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. 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.) Solutions 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: 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 Implement the damped trend Use the forecasts to do an ABC classification Replace monthly orders with: Class A JIT Class B EOQ/safety stock Class C 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 for the next year 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 Inventory control system recommendations 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 10,000 Annual buys JIT 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 Recommendations Benchmark the forecasts with a random walk Judge forecast accuracy in operational terms Customer service measures Average backorder delay time Percent of time in stock Probability of stockout Average dollars backordered Inventory investment on the balance sheet Purchasing workload or production setups www.bauer.uh.edu/gardner