PRODUCTIONS/OPERATIONS%20MANAGEMENT

1
Lecture
3
Decision Theory Chapter 5S
2
Decision Environments

• Certainty - Environment in which relevant
  parameters have known values
• Risk - Environment in which certain future events
  have probabilistic outcomes
• Uncertainty - Environment in which it is
  impossible to assess the likelihood of various
  future events

3
Decision Making under Uncertainty

• Maximin - Choose the alternative with the best of
  the worst possible payoffs
• Maximax - Choose the alternative with the best
  possible payoff
• Minimax Regret - Choose the alternative that has
  the least of the worst regrets

4
Payoff Table An Example
Possible Future Demand
Low Moderate High
Small facility 10 10 10
Medium facility 7 12 12
Large facility - 4 2 16
Values represent payoffs (profits)
5
Maximax Solution

Note choose the minimize the payoff option if
the numbers in the previous slide represent costs
6
Maximin Solution

7
Minimax Regret Solution

8
Decision Making Under Risk - Decision Trees
9
Decision Making with Probabilities

• Expected Value Approach
• Useful if probabilistic information regarding the
  states of nature is available
• Expected return for each decision is calculated
  by summing the products of the payoff under each
  state of nature and the probability of the
  respective state of nature occurring
• Decision yielding the best expected return is
  chosen.

10
Example Burger Prince

• Burger Prince Restaurant is considering opening a
  new restaurant on Main Street.
• It has three different models, each with a
  different seating capacity.
• Burger Prince estimates that the average number
  of customers per hour will be 80, 100, or 120
  with a probability of 0.4, 0.2, and 0.4
  respectively
• The payoff (profit) table for the three models is
  as follows.
• s1 80 s2 100 s3 120
• Model A 10,000 15,000
  14,000
• Model B 8,000 18,000
  12,000
• Model C 6,000 16,000
  21,000
• Choose the alternative that maximizes expected
  payoff

11
Decision Tree
Payoffs
.4
s1
10,000
.2
s2
2
15,000
s3
.4
d1
14,000
.4
s1
8,000
d2
1
.2
3
s2
18,000
s3
d3
.4
12,000
.4
s1
6,000
4
s2
.2
16,000
s3
.4
21,000
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Management Scientist Solutions

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Lecture
2
Forecasting Chapter 3
14
Forecast

• A statement about the future value of a variable
  of interest such as demand.
• Forecasts affect decisions and activities
  throughout an organization
• Accounting, finance
• Human resources
• Marketing
• Operations
• Product / service design

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Uses of Forecasts
Accounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
Operations Schedules, MRP, workloads
Product/service design New products and services
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Elements of a Good Forecast
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Steps in the Forecasting Process
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Types of Forecasts

• Judgmental - uses subjective inputs
• Time series - uses historical data assuming the
  future will be like the past
• Associative models - uses explanatory variables
  to predict the future

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Judgmental Forecasts

• Executive opinions
• Sales force opinions
• Consumer surveys
• Outside opinion
• Delphi method
• Opinions of managers and staff
• Achieves a consensus forecast

20
Time Series Forecasts

• Trend - long-term movement in data
• Seasonality - short-term regular variations in
  data
• Cycle wavelike variations of more than one
  years duration
• Irregular variations - caused by unusual
  circumstances

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Forecast Variations
Figure 3.1
Irregularvariation
Trend
Cycles
90
89
88
Seasonal variations
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Smoothing/Averaging Methods

• Used in cases in which the time series is fairly
  stable and has no significant trend, seasonal, or
  cyclical effects
• Purpose of averaging - to smooth out the
  irregular components of the time series.
• Four common smoothing/averaging methods are
• Moving averages
• Weighted moving averages
• Exponential smoothing

23
Example of Moving Average

• Sales of gasoline for the past 12 weeks at your
  local Chevron (in 000 gallons). If the dealer
  uses a 3-period moving average to forecast sales,
  what is the forecast for Week 13?

• Past Sales
• Week Sales Week
  Sales
• 1 17
  7 20
• 2 21
  8 18
• 3 19
  9 22
• 4 23
  10 20
• 5 18
  11 15
• 6 16 12 22

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Management Scientist Solutions

MA(3) for period 4 (172119)/3 19
Forecast error for period 3 Actual Forecast
23 19 4
25
MA(5) versus MA(3)
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Exponential Smoothing

• Premise - The most recent observations might have
  the highest predictive value.
• Therefore, we should give more weight to the more
  recent time periods when forecasting.

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Exponential Smoothing
Ft1 Ft ?(At - Ft)

• Weighted averaging method based on previous
  forecast plus a percentage of the forecast error
• A-F is the error term, ? is the feedback

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Picking a Smoothing Constant
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Linear Trend Equation
Suitable for time series data that exhibit a long
term linear trend
Ft
Ft a bt
a

• Ft Forecast for period t
• t Specified number of time periods
• a Value of Ft at t 0
• b Slope of the line

0 1 2 3 4 5 t
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Linear Trend Example
Linear trend equation
F11 20.4 1.1(11) 32.5
Sale increases every time period _at_ 1.1 units
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Actual vs Forecast
Linear Trend Example
35
30
25
20
Actual
Actual/Forecasted sales
15
Forecast
10
5
0
1
2
3
4
5
6
7
8
9
10
Week
F(t) 20.4 1.1t
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Forecasting with Trends and Seasonal Components
An Example

• Business at Terry's Tie Shop can be viewed as
  falling into three distinct seasons (1)
  Christmas (November-December) (2) Father's Day
  (late May - mid-June) and (3) all other times.
• Average weekly sales () during each of the three
  seasons
• during the past four years are known and given
  below.
• Determine a forecast for the average weekly sales
  in year 5 for each of the three seasons.
• Year
• Season 1 2
  3 4
• 1 1856 1995
  2241 2280
• 2 2012 2168
  2306 2408
• 3 985 1072
  1105 1120

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Management Scientist Solutions

34
Interpretation of Seasonal Indices

• Seasonal index for season 2 (Fathers Day)
  1.236
• Means that the sale value of ties during season 2
  is 23.6 higher than the average sale value over
  the year
• Seasonal index for season 3 (all other times)
  0.586
• Means that the sale value of ties during season 3
  is 41.4 lower than the average sale value over
  the year

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Forecast Accuracy

• Error - difference between actual value and
  predicted value
• Mean Absolute Deviation (MAD)
• Average absolute error
• Mean Squared Error (MSE)
• Average of squared error

36
Associative Forecasting

• Predictor variables - used to predict values of
  variable interest
• Regression - technique for fitting a line to a
  set of points
• Least squares line - minimizes sum of squared
  deviations around the line

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Regression Analysis An Example
Home-Size (Square feet) Price
600 72,000
1050 116,300
1800 152,000
922 80,500
1950 141,900
1783 124,000
1008 117,000
1840 165,900
3700 153,500
1092 126,500
1950 122,000
1403 140,000
1680 223,000
1000 99,500
2310 211,900
1300 121,900
1930 169,000
3000 156,000
1362 123,500
1750 136,000
2080 194,900
1344 128,500
2130 302,000
1500 142,000
2400 146,000
2272 180,000
1050 126,500
1610 139,500

• Linear model seems reasonable
• A straight line is fitted to a set of sample
  points

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Regression Results

• Use MS-Excel macro
• Template posted at class website

y 85972.78 35.65x Price 85972.87
35.65(Square footage)
Forecast price of a 2000 square feet house y
85972.78 35.65(2000) 157,272.78
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Forecast Accuracy

• Error - difference between actual value and
  predicted value
• Mean Absolute Deviation (MAD)
• Average absolute error
• Mean Squared Error (MSE)
• Average of squared error

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MAD and MSE
?
?
Actual
forecast
MAD


n
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Measure of Forecast Accuracy

• MSE Mean Squared Error

42
Forecasting Accuracy Estimates Example 10 of
textbook
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Sources of Forecast errors

• Model may be inadequate
• Irregular variations
• Incorrect use of forecasting technique

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Characteristics of Forecasts

• They are usually wrong
• A good forecast is more than a single number
• Aggregate forecasts are more accurate
• The longer the forecast horizon, the less
  accurate the forecast will be
• Forecasts should not be used to the exclusion of
  known information

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Choosing a Forecasting Technique

• No single technique works in every situation
• Two most important factors
• Cost
• Accuracy
• Other factors include the availability of
• Historical data
• Computers
• Time needed to gather and analyze the data
• Forecast horizon