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Title: 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
12
Management Scientist Solutions

13
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

15
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
16
Elements of a Good Forecast
17
Steps in the Forecasting Process
18
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

19
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

21
Forecast Variations
Figure 3.1
Irregularvariation
Trend
Cycles
90
89
88
Seasonal variations
22
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

24
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)
26
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.

27
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

28
Picking a Smoothing Constant
29
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
30
Linear Trend Example
Linear trend equation
F11 20.4 1.1(11) 32.5
Sale increases every time period _at_ 1.1 units
31
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
32
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

33
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

35
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

37
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

38
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
39
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

40
MAD and MSE
?
?
Actual
forecast
MAD


n
41
Measure of Forecast Accuracy
  • MSE Mean Squared Error

42
Forecasting Accuracy Estimates Example 10 of
textbook
43
Sources of Forecast errors
  • Model may be inadequate
  • Irregular variations
  • Incorrect use of forecasting technique

44
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

45
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
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