Transcript PRODUCTIONS/OPERATIONS MANAGEMENT

Lecture
2
Decision Theory
Chapter 5S
1
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
2
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
3
Payoff Table: An Example
Possible Future Demand
Small
facility
Medium
facility
Large
facility
Low
Moderate
High
$10
$10
$10
7
12
12
-4
2
16
Values represent payoffs (profits)
4
Maximax Solution
Note: choose the
“minimize the
payoff” option if
the numbers in
the previous slide
represent costs
5
Maximin Solution
6
Minimax Regret Solution
7
Decision Making Under Risk - Decision Trees
Payoff 1
Decision Point
Chance Event
Payoff 2
2
Payoff 3
1
B
Payoff 4
2
Payoff 5
Payoff 6
8
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.
9
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
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Decision Tree
d1
1
d2
d3
2
3
4
s1
s2
s3
.4
.2
.4
s1
.4
s2
s3
.2
s1
s2
s3
.4
.4
.2
.4
Payoffs
10,000
15,000
14,000
8,000
18,000
12,000
6,000
16,000
21,000
11
Management Scientist Solutions
EVPI = Expected payoff under certainty –
Expected payoff under risk
12
Lecture
2
Forecasting
Chapter 3
13
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
14
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
15
Elements of a Good Forecast
Timely
Reliable
Accurate
Written
16
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Prepare the forecast
Step 4 Gather and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
17
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
18
Judgmental Forecasts

Executive opinions

Sales force opinions

Consumer surveys

Outside opinion
 Delphi
method

Opinions of managers and staff

Achieves a consensus forecast
19
Time Series Forecasts

Trend - long-term movement in data
 Seasonality - short-term regular variations in
data
 Cycle – wavelike variations of more than one
year’s duration
 Irregular variations - caused by unusual
circumstances
20
Forecast Variations
Figure 3.1
Irregular
variatio
n
Trend
Cycles
90
89
88
Seasonal variations
21
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
22
Example of Moving Average


Sales of gasoline for the past 12 weeks at your local
Chevron (in ‘000 gallons). If the dealer uses a 3period moving average to forecast sales, what is the
forecast for Week 13?
Past Sales
Week
1
2
3
4
5
6
Sales
17
21
19
23
18
16
Week
7
8
9
10
11
12
Sales
20
18
22
20
15
22
23
Management Scientist Solutions
MA(3) for period 4
= (17+21+19)/3 = 19
Forecast error for period 3
= Actual – Forecast =
23 – 19 = 4
24
MA(5) versus MA(3)
Actual
1
2
3
4
5
6
7
8
9
10
11
12
MA(3)
17
21
19
23
18
16
20
18
22
20
15
22
MA(5)
MA Forecast Graph
19
21
20
19
18
18
20
20
19
19.6
19.4
19.2
19
18.8
19.2
19
Actual/MA Forecast sale
values
Week
25
20
Actual
15
MA(3)
10
MA(5)
5
0
1
2 3
4
5
6 7
8
9 10 11 12
Week
25
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.
26
Exponential Smoothing
Ft+1 = 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
0  1
27
Picking a Smoothing Constant
Actual
Demand
50
.4
45
 .1
40
35
1
2
3
4
5
6
7
8
9 10 11 12
Period
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Linear Trend Equation
Suitable for time series data that exhibit a long term linear trend
Ft
Ft = a + bt
a




0 1 2
Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line
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 @ 1.1 units
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Actual vs Forecast
Actual/Forecasted sales
Linear Trend Example
35
30
25
20
Actual
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
32
Management Scientist Solutions
33
Interpretation of Seasonal Indices

Seasonal index for season 2 (Father’s 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
34
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
35
Regression Analysis – An Example
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
$350,000
$300,000
$250,000
$200,000
Series2
$150,000
$100,000
$50,000
$0
10
00
10
08
19
50
17
83
10
50
17
50
14
03
15
00
18
00
30
00
19
30
20
80
16
80
Price
60
0
Home-Size (Square feet)
• Linear model seems reasonable
• A straight line is fitted to a set of sample points
36
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
38
MAD and MSE
MAD
=
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n
39
Measure of Forecast Accuracy

MSE = Mean Squared Error
Week # Actual (A) Forecast(F) Error =E =A-F E(squared)
1
21.6
21.5
0.1
0.01
2
22.9
22.6
0.3
0.09
3
25.5
23.7
1.8
3.24
4
21.9
24.8
-2.9
8.41
5
23.9
25.9
-2
4
6
27.5
27
0.5
0.25
7
31.5
28.1
3.4
11.56
8
29.7
29.2
0.5
0.25
9
28.6
30.3
-1.7
2.89
10
31.4
31.4
0
0
Sum of E(squared)
30.7
40
Forecasting Accuracy Estimates
Example 10 of textbook
Period
1
2
3
4
5
6
7
8
MAD=
MSE=
Actual
217
213
216
210
213
219
216
212
Forecast
215
216
215
214
211
214
217
216
(A-F)
2
-3
1
-4
2
5
-1
-4
-2
|A-F|
2
3
1
4
2
5
1
4
22
(A-F)^2
4
9
1
16
4
25
1
16
76
2.75
9.50
41
Sources of Forecast errors

Model may be inadequate
 Irregular variations
 Incorrect use of forecasting technique
42
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
43
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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