Transcript Facility Location Models

IES 371
Engineering Management
Chapter 13: Forecasting
Week 12
August 24, 2005
Objectives
 Understand and practice on various forecasting method
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Dr. Karndee Prichanont
IES371 1/2005
Strategic Role of Forecasting
 Focus on supply chain management
 Short term role of product demand
 Long term role of new products, processes, and
technologies
 Focus on Total Quality Management
 Satisfy customer demand
 Uninterrupted product flow with no defective items
 Necessary for strategic planning
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Dr. Karndee Prichanont
IES371 1/2005
Demand Forecast Applications
Time Horizon
Application
Short Term
(0–3 months)
Forecast quantity
Individual
products or
services
Decision area
Inventory
management
Final assembly
scheduling
Workforce
scheduling
Master production
scheduling
Time series
Causal
Judgment
Forecasting
technique
Medium Term
(3 months–
2 years)
Long Term
(more than
2 years)
Total sales
Groups or families
of products or
services
Staff planning
Production
planning
Master production
scheduling
Purchasing
Distribution
Total sales
Causal
Judgment
Causal
Judgment
Facility location
Capacity
planning
Process
management
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Dr. Karndee Prichanont
IES371 1/2005
Components for Forecasting Demand



Time
(a) Trend
Demand behavior


Random
movement
Trend
Cycle
Seasonal
Forecasting method
Forecasting process
Time
(b) Cycle
Demand

Demand
Short to mid-range
 Long-range
Depend on each firm
and industry type

Demand
Time frame
Demand

Time
(c) Seasonal pattern
Time
(d) Trend with seasonal pattern
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Dr. Karndee Prichanont
IES371 1/2005
Forecasting Techniques

Judgment method
Qualitative method that translates the opinions of managers,
expert opinions, customer surveys, and sale-force estimate into
quantitative estimates

Causal method
Use of past data on independent variables to derive mathematical
relationship Demand = f(relevant factors)


Linear Regression
Time Series analysis
statistical technique using past data for short-term forecasting
applications

Naïve forecast

Moving average

Weighted moving average
 Exponential smoothing
 Adjusted exponential smoothing
 Linear trend line
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Dr. Karndee Prichanont
IES371 1/2005
Causal Method –
Linear Regression Method


Mathematical relationship
between two or more
variables
b
What causes to behave in a
certain way?
a  y  bx

Linear regression: y = a + bx

Correlation


Strength of the relationship
between dependent and
independent variables
r
 xy  nx y
2
2
x

n
x

 xy   x y
n x   x n y   y 
n
2
2
2
2
Range of [-1.00, 1.00]
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Dr. Karndee Prichanont
IES371 1/2005
Causal Method –
Linear Regression Method
Dependent variable
Y
Deviation,
Estimate of or error
Y from
regression
equation
{
Regression
equation:
Y = a + bX
Actual
value
of Y
Value of X used
to estimate Y
X
Independent variable
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Dr. Karndee Prichanont
IES371 1/2005
Ex 1: Causal Method –
Linear Regression Method
Carpet City wants to develop a means to forecast its carpet sales. The carpet
store manager believes that the store’s sales are directly related to the
number of new housing starts in town. The manager has gathered data
from county records of monthly house construction permits and from store
records on monthly sales. These data are as follows:
Month
Monthly Carpet
Sales (1000s YD)
Montly
Construction
Permits
1
2
3
4
5
6
7
8
9
10
5
10
4
3
8
2
12
11
9
14
21
35
10
12
16
9
41
15
18
26
Required
• Develop a linear regression model
for this data and forecast sales if 30
construction permits for new home
are filed
• Determine the strength of the
casual relationship between
monthly sales and new home
construction using correlation
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Dr. Karndee Prichanont
IES371 1/2005
Time Series MethodSimple Moving Average




Use several demand values in the recent past
Smooth out randomness
Suitable for stable demand
Number of periods in the moving average   smoother
forecast
Sum of last n demands
Ft 1 
n
Dt  Dt 1  ... Dt  n

n
n = Total number of periods in the average
Dt = Demand in period t
Ft+1 = Forecast for period t +1
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Dr. Karndee Prichanont
IES371 1/2005
Ex 2: Time Series MethodSimple Moving Average
The manager forecast weekly demand for his specialty pizza
so that he can order pizza shells weekly. Forecast the
demand for pizza for June 23 to July 14 by using the
simple moving average method with n = 3
Recently demand has been as follows:
Week of
Pizzas
Week of
Pizzas
June 2
June 9
June 16
50
65
52
June 23
June 30
July 7
56
55
60
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Dr. Karndee Prichanont
IES371 1/2005
Time Series Method-
Weighted Moving Average



More closely reflect data fluctuations
Recent data, more weight
Weight: trial-and-error experiment
Ft 1 
t
W D
i
i 1
i
Wi = weight for period i, [0%, 100%]
 Wi = 1.00
Ex 3:
With the demand data in Example 2, forecast the demand
for pizza by using WMA method with n = 3 and weights of
0.50, 0.30, and 0.20, with 0.50 applying to the most
recent demand
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Dr. Karndee Prichanont
IES371 1/2005
Time Series Method-
Exponential Smoothing





Weights the most recent data more strongly
React to recent changes in demand
Seasonal pattern of demand
Widely used in many businesses
Requires minimal data
Ft 1  Dt  1  Ft
Ft+1 = the forecast for the next period
Dt = actual demand in the current period
Ft = the previously determined forecast for
the current period
 = smoothing constant (weighted factor)
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Dr. Karndee Prichanont
IES371 1/2005
Ex 4: Time Series MethodExponential Smoothing
Use the exponential smoothing method to forecast the number of
units for June to January. The initial forecast for May was 105
units;  = 0.2
The monthly demand for units manufactured of a company has
been as follows:
Month
Units
Month
Units
May
June
July
August
100
80
110
115
September
October
November
December
105
110
125
120
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Dr. Karndee Prichanont
IES371 1/2005
Time Series MethodLinear Trend Line


For demand with obvious trend over time
A least squares regression line
y = a + bx




Dependent variable (y) = Forecasted
demand
Independent variable (x) = Time
a = intercept at period 0
b = Slope of the line
b
 xy  nx y
2
2
 x  nx
a  y  bx
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Dr. Karndee Prichanont
IES371 1/2005
Choosing a Time-Series Method
Forecast Error

Forecast error

Cumulative sum of forecast errors (CFE)

Mean squared error (MSE)

Standard deviation

Mean absolute deviation (MAD)

Mean absolute percent error (MAPE)
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Dr. Karndee Prichanont
IES371 1/2005
Tracking Signal
Out of control
+2.0 —
Control limit
+1.5 —
Tracking signal
CFE
Tracking signal =
MAD
+1.0 —
+0.5 —
0—
–0.5 —
–1.0 —
Control limit
–1.5 —
0
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5
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10
15
20
Observation number
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25
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