Forecasting for Operations Dr Everette S Gardner Jr

Forecasting for Operations Dr. Everette S. Gardner, Jr. 1

Forecasting for operations n n 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 n 2 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? 3

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The Importance of Forecasting n Forecasts determine: q q 5 Master schedules Economic order quantities Safety stocks JIT requirements to both internal and external suppliers

The Importance of Forecasting (cont. ) q Better forecast accuracy always cuts inventory investment. q Example: q q q 6 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 q Forecasts are based on weighted moving averages of Level q Trend q Seasonality q q Averages 7 give more weight to recent data

Origins of exponential smoothing n Simple exponential smoothing – The thermostat model q q 8 Error = Actual data – forecast New forecast = Old Forecast + (Weight x Error) n Invented by Navy operations analyst Robert G. Brown in 1944 n 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) 9

Forecast profiles from exponential smoothing Additive Constant Level Linear Trend Exponential Trend Damped Trend 10 Multiplicative Nonseasonal Seasonality

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 consistent growth and little noise, the forecasts usually follow a 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 noise in the data: 14

Case 1: U. S. Navy distribution system n Scope q q q n Decision Rules q q q 15 50, 000 line items stocked at 11 supply centers 240, 000 demand series $425 million inventory investment Simple exponential smoothing Replenishment by economic order quantity Safety stocks set to minimize backorder delay time

U. S. Navy distribution system (cont. ) n Problems q q n Characteristics of demand series q q q n 90% nonseasonal Frequent outliers and jump shifts in level Trends, usually erratic, in most series Solution q 16 Customer pressure to reduce backorder delay No additional inventory budget available Automatic forecasting with the damped trend

U. S. Navy distribution system (cont. ) n Research design 1 q q Random sample (5, 000 items) selected Models tested n n q Error measure n n Mean absolute percentage error (MAPE) Results 1 q q 17 Random walk benchmark Simple, linear-trend, and damped-trend smoothing Damped trend gave the best MAPE Impact of backorder delay unknown

U. S. Navy distribution system (cont. ) n Research design 2 q q The mean absolute percentage error was discarded Monthly inventory values were computed: n n n Results 2 q q 18 EOQ Standard deviation of forecast error Safety stock Average backorder delay Damped trend gave the best backorder delay Management was not convinced

U. S. Navy distribution system (cont. ) n Research design 3 q q q n Results 3 q q q 19 6 -year simulation of inventory performance, using actual daily demand lead time data Stock levels updated after each transaction Forecasts updated monthly 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 20

Case 2: Snack-food manufacturer n Scope q q q n Problems q q 21 82 snack foods Food stocks managed by commodity traders Packaging materials managed with subjective forecasts and inventory levels Excess stocks of packaging materials Impossible to predict inventory on the balance sheet

11 -Oz. corn chips Monthly packaging inventory and usage Actual Inventory from subjective forecasts Month 22 Monthly Usage

Snack-food manufacturer (cont. ) n Solutions q q q 23 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 Outlier 24

Investment analysis: 11 -oz. corn chips 25

Safety stocks vs. shortages 11 -oz. corn chips 26

Safety stocks vs. forecast errors 11 -oz. corn chips Safety stock Forecast errors 27

11 -Oz. corn chips Target vs. actual packaging inventory Actual Inventory from subjective Actual Inventory forecasts from subjective forecasts Target maximum inventory based on damped trend 28 Monthly Usage

How to forecast regional demand n n 29 Forecast total units with the damped trend Forecast regional percentages with simple exponential smoothing

Damped-trend performance 11 -oz. corn chips Outlier 30

Regional sales percentages: Corn chips 31

Case 3: Water filtration systems company n Scope q Annual sales of $15 million q Inventory of $5. 8 million, with 24, 000 stock records n Inventory system Reorder monthly to maintain 3 months of stock q Numerous subjective adjustments Forecasting system q 6 -month moving average q No update to average if demand = 0 q Numerous subjective adjustments q n 32

Problems n Purchasing and receiving workload q n Forecasting q q n 33 70, 000 orders per year Total forecasts on the stock records = $28 million Annual sales = $15 million Frequent stockouts due to forecast errors

Solutions n n Develop a decision rule for what to stock Implement the damped trend Use the forecasts to do an ABC classification Replace monthly orders with: q q q 34 Class A Class B Class C JIT EOQ/safety stock Annual buys

What to stock? n Cost to stock Average inventory balance x holding rate + Number of stock orders x transportation cost n 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 35

Water filtration company: Inventory status 36

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 37 $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 C Any Control System Annual buy 38

Annual purchasing workload Total savings = 58, 000 orders (76%) EOQ JIT 39

Inventory investment Total savings = $591, 000 (15%) EOQ JIT 40

Recommendations n n Benchmark the forecasts with a random walk Judge forecast accuracy in operational terms q Customer service measures n n q q 41 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

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