Forecasting - 4
Forecasting - 3
Demand Pooling
Ardavan Asef-Vaziri
Based on
Operations management: Stevenson
Chapter 7
Operations Management: Jacobs, Chase, and Aquilano
Demand Forecasting
Supply Chain Management: Chopra and Meindl
in a Supply Chain
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 1
Forecasting - 4
Operations Management
Session 16: Trend and Seasonality
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 2
Forecasting - 4
Previous Lecture
The importance of forecasting?
Forecast
 Forecast is not a single number
 Error measure MAD
 Moving average
 Exponential smoothing
 Tradeoff: stability and responsiveness
 Static Model for trend and Seasonality
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 3
Forecasting - 4
Today’s Lecture
An application of the exponential smoothing
method
 Risk-pooling effect again!
Trend forecast
Seasonal forecast
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 4
Forecasting - 4
Forecasts and Probability Distributions: How many
to stock?
A firm produces Red and Blue T-Shirts
Month/demand
January
February
March
April
May
June
July
August
September
October
Ardavan Asef-Vaziri
6/4/2009
Red Shirts
909.9
616.7
1073.3
1382.9
1359.5
1519.9
344.9
Blue Shirts
1185.0
546.2
1229.5
1248.7
1337.9
1539.6
1300.8
Measures of Effectiveness 5
Forecasting - 4
Forecasts and Probability Distributions ( = 0.3)
Month
T-Shirt Demand
Forecast
January
909.9
February
616.7
909.9
March
1073.3
821.94
April
1382.9
897.348
May
1359.5
1043.014
June
1519.9
1137.96
July
344.9
1252.542
August
929.7
980.2492
September
1328.5
965.0844
674
1074.109
October
November
Ardavan Asef-Vaziri
6/4/2009
954.0764
Measures of Effectiveness 6
Forecasting - 4
Forecasts and Probability Distributions
 Suppose the company stocks 954 T-shirts, the forecasted
number. What is the probability the company will have a
stockout, that is, that there will not be enough T-shirts to satisfy
demand?
 The company does not want to have unsatisfied demand, as that
would be lost revenue. So the company overstocks. Suppose
the company stocks 1,026 units.
 What is the probability that the actual demand will be larger than
1,026?
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 7
Forecasting - 4
There is a Distribution Around the Forecasted Sale
Standard Deviation of Error = 1.25 MAD
 Error is assumed to NORMALLY DISTRIBUTED with
• A MEAN (AVERAGE) = 0
• STANDARD DEVIATION = 1.25* MAD
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 8
Forecasting - 4
Forecasts and Probability Distributions ( = 0.3)
Month
T-Shirt Demand
Forecast
AD
January
909.9
February
616.7
909.9
293.2
March
1073.3
821.94
251.36
April
1382.9
897.348
485.552
May
1359.5
1043.014
316.4864
June
1519.9
1137.96
381.9405
July
344.9
1252.542
907.6417
August
929.7
980.2492
50.54916
September
1328.5
965.0844
363.4156
674
1074.109
400.1091
October
November
Ardavan Asef-Vaziri
954.0764
6/4/2009
Measures of Effectiveness 9
Forecasting - 4
How many to stock
Suppose the company desires that the probability of
not being able to meet demand is 2.5%
P( Nov. demand  amt. stocked)
 P( N(954,1.25  MAD)  amt. stocked)
amt. stocked - 954 

 P N(0,1) 

1.25  MAD 

Look-up on normal table
 0.025
(show using book)
amt. stocked - 954
when
 1.96
1.25  MAD
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 10
Forecasting - 4
How many to stock
Amt. stocked  954
 1.96
1.25  MAD
implies
Amt. stocked  1.96 1.25  MAD  954  1892
Note that MAD=383 in this example.
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 11
Forecasting - 4
The Forecast for a Blue Products ( = 0.3)
January
February
March
April
May
June
July
August
September
October
Ardavan Asef-Vaziri
6/4/2009
1185.0
546.2
1229.5
1248.7
1337.9
1539.6
1300.8
1084.4
1211.8
965.6
1185.0
993.3
1064.2
1119.5
1185.1
1291.4
1294.2
1231.3
1225.4
1147.5
638.7429
236.1592
184.5132
218.4141
354.516
9.349969
209.8464
19.48862
259.8598
236.7656
Measures of Effectiveness 12
Forecasting - 4
Blue Product Inventory Level
The stocking level, of the blue product, for period
11 is:
1148+1.96*(1.25*237)=1728
Recall that:
amt. stocked = forecast + 1.96x1.25xMAD
implies the probability of not satisfying demand is
P( demand > amt. stocked ) = 0.025.
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 13
Forecasting - 4
Total Inventory Level
 The total inventory for Red and Blue is:
1892 + 1728 = 3620
 P( Red demand > # of Red T-shirts stocked ) = 0.025
P( Blue demand > # of Blue T-shirts stocked ) = 0.025
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 14
Forecasting - 4
Aggregate Forecasts
 Can we more accurately forecast the combined demand?
 Suppose we can make Gray Shirt and then dye the T-shirts
either red or blue.
 What is the Demand for Gray Shirts?
 We look at the sum of the demands in the past
 We forecast the demand for the two products combined
 We compute the MAD for the aggregate forecast
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 15
Forecasting - 4
Forecast for the Aggregate Demand
Month/demand
January
February
March
April
May
June
July
August
September
October
November
Red Shirts Blue Shirts Gray Shirts
909.9
1185.0
2094.9
616.7
546.2
1162.9
1073.3
1229.5
2302.8
1382.9
1248.7
2631.6
1359.5
1337.9
2697.5
1519.9
1539.6
3059.5
344.9
1300.8
1645.7
929.7
1084.4
2014.1
1328.5
1211.8
2540.3
674.0
965.6
1639.5
Forecast
AD
2094.9
1815.292
1961.535
2162.565
2323.031
2543.976
2274.489
2196.378
2299.549
2101.549
931.9782
487.4767
670.1002
534.888
736.4826
898.2896
260.3722
343.9045
660.0016
613.722
Inventory of Gray = 2102 + 1.96*1.25*614 = 3603
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 16
Forecasting - 4
Aggregate Demand Forecast Conclusions
By stocking 3603 Gray T-shirts, we ensure
P( T-shirt demand > # stocked ) = 0.025
Otherwise, we needed to stock 1892 blue T-shirts
and 1728 red T-shirts for a combined number of
1892+1728 = 3620 T-shirts to ensure that
P( red T-shirt demand > # red shirts stocked)
= P( blue T-shirt demand > # blue shirts stocked)
= 0.025
3603 < 3620 … we need to stock less T-shirts to
ensure a given stockout probability (2.5% in this
example) when we have an aggregate forecast.
Ardavan Asef-Vaziri
6/4/2009
Measures of Effectiveness 17