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6/9/2014
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Chapter 7
Forecasting Demand
Aims of the Chapter
After reading this chapter you should be able to do the following:• discuss the role of forecasting in inventory management;
• review different approaches to forecasting;
• use a variety of judgmental forecasting methods;
• define ‘time series’ and appreciate their importance for inventory
control;
• calculate forecast errors;
• describe the characteristics of causal forecasting and use linear
regression;
• describe the characteristics of projective forecasting and use
forecasts based on simple averages, moving averages and
exponential smoothing;
• forecasts demand with seasonality and trend;
• consider the planning needed for forecasts.
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Forecasting supporting management decisions
Use of Forecasts
Forecasting data:
• Demand
• Costs
• Lead time
Inputs to forecasting process:
• Forecasting model
• Values for parameters
• Historical data
• Subjective inputs
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Information needed for forecasts
Use of Forecasts
The forecasts should be:
• accurate – with small errors
• unbiased – so they do not always under- or over-estimate
demand
• responsive to changes in demand
• not affected by the odd unusual figure
• in time for its purpose
• cost-effective
• easy to understand.
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Use of Forecasts
Specific areas need management inputs:
• items that are particularly important or expensive,
• have large or erratic forecasting errors,
• have demand that suddenly changes,
• have a major change of some other type,
• have no recent demand,
• or have recently been introduced to stock.
Methods of Forecasting
There are so many different ways of forecasting, so many different
things to forecast and so many different circumstances, that no
single method of forecasting is always the best.
• time covered in the future
• availability of historical data
• relevance of historical data to the future
• type of product
• variability of demand
• accuracy needed and cost of errors
• benefits expected from the forecasts
• amount of money and time available for the forecast.
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Methods of Forecasting
1. Long-term forecasts look ahead several years – the time needed
to build a new factory or organize new facilities. They usually look at
overall demand which gives enough information to plan budgets and
major facilities over the next few years (strategic decisions).
2. Medium-term forecasts look ahead between three months and a
year – the time needed to replace an old product by a new one or
organize resources (tactical decisions).
3. Short-term forecasts cover the next few weeks – describing the
continuing demand for a product or scheduling operations
(operational decisions).
• The time horizon affects the choice of forecasting method,
because of the availability and relevance of historic data, the time
available to do the forecasting, the cost involved and the effort
considered worthwhile.
Methods of Forecasting
• Qualitative (judgmental) forecasts
1. Personal insight
2. Panel consensus
3. Market surveys
4. Historical analogy
5. Delphi method
• Quantitative forecasts
1. Projective methods look at the pattern of past demand
and extend this into the future.
2. Causal methods look at the factors that affect demand
and use these to forecast.
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Methods of Forecasting
Forecasting methods
Qualitative/ judgmental
Personal insight
Panel consensus
Market surveys
Historical analogy
Delphi method
Quantitative/ statistical
Projective methods
Causal methods
Qualitative Methods of Forecasting
1. Personal insight• uses a single expert who is familiar with the situation to
produce a forecast based on his/her own judgment.
2. Panel consensus• by collecting together several experts and allowing them to
talk freely to each other until they reach a consensus.
3. Market surveys• collect data from a sample of customers, analyze their views,
and then draw inferences about the population at large.– a sample of that accurately represents the population;
– carefully worded, useful, unbiased questions;
– fair and honest answers;
– reliable analyses of the answers;
– valid conclusions drawn from the analyses.
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Qualitative Methods of Forecasting
Qualitative (judgmental) forecasts
4. Historical analogy• uses the demand of a similar item that was introduced in the
past to judge the demand for a new item.
Qualitative Methods of Forecasting
Qualitative (judgmental) forecasts
5. Delphi method• A number of experts are posted a questionnaire;
• Each reply is anonymous to avoid the influences of status;
• The replies are analyzed and summaries are passed back to
the experts.
• Now each expert is asked to reconsider their original reply in
the light of the summarized replies from others.
• They may adjust their answers for a second round of
opinions.
• This process is repeated several times – usually between
three and six.
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Time Series
Time series: series of observations taken at regular intervals of
time.
• constant series, where demand continues at roughly the
same level over time (such as demand for bread or annual
rainfall);
• trend, where demand either rises or falls steadily (such as
demand for 3G phones or the price of petrol);
• seasonality, where demand has a cyclical component (such
as demand for ice cream or electricity).
Time Series
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Time Series
• There are always differences between actual demand and
the underlying pattern.
• These differences form a random noise that is superimposed
on the underlying pattern.
• 𝐴𝑐𝑡𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 = 𝑢𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑝𝑎𝑡𝑡𝑒𝑟𝑛 + 𝑟𝑎𝑛𝑑𝑜𝑚 𝑛𝑜𝑖𝑠𝑒• The noise is a completely random effect that is caused by
many factors, such as varying customer demand, hours
worked, speed of working, weather, rejections at inspections,
time of year, wider economic influences, errors in available
data, delays in updating information, poor communications.
• It is the noise that makes forecasting difficult.
• With a good forecast this error should be relatively small.
Time Series
• There are always differences between actual demand and
the underlying pattern.
• These differences form a random noise that is superimposed
on the underlying pattern.
• 𝐴𝑐𝑡𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 = 𝑢𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑝𝑎𝑡𝑡𝑒𝑟𝑛 + 𝑟𝑎𝑛𝑑𝑜𝑚 𝑛𝑜𝑖𝑠𝑒• The noise is a completely random effect that is caused by
many factors, such as varying customer demand, hours
worked, speed of working, weather, rejections at inspections,
time of year, wider economic influences, errors in available
data, delays in updating information, poor communications.
• It is the noise that makes forecasting difficult.
• 𝐸𝑟𝑟𝑜𝑟 = 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 − 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑
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Worked Example 1:
Errors in Forecasting
Hendra Holidays has compared the actual number of holidays
it booked each week with its short-term forecasts. What are
the errors? What do these errors show?
Week 1 2 3 4 5 6
Demand 101 121 110 98 114 126
Forecast 107 117 112 104 112 120
𝐸𝑟𝑟𝑜𝑟 = 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 − 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑
Week 1 2 3 4 5 6
Demand 101 121 110 98 114 126
Forecast 107 117 112 104 112 120
Error 6 -4 2 6 -2 -6
Abs. Error 6 4 2 6 2 6
Error Sq. 36 16 4 36 4 36
Worked Example 2:
Causal Forecasting
Kurt Steinman’s computer supply business is growing, and
sales over the past 10 months have been as follows.
If Kurt uses linear regression to forecast demand for the next
three months, what results will he get?
Month 0 1 2 3 4 5 6 7 8 9
Demand 3 4 8 10 15 18 20 22 27 28
Month 10 11 12
Forecast 31.80 34.76 37.73
Slope= 2.9636
Intercept= 2.1636
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Worked Example 3:
Causal Forecasting
Over the past 16 weeks Burridge Transport Ltd has recorded
the following number of loads moved for a particular
customer. What can the company learn from these figures?Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Demand 194 187 163 172 160 154 143 156 131 167 143 135 126 95 112 107
y = -5.3309x + 191.88R² = 0.8197
0
50
100
150
200
250
0 2 4 6 8 10 12 14 16 18
Dem
an
d
Week
Worked Example 4:Projective Forecasting (Simple Average)
Use simple averages to forecast demand for period 6 of the
following two time series. How accurate are the forecasts?
What are the forecasts for period 27?
Week 1 2 3 4 5
Series 1 49 50 49 52 50
Series 2 70 33 76 29 42
Week 1 2 3 4 5 Avg.
Series 1 49 50 49 52 50 50
Series 2 70 33 76 29 42 50
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Worked Example 5:Projective Forecasting (Moving Average)
Demand for an item over the past 6 months has been as follows:
The market for this item is unstable, and any data over 3
months old is unreliable. Use a moving average to forecast
demand for the item.
Month 1 2 3 4 5 6 7 8
Demand 203 194 188 206 173 119 209 194
Month 1 2 3 4 5 6 7 8 9
Demand 203 194 188 206 173 119 209 194
Moving Avg. 195 196 189 166 167 174
Worked Example 6:Projective Forecasting (Moving Average)
Demand for an item over the past 11 weeks is as follows. Use
moving averages over different periods to find one week ahead
forecasts.
Month 1 2 3 4 5 6 7 8 9 10 11
Demand 42 33 36 45 54 63 69 72 75 78 98
Month 1 2 3 4 5 6 7 8 9 10 11 12
Demand 42 33 36 45 54 63 69 72 75 78 98
Moving Avg(3) 37.0 38.0 45.0 54.0 62.0 68.0 72.0 75.0 83.7
Moving Avg(4) 39.0 42.0 49.5 57.8 64.5 69.8 73.5 80.8
Moving Avg(6) 45.5 50.0 56.5 63.0 68.5 75.8
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Worked Example 6:Projective Forecasting (Moving Average)
0
20
40
60
80
100
120
0 2 4 6 8 10 12 14
Worked Example 7:Projective Forecasting (Exponential Smoothing)
An item has the following weekly demand. Use exponential
smoothing with α = 0.2 and an initial forecast for week 1 of 102
units to find one period ahead forecasts.
Month 1 2 3 4 5 6 7 8
Demand 107 115 94 89 98 91 101 112
Month 1 2 3 4 5 6 7 8 9
Demand 107 115 94 89 98 91 101 112
Forecast 102.0 103.0 105.4 103.1 100.3 99.8 98.1 98.7 101.3
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Worked Example 8:Projective Forecasting (Exponential Smoothing)
The following time series has a clear step upwards in demand
in month 4. Use an initial forecast of 50 to compare exponential
smoothing forecasts with varying values of α.Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Demand 48 50 150 145 155 150 148 152 150 149 150 161 155 148
Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
α= Demand 48 50 150 145 155 150 148 152 150 149 150 161 155 148
0.1 Forecast 50 49.8 49.8 59.8 68.4 77.0 84.3 90.7 96.8 102.1 106.8 111.1 116.1 120.0 122.8
0.2 Forecast 50 49.6 49.7 69.7 84.8 98.8 109.1 116.9 123.9 129.1 133.1 136.5 141.4 144.1 144.9
0.3 Forecast 50 49.4 49.6 79.7 99.3 116.0 126.2 132.7 138.5 142.0 144.1 145.9 150.4 151.8 150.6
0.4 Forecast 50 49.2 49.5 89.7 111.8 129.1 137.5 141.7 145.8 147.5 148.1 148.9 153.7 154.2 151.7
Worked Example 8:Projective Forecasting (Exponential Smoothing)
0
20
40
60
80
100
120
140
160
180
0 2 4 6 8 10 12 14 16 18
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Worked Example 9:Projective Forecasting (Winter’s Model)
Over the past 12 quarters the demand for an item has been as
follows:
How would you forecast demand for the next five quarters?
Quarter 1 2 3 4 5 6 7 8 9 10 11 12
Demand 602 620 304 396 798 804 602 630 941 896 664 736
Worked Example 9:Projective Forecasting (Winter’s Model)
Quarter Actual Trend and Seasonal Model
t A(t) L(t) T(t) S(t) F(t) Deseasonal
1 602 1.177 511.27
Initializati
on
2 620 1.198 517.68
3 304 0.762 398.96
4 396 0.863 458.91
5 798 1.177 677.73
6 804 1.198 671.32
7 602 0.762 790.04
8 630 758.23 46.78 0.863 730.09
9 941 803.26 46.08 1.176 947.86 Ex-Post
10 896 818.98 33.94 1.177 1017.20 Forecast
11 664 858.46 36.16 0.764 649.91
12 736 882.11 31.15 0.857 771.97
13 1074.24 913.26 31.15 1.176 1074.24 Forecast
14 1111.51 944.41 31.15 1.177 1111.51
15 745.61 975.57 31.15 0.764 745.61
16 862.96 1006.72 31.15 0.857 862.96
17 1220.81 1037.87 31.15 1.176 1220.81
a= 0.3
b= 0.4
g= 0.2
