Forecasting for Operations
Dr. Everette S. Gardner, Jr.
1
Forecasting for operations
 Why we should forecast with models
 The importance of forecasting
 Exponential smoothing in a nutshell
 Case studies
1. Customer service: U.S. Navy distribution system
2. Inventory investment: Mfg. of snack foods
3. Inventory investment: Auto parts distributor
4. Purchasing workload: Mfg. of water filtration systems
 Recommendations: How to improve forecast
accuracy
Paper folding forecast
A sheet of notebook paper is 1/100 of
an inch thick.
I fold the paper 40 times.
How thick will it be after 40 folds?
Fold
Start
Inches
0.01
Miles
1
0.02
5
0.32
10
10.24
20
10,485.76
0.17
25
335,544.32
5.30
30
10,737,418.24
169.47
35
343,597,383.68
5,422.94
40
10,995,116,277.76
173,534.03
The Importance of Forecasting

Forecasts determine:




Master schedules
Economic order quantities
Safety stocks
JIT requirements to both internal and external
suppliers
The Importance of Forecasting (cont.)

Better forecast accuracy always cuts inventory
investment. Example:



Forecast accuracy is measured by the standard
deviation of the forecast error
Safety stocks are usually set at 3 times the
standard deviation
If the standard deviation is cut by $1, safety stocks
are cut by $3
Exponential smoothing methods

Forecasts are based on weighted moving
averages of

Level
 Trend
 Seasonality

Averages give more weight to recent data
Origins of exponential smoothing
 Simple exponential smoothing –
The thermostat model


Error = Actual data – forecast
New forecast = Old Forecast + (Weight x Error)
 Invented by Navy operations analyst
Robert G. Brown in 1944
 First application: Using sonar data to
forecast the tracks of Japanese submarines
Exponential smoothing at work
“A depth charge has a
magnificent laxative
effect on a submariner.”
Lt. Sheldon H. Kinney,
Commander,
USS Bronstein (DE 189)
Forecast profiles from exponential smoothing
Nonseasonal
Constant
Level
Linear
Trend
Exponential
Trend
Damped
Trend
Additive
Seasonality
Multiplicative
Seasonality
Automatic Forecasting with the damped trend
In constant-level data, the forecasts emulate simple
exponential smoothing:
36
35
34
33
32
31
30
29
28
27
26
Automatic Forecasting with the damped trend
In data with consistent growth and little noise, the
forecasts usually follow a linear trend:
60
55
50
45
40
35
30
25
20
Automatic Forecasting with the damped trend
When the trend is erratic, the forecasts are damped:
50
45
40
35
30
25
20
Saturation level
Automatic Forecasting with the damped trend
The damping effect increases with noise in the data:
50
45
40
35
30
25
20
Saturation level
Case 1: U.S. Navy distribution system
 Scope
 50,000 line items stocked at 11 supply centers
 240,000 demand series
 $425 million inventory investment
 Decision Rules
 Simple exponential smoothing
 Replenishment by economic order quantity
 Safety stocks set to minimize backorder delay time
U.S. Navy distribution system (cont.)
 Problems
 Customer pressure to reduce backorder delay
 No additional inventory budget available
 Characteristics of demand series
 90% nonseasonal
 Frequent outliers and jump shifts in level
 Trends, usually erratic, in most series
 Solution
 Automatic forecasting with the damped trend
U.S. Navy distribution system (cont.)
 Research design 1
 Random sample (5,000 items) selected
 Models tested



Random walk benchmark
Simple, linear-trend, and damped-trend smoothing
Error measure

Mean absolute percentage error (MAPE)
 Results 1
 Damped trend gave the best MAPE
 Impact of backorder delay unknown
U.S. Navy distribution system (cont.)
 Research design 2
 The mean absolute percentage error was discarded
 Monthly inventory values were computed:




EOQ
Standard deviation of forecast error
Safety stock
Average backorder delay
 Results 2
 Damped trend gave the best backorder delay
 Management was not convinced
U.S. Navy distribution system (cont.)
 Research design 3
6-year simulation of inventory performance, using
actual daily demand and lead time data
 Stock levels updated after each transaction
 Forecasts updated monthly
 Results 3
 Again, damped trend was the clear winner
 Results very similar to steady-state predictions
 Backorder delay reduced by 6 days (19%) with no
additional inventory investment

Average delay in filling backorders
U.S. Navy distribution system
50
Random walk
Backorder days
45
Linear trend
40
35
Simple smoothing
30
Damped trend
25
370
380
390
400
410
Inventory investment (millions)
420
430
Case 2: Snack-food manufacturer
 Scope
 82 snack foods
 Food stocks managed by commodity traders
 Packaging materials managed with subjective
forecasts and inventory levels
 Problems
 Excess stocks of packaging materials
 Impossible to predict inventory on the balance sheet
11-Oz. corn chips
Monthly packaging inventory and usage
$2,500,000
$2,000,000
Actual Inventory
from subjective
forecasts
$1,500,000
$1,000,000
$500,000
$0
Month
Monthly Usage
Snack-food manufacturer (cont.)
 Solution
 Automatic forecasting with the damped trend
 Replenishment by economic order quantity
 Safety stocks set to meet target probability of
shortage
Damped-trend performance
11-oz. corn chips
$500,000
Outlier
$450,000
$400,000
$350,000
$300,000
$250,000
$200,000
Actual
Forecast
Investment analysis: 11-oz. corn chips
Forecast annual usage
Economic order quantity
Standard deviation of forecast errors
$4,138,770
$318,367
$34,140
Nbr. shortages
per 1,000
Probability Safety
order cycles of shortage stock
100.0000
0.1000
$43,758
50.0000
0.0500
$56,167
1.0000
0.0010
$105,510
0.0100
0.0000
$145,601
0.0001
0.0000
$177,496
Order
quantity
$318,367
$318,367
$318,367
$318,367
$318,367
Maximum
investment
$362,125
$374,534
$423,877
$463,968
$495,863
Safety stocks vs. shortages
11-oz. corn chips
$200,000
$180,000
Target
Safety stock
$160,000
$140,000
$120,000
$100,000
$80,000
$60,000
$40,000
$20,000
$0
0
10
20
30
40
50
60
70
Shortages per 1,000 order cycles
80
90
100
Safety stocks vs. forecast errors
11-oz. corn chips
$200,000
Safety stock
$150,000
$100,000
$50,000
$0
($50,000)
($100,000)
($150,000)
($200,000)
Forecast errors
11-Oz. corn chips
Target vs. actual packaging inventory
$2,500,000
$2,000,000
Actual Inventory
from subjective
Actual Inventory
forecasts
from subjective
forecasts
$1,500,000
$1,000,000
$500,000
$0
Target maximum
inventory based on
damped trend
Month
Monthly Usage
How to forecast regional demand
 Forecast total units with the damped trend
 Forecast regional percentages with simple
exponential smoothing
Damped-trend performance
11-oz. corn chips
$500,000
Outlier
$450,000
$400,000
$350,000
$300,000
$250,000
$200,000
Actual
Forecast
Regional sales percentages: Corn chips
50%
40%
30%
East
South
North
20%
West
10%
0%
Mar
Jun
Sep
Dec
Mar
Jun
Sep
Dec
Case 3: Auto parts distributor
 Scope




24 distribution centers
350 company-owned stores, 1,600 affiliated stores
Millions of time series
Independent marketing, finance, and operations forecasts
 Inventory system

Standard EOQ/safety stock
 Operations forecasting system


Multiplicative seasonal adjustment for all time series
Simple exponential smoothing of seasonally-adjusted data
Forecast profiles from exponential smoothing
Nonseasonal
Constant
Level
Linear
Trend
Exponential
Trend
Damped
Trend
Additive
Seasonality
Multiplicative
Seasonality
Seasonal adjustment procedures
 Multiplicative
 Range of seasonal fluctuation grows with the data
 Seasonal index is a ratio
 Seasonally adjusted data = Actual sales / Index
 Additive
 Range of seasonal fluctuation is constant
 Seasonal index is stated in units
 Seasonally adjusted data = Actual sales – index
Auto parts distributor (cont.)
 Multiplicative seasonality is infeasible for data with
zeroes
 Company solution for data with zeroes


Add a large constant to each month’s sales before
seasonal adjustment
Subtract the constant afterward
Auto parts distributor (cont.)
 Effects of company seasonal adjustment
procedure



Many non-seasonal time series were adjusted
Variance of seasonally-adjusted data was almost
always greater than original data
Inflated variance led to



Excess safety stocks
Purchases much larger than true requirements
Frequent subjective adjustments of forecasts
Auto parts distributor
Example of inflated variance
80
70
60
50
40
30
20
10
0
Original data
Company seas. adjustment
Auto parts distributor (cont.)
 Proposals to Management
 Test for seasonality before adjustment
 Use additive seasonal adjustment, which works
regardless of zeroes in the data:
Actual data – index = Adjusted data

Develop tradeoff curves between inventory investment
and customer service
Auto parts distributor
Seasonal adjustment comparisons: no zeroes
80
70
60
50
40
30
20
10
0
Original data
Company seas. adjustment
Additive seas. adjustment
Auto parts distributor
Seasonal adjustment comparisons: With zeroes
180
160
140
120
100
80
60
40
20
0
Original data
Company seas. adjustment
Additive seas. adjustment
Auto parts distributor:
Estimated savings
Inventory
Florida
Fast-movers
Temperature control
Minnesota
Fast-movers
Temperature control
Missouri
Fast-movers
Temperature control
California
Fast-movers
Temperature control
Total percentage
Total dollars (millions)
Safety stock
reduction
95% confidence limits
lower
upper
16%
22%
14%
16%
18%
28%
18%
43%
15%
33%
20%
52%
17%
19%
15%
11%
19%
27%
19%
20%
16%
13%
21%
27%
19%
$5.1
17%
$4.7
21%
$5.4
Case 4: Water filtration systems company
 Scope
Annual sales of $15 million
 Inventory of $5.8 million, with 24,000 stock records
 Inventory system
 Reorder monthly to maintain 3 months of stock
 Numerous subjective adjustments

 Forecasting system



6-month moving average
No update to average if demand = 0
Numerous subjective adjustments
Problems
 Purchasing and receiving workload

70,000 orders per year
 Forecasting

Total forecasts on the stock records = $28 million

Annual sales = $15 million
 Frequent stockouts due to forecast errors
Solutions
 Develop a decision rule for what to stock
 Forecast demand for all items with the
damped trend
 Use the forecasts to do an ABC classification
 Replace the monthly ordering policy with a
hybrid inventory control system:



Class A
Class B
Class C
JIT
EOQ/safety stock
Annual buys
What to stock?

Cost to stock
Average inventory balance x holding rate +
Number of stock orders x transportation cost

Cost to not stock
Number of customer orders x drop-ship transportation cost
Note: Transportation costs for not stocking may be both
in-and out bound, depending on whether we choose to
drop-ship from the vendor.
Water filtration company:
Inventory status
2,200 obsolete
9%
7,526 with no hits
in 12 months
33%
6,336 active items
27%
2,928 substitute
items
13%
4,202 with
inadequate
demand to stock
18%
ABC classification based on
damped-trend forecasts
Class
Sales forecast
System
Items
Dollars
A
> $36,000
JIT
3%
75%
EOQ
49%
18%
Annual buy
48%
7%
B
C
$600 - $35,999
< $600
The hybrid inventory control system
Inventory
Class
Production
Schedule
Lead-time
Behavior
JIT
A, B
Level
Certain
MRP
A, B
Variable
Reliable
EOQ / Safety stock
A, B
Variable
Variable
C
Any
Any
Control System
Annual buy
Annual purchasing workload
Total savings = 58,000 orders (76%)
40,000
Monthly ordering
ABC system
35,000
30,000
25,000
EOQ
20,000
EOQ
15,000
JIT
Annual
buys
10,000
JIT
5,000
0
A
B
C
Inventory investment
Total savings = $591,000 (15%)
Monthly ordering
ABC system
3,000,000
2,500,000
JIT
2,000,000
EOQ
1,500,000
EOQ
1,000,000
Annual
buys
JIT
500,000
0
A
B
C
Conclusions
 Test all demand series for seasonality
 For series that pass the test, compare additive
and multiplicative seasonal adjustment
 Forecast at the highest possible level of
aggregation
 For total units, forecast with the damped trend
model
Conclusions (cont.)
 Break down total forecasts with simple smoothing
applied to category percentages



Regions
Pack sizes
Colors
 Benchmark the forecasts with a random walk
 Get operations and marketing together and
produce one corporate forecast
Conclusions (cont.)
 Judge forecast accuracy in financial and
operational terms

Customer service measures






Backorder delay time
Percent of time in stock
Probability of stockout
Dollars backordered
Inventory investment on the balance sheet
Purchasing workload or production setups
www.bauer.uh.edu/gardner