Forecasting for Operations

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 OperationsCase 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 forecastingwith 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 forecastingwith the damped trend In constant-level data, the forecasts emulate simple exponential smoothing:

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

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

13. Automatic forecastingwith 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 backordersU.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. salesMonthly, 11-oz. corn chips Inventory Sales

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 performance11-oz. corn chips

22. Investment analysis11-oz. Corn chips

23. Safety stocks vs. shortages11-oz. Corn chips

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

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

26. Target inventory analysis

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 distributorSeasonal adjustment of continuous data

34. Auto parts distributorSeasonal 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