 50 week period are:
Suppose we wanted to simulate the policies Jack sells over the next
50 weeks. 24
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Another Example (contd.) Step 1 Compute Probabilities,
Cumulative Probabilities and assign Random Numbers The trick for
assigning random numbers is easy. Compute the cumulative
probability, start from 00 to 1 less than the cum frequency. For
the next row, start from the next random number to 1 less than the
cum prob., etc. Step 2 Simulate the next 50 orders 25
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#Policies Simulation 26
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#Policies Example (contd.) Suppose 30% of the policies are Life
and 70% are Supplemental, simulate the type of policies for the
next 15 weeks. Suppose 25% of the Life policies are for $100K, 50%
for $250K, and 25% for $500K, simulate the value of the policies
for the next 15 weeks. 27
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Breakout Exercise (in teams) Download the Medicare data, CMS
Beneficiary_2010_data.xlsx from the website Do a simulation for the
# chronic conditions for 1000 beneficiaries. If you wished to build
a hospital for Medicare patients and wanted to figure out the
number of beds needed, what data would you need to collect? Be
specific. Send your file to me with the filename,
Breakout2_TeamNN.xlsx 28
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Simulating Standard Distributions In Excel, use \Data\Data
Analysis and then select Random Number Generation. This tool can
simulate the following distributions: Normal Uniform Exponential
Poisson Discrete The random numbers generated do not change when F9
is pressed (that is, once generated, they stay fixed). Excel
functions can be used to generate some of these and other
distributions. This can be done on the fly and is very handy, as we
will see next. 29
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Standard Distributions (contd.) Random numbers following
certain distributions can be generated to change with every press
of F9. This can be very useful in practice. Generating Normally
distributed random numbers: Suppose you wanted to generate Normal
random numbers with a mean of 50 and standard deviation of 5.
=NORMINV(RAND(),50,5) Generating Uniformly distributed random
numbers: Suppose you wanted to generate sales per day that were
Uniformly distributed between 6 and 12 (inclusive).
=RANDBETWEEN(6,12) 30
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Standard Distributions (contd.) Generating Exponentially
distributed random numbers: Suppose you want to simulate the next
breakdown of a machine that fails exponentially with a mean of 5
hours, then use = 5*LN(RAND()) Exponential distribution can be used
for time between arrivals of events (breakdowns, customers to a
restaurant, customer service calls, cars at a toll plaza, customer
orders, etc.) For number of arrivals of events, use Poisson
distribution (number of breakdowns/day, #customers to a
restaurant/hour, #customer service calls/hour, etc.) Exponential
and Poisson distributions are sister distributions, both require
only one number, the Mean time between arrivals (unlike the Normal
distribution which requires the mean and standard deviation).
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Standard Distributions (contd.) Generating Binomially
distributed random numbers: Use Binomial when you have a yes/no,
response/no response, kind of binary situation =
CRITBINOM(n,p,rand()) Where n is the number of trials, and p is the
probability of success 32
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Standard Distributions (contd.) Generating Poisson distributed
random numbers: You need the average for the Poisson distribution.
Use Random Number Generator under \Data\Data Analysis Generating
Discrete distributed random numbers: Use Random Number Generator
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Jazz Festival CD Production Sally Ward wants to press CDs
immediately after the Friday performance of the Festival in
Cambridge, and sell CDs on Saturday and Sunday performances. Costs
for manufacture of CDs and revenues are as follows: Fixed
costs$15,000 Unit manufacturing costs$4.50 Revenue/unit sold$15.00
Sales depend on attendance on Friday, Saturday and Sunday. From
past years she obtains the following equation for attendance
Att(Sat+Sun)= 36,578+ 0.7091 Att(Friday)(1) Which has a residual
error of 5952 (more on this later). She figures 4-12% of people who
attend the Saturday and Sunday performances will make CD purchases.
The attendance of this Friday was 21,500. How many CDs should she
press that night for sale on Saturday and Sunday? Solution:
Plugging 21,500 into (1) we get an expected attendance on Sat and
Sun of 51,823. Therefore the attendance is going to follow a Normal
distribution with mean of 51,823 and standard deviation of 5952
(the residual error stated above). 34
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Breakout Exercise (in teams) A soon-to-graduate MSBAPM student
is considering starting her own analytic consulting business. In
assessing the market, she finds that she can respond to 10 Requests
for Proposals (RFPs) every month. The chance of her getting
approved depends on the hourly pricing she uses, which she
estimates below. She figures the probability of approval follows a
binomial distribution (meaning when she submits 10 RFPs and the
chance of approval is 50%, she will not always get 5 projects
approved, it could be 3,4,5,6,). Being an entrepreneur, she is
willing to work 240 hours a month, and any extra hours she will
farm out to a student contractor at $25/hour. Suppose the hours per
project follows a Poisson distribution with a mean of 50 hours.
(Note: No need to simulate each project separately, assume all
projects in a month have same duration.) Determine what her pricing
should be to maximize her annual earnings. Send your file to me
with the filename, Breakout3_TeamNN.xlsx 35
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Critical Thinking Simulation does not find you the optimal
solution right away, but allows you to evaluate alternatives and
pick the best one. The number of iterations needed should be enough
to stabilize your results. If your result bounces around, you need
more iterations. There is software available for Monte Carlo
simulation, such as @Risk and Crystal Ball. These are easy to use,
but Excel works perfectly fine as well. Can you simulate continuous
time processes using Monte Carlo simulation? Like the inventory
simulation, entities (parts, orders) travel through the process in
time. This is difficult to do using MC techniques, which are better
for discrete time, static simulations. There are better software
available for process simulation, such as Arena. Using simulation
software does not excuse you from modeling correctly. They only
help you avoid the chore of keeping track of the accounting for
various events happening simultaneously. 36
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Business Optimization Modeling 37
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Prof. Suresh Nair 38 Business Optimization In most business
situations, managers have to achieve objectives while working
within several resource constraints. For example, maximizing sales
within an advertising budget, improving production with existing
capacity, reducing costs while maintaining service metrics, etc.
Mathematical modeling can help in such situations. Linear
Programming (LP) is the most important of these techniques. It had
its origins during WW2 as a means of improving the effectiveness of
men and materiel in the war effort. It is used in a wide array of
applications, such as Determining the optimal product mix,
transportation plans, production schedules, advertising and media
planning, investment decisions, routing of trucks, location siting,
assignment of people to tasks, etc. We will learn about how LP
helps decision making by considering several of these applications.
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LINEAR PROGRAMMING Example: (Maximization) A firm makes 2 kinds
of TV sets, A&B. The profit from A is $300, and the profit from
B is $250. The limitations are Labor: It takes 2 hours to assemble
A, and 1 hour to assemble B. There are only 40 labor hours in a
day. Machine: It takes 1 hour of machine time for A and 3 hours for
B. There are only 45 machine hours in a day. Marketing: They cannot
sell more than 12 units of A per day. How many of A&B should be
produced each day? 39
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Mathematical model Suppose X1 = The number of units of A to be
produced X2 = The number of units of B to be produced Then the
mathematical model can be stated as: Maximize Profits:300X1 +
250X2Objective Function Subject to the following constraints
Labor2X1+1X2
