1. Forecasting for Operations
Everette S. Gardner, Jr., Ph.D.
Bauer College of Business
University of Houston
October 30, 2006

2. Forecasting for Operations
Operational systems typically include large numbers of time series. Problems in evaluating forecast accuracy:
Pooled data structures
Pooled averages
Choice of error statistic
Cumulating over lead times
Stability of error measures across origins
Method selection
Product hierarchies
References
Tashman (IJF, 2000)
Fildes (Management Science, 1989; IJF, 1992)

3. Forecasting for Operations
We can bypass many of these problems by judging the impact of forecasting in financial or operational terms:
Customer service
Inventory investment
Purchasing workload
Capacity requirements
Production scheduling efficiency

4. Forecasting for Operations Case Studies:
Customer service
U.S. Navy distribution system
Inventory investment
Manufacturer of snack foods
Purchasing workload
Manufacturer/distributor of water filtration systems
Capacity requirements
Distributor of cleaning supplies
Production scheduling efficiency
Manufacturer of cookware

5. 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

6. U. S. Navy distribution system
Problem
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 about half of the series
Solution
Automatic forecasting with the damped trend

7. Origins of the damped trend
Reference
Gardner & McKenzie, Management Science, 1985
Operational requirement
Automatic forecasting system for military repair and maintenance parts
Theory
Lewandowski, IJF, 1982 (M1-Competition)
Trend extrapolation should become more
conservative as the forecast horizon increases.

8. The damped trend Error = Actual demand – Forecast
Level= Forecast + Weight1(Error)
Trend = (Previous trend) + Weight2(Error)
Forecast for t+1= Level + Trend
Forecast for t+2 = Level + Trend + 2 Trend .

9. Automatic forecasting with the damped trend
Constant-level data
Forecasts emulate simple smoothing
Consistent trend
Forecasts emulate Holt’s linear trend
Erratic trend
Forecasts are damped

10. Automatic forecasting with the damped trend
In constant-level data, the forecasts emulate simple exponential smoothing:

11. Automatic forecasting with the damped trend
In data with a consistent trend and little noise, the forecasts emulate Holt’s linear trend:

12. Automatic forecasting with the damped trend
When the trend is erratic, the forecasts are damped:

13. Automatic forecasting with the damped trend
The damping effect increases with the level of noise in the data:

14. U. S. Navy distribution system
Research design 1
Random sample (5,000 items) selected.
Models tested:
Random walk benchmark
Simple, linear-trend, and damped-trend smoothing
Error measures
Mean absolute percentage error (MAPE)
Geometric root mean squared error (GRMSE)
Results 1
Damped trend was clear winner.
Impact on backorder delay unknown.

15. U. S. Navy distribution system
Research design 2
Error measures were discarded and monthly inventory values were computed:
EOQ
Standard deviation of forecast error
Safety stock
Steady-state estimate of average backorder delay
Results 2
Again, damped trend was clear winner.
Management was not convinced and requested more evidence.

16. U. S. Navy distribution system
Research design 3
6-year simulation of inventory performance
Actual daily demand history used.
Stock levels updated after each transaction.
Reorders placed using actual leadtimes from the past.
Forecasts, EOQs, and safety stocks updated monthly.
Backorder delays summarized monthly
Results 3
Again, damped trend was clear winner.
Results very similar to steady-state predictions.
Backorder delay reduced by 6 days (19%) with no additional inventory investment.

17. Average delay in filling backorders U.S. Navy distribution system

18. Snack-food manufacturer
Company
Manufacturer of 80 snack foods
Food inventories managed by commodity trading rules
No formal decision rules for packaging inventories
Subjective forecasting
Problem
Excess stocks of packaging materials
Difficult to set a target value for inventory investment on the balance sheet

19. Packaging material inventory vs. sales Monthly, 11-oz. corn chips

20. Snack-food manufacturer
Solution
Automatic forecasting with the damped trend
Replenishment by economic order quantity
Safety stocks set to meet target probability of shortage

21. Damped-trend performance 11-oz. corn chips

22. Investment analysis 11-oz. Corn chips

23. Safety stocks vs. shortages 11-oz. Corn chips

24. Safety stocks vs. forecast errors 11-oz. Corn chips

25. Target inventory vs. sales Monthly, 11-oz. corn chips
Actual Inventory
Target inventory
Sales

26. Target inventory analysis
Actual inventory based on subjective decisions
$ million
Target inventory based on the damped trend and EOQ/Safety stocks
$ million
Projected savings
$ million

27. Auto parts distributor
Company
24 distribution centers
350 company-owned stores, 1,600 affiliated stores
Millions of time series
Forecasting system
Trigg & Leach adaptive exponential smoothing:
Parameter = |Smoothed error/Smoothed MAD|
Every demand series treated as multiplicative seasonal:
Actual demand / index = Adjusted demand
Predetermined group seasonal indices used for most series

28. Auto parts distributor
Forecasting system (continued)
For intermittent series, multiplicative seasonal adjustment is infeasible. Company solution:
Add a large constant before seasonal adjustment
Remove the constant afterward
Inventory control system
EOQ
Safety stocks
Based on MAD
Set to meet target probability of shortage

29. Auto parts distributor
Problems
Samples showed that seasonal adjustment inflated the variance of most demand series
Inflated variances led to purchases much larger than true requirements

30. Auto parts distributor: Example of inflated variance

31. Auto parts distributor
Proposals to management
Replace adaptive smoothing with simple smoothing
Replace MAD with RMSE
Forecast intermittent series with intermittent methods
Test series for seasonality
Use additive seasonal adjustment
Actual demand – index = Adjusted demand
Develop tradeoff curves between inventory investment and customer service

32. Auto parts distributor
Instructions from management
Fix seasonal adjustment first
Minimize sample sizes
Minimize implementation programming
Research plan
Stratified random sample of 691 series from four distribution centers
Seasonal identification based on variance reduction
Additive seasonal adjustment

33. Auto parts distributor Seasonal adjustment of continuous data

34. Auto parts distributor Seasonal adjustment of intermittent data

35. Auto parts distributor: Estimated savings

36. Auto parts distributor
Sensitivity analysis
Simple smoothing produced significantly smaller safety stocks than adaptive smoothing
Periodic refitting of the simple smoothing model did not improve results
Replacement of the MAD with the RMSE made little difference in safety stocks
Autocorrelation analysis was no better than the simple variance test for seasonal identification
Croston’s method for intermittent data was no better than simple smoothing

37. Auto parts distributor
Lessons
It is dangerous to ignore seasonality testing in inventory series
It is dangerous to assume that every seasonal time series is multiplicative
Group seasonal indices can perform poorly in noisy data

38. Cookware manufacturer
Number of production set-ups per month
(Exponential smoothing implemented in May)

39. Cookware manufacturer
Production runs by color, before and after exponential smoothing

40. Conclusions Judge forecast accuracy in financial or operational terms
Customer service
Inventory investment on the balance sheet
Purchasing workload
Capacity requirements
Benchmark forecast accuracy with exponential smoothing