Forecasting/MAD/Exponential Smoothing problem solving homework (Operations Management)
MDNAQ
w03_forcasting.pptxWeek 3: Demand Forecasting
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Outline
Forecasting
Types of forecasts
Approaches to forecasts
What is Forecasting?
Process of predicting a future event
Forecasting is an underlying basis of many business decisions
Production
Inventory
Personnel
Facilities
Sales will be $200 Million!
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9
Common Forecasting Examples
Weather forecast (for Ships/fishermen)
Stock market forecast (stock mkt. players)
Forecast of economic growth
Sales/demand forecast
Forecast getting married next session
Short-range forecast
Up to 1 year, generally less than 3 months
Purchasing, job scheduling, workforce levels, job assignments, production levels
Medium-range forecast
3 months to 3 years
Sales and production planning, budgeting
Long-range forecast
3+ years
New product planning, facility location, research and development
Forecasting Time Horizons
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Seven Steps in Forecasting
Determine the use of the forecast
Select the items to be forecasted
Determine the time horizon of the forecast
Select the forecasting model(s)
Gather the data
Make the forecast
Validate and implement results
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Forecasting Approaches
Used when situation is ‘stable’ & historical data exist
Existing products
Current technology
Involves mathematical techniques
e.g., forecasting sales of color televisions
2.Quantitative Methods
Used when situation is vague &
little data exist for new products
or new technology.
Involves intuition, experience. e.g., forecasting sales on Internet
1.Qualitative Methods
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1.Overview of Qualitative Methods
Delphi method: Jury of executive opinion- Pool opinions of high-level experts
Market research: estimates from individual salespersons
Consumer Market Survey
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2. Overview of Quantitative Approaches
Naive approach
Moving averages: Simple moving average, weighted moving average
Exponential smoothing
Trend projection
Linear regression
Time-series Models
Causal models
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Trend
Seasonal
Cyclical
Random
Time Series Components
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Components of Demand
Demand for product or service
| | | |
1 2 3 4
Year
Average demand over four years
Seasonal peaks
Trend component
Actual demand
Random variation
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1. Naive Approach
Assumes demand in next period is the same as demand in most recent period
e.g., If May sales were 48 units, then June sales will be 48 units
Sometimes cost effective and efficient- starting point of many forecasting technique
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S MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing
Provides overall impression of data over time
2(i). Simple Moving Average (SMA)
Moving average =
∑ demand in previous n periods
n
Ft = Forecast for the coming period
N = Number of periods to be averaged
A t-1 = Actual occurrence in the past period for up to “n” periods
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January 10
February 12
March 13
April 16
May 19
June 23
July 26
Actual 3-Month
Month Shed Sales Moving Average
(12 + 13 + 16)/3 = 13 2/3
(13 + 16 + 19)/3 = 16
(16 + 19 + 23)/3 = 19 1/3
Moving Average Example
10
12
13
(10 + 12 + 13)/3 = 11 2/3
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Simple Moving Average Problem (1)
Question: What are the 3-week and 6-week moving average forecasts for demand?
Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts
Used when trend is present
Older data usually less important
Weights based on experience and intuition
2(ii). Weighted Moving Average
Weighted moving average
=
∑ (weight for period n) x (demand in period n)
∑ weights
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Weighted Moving Average
Weights Applied Period
3 Last month
2 Two months ago
1 Three months ago
6 Sum of weights
January 10
February 12
March 13
April 16
Actual 3-Month Weighted
Month Shed Sales Moving Average
10
12
13
[(3 x 13) + (2 x 12) + (10)]/6 = 121/6
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Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant ()
Ranges from 0 to 1
Subjectively chosen
a = Smoothing constant
Involves little record keeping of past data
3. Exponential Smoothing
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Exponential Smoothing
New forecast = last period’s forecast
+ a (last period’s actual demand
– last period’s forecast)
Ft = Ft – 1 + a(At – 1 - Ft – 1)
where Ft = forecast for period t
Ft – 1 = previous forecast
a = smoothing (or weighting) constant (0 a 1)
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Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
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Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = 142 + .2(153 – 142)
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Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = 142 + .2(153 – 142)
= 142 + 2.2
= 144.2 ≈ 144 cars
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Exponential Smoothing Problem (2) Data
Question: What are the exponential smoothing forecasts for periods 2-5 using =0.5?
Assume F1=D1
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Exponential Smoothing Problem (2) Solution
F2=820+(0.5)(820-820)=820
F3=820+(0.5)(775-820)=797.75
Choosing , forecast error
The objective is to obtain the most accurate forecast no matter the technique
We generally do this by selecting the model that gives us the lowest forecast error
Forecast error = Actual demand - Forecast value
= At - Ft
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Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |actual - forecast|
n
Mean Squared Error (MSE)
MSE =
∑ (forecast errors)2
n
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Example
| Time | Actual | Forecasted with | Absolute Error | Forecasted with | Absolute Error |
| 2001 | 168 | 175.5 | 7.5 | 177.5 | 9.5 |
| 2002 | 159 | 174.75 | 15.75 | 172.5 | 13.5 |
| 2003 | 175 | 173.18 | 1.82 | 165.87 | 9.13 |
| 2004 | 190 | 173.36 | 16.64 | 173.43 | 16.57 |
| MAD | (41.71/4) =10.42 | (48.7/4) =12.17 |
a =0.1
a =.5
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Seasonal Variations In Data
The multiplicative seasonal model can adjust trend data for seasonal variations in demand
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Forecasting in the Service Sector
Presents unusual challenges
Special need for short term records
Needs differ greatly as function of industry and product
Holidays and other calendar events
Unusual events
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Fast Food Restaurant Forecast
20% –
15% –
10% –
5% –
11-12 1-2 3-4 5-6 7-8 9-10
12-1 2-3 4-5 6-7 8-9 10-11
(Lunchtime)
(Dinnertime)
Hour of day
Percentage of sales
Figure 4.12
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Tutorial
2/7/2016
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Question 1
1
2
3
4
5
6
7
8
9
10
11
12
487
602
551
587
509
457
349
386
490
507
516
573
Month
demand
Month
Demand
13
14
15
16
17
18
19
20
21
22
23
24
528
622
608
592
536
504
461
391
437
503
562
570
Month
25
26
27
28
29
30
31
32
33
34
35
36
Demand
517
595
619
602
545
486
431
416
444
492
538
575
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Questions:
Computer 3-months moving average of this demand. Does this
series still show seasonal variation.
b. Compute 12-months moving average of this demand.
c. Plot the original data and two moving average and interpret the
result.
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2. Practice moving average forecast
Q2. Compute the 3-period and 5 –period moving average for the
following data
Week
1
2
3
4
5
6
7
8
9
Actual sales
110
102
108
121
112
105
114
106
115
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Week
1
2
3
4
5
6
7
8
9
Actual sales
110
102
108
121
112
105
114
106
115
Q3.Compute 4-period weighted moving average and find out the sales
for the week 10.
Weights
period-1 0.1
period-2 0.2
period-3 0.3
period-4 0.4
3. Practice weighted moving average forecast
n
A
+
...
+
A
+
A
+
A
=
F
n
-
t
3
-
t
2
-
t
1
-
t
t
n
A
+
...
+
A
+
A
+
A
=
F
n
-
t
3
-
t
2
-
t
1
-
t
t
Week
Demand
1
650
2
678
3
720
4
785
5
859
6
920
7
850
8
758
9
892
10
920
11
789
12
844
Sheet: Sheet1
Week
Demand
WeekDemand
1820
2775
3680
4655
5
Week
Demand
0.5
1
820
820.00
2
775
820.00
3
680
797.50
4
655
738.75
5
696.88
