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Forecasting for Operations

Forecasting for Operations. Everette S. Gardner, Jr., Ph.D. Bauer College of Business University of Houston October 30, 2006. Forecasting for Operations. Operational systems typically include large numbers of time series. Problems in evaluating forecast accuracy: Pooled data structures

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Forecasting for Operations

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  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

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