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

2 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

3 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?

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

6 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

7 Exponential smoothing methods  Forecasts are based on weighted moving averages of  Level  Trend  Seasonality  Averages give more weight to recent data

8 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

9 Exponential smoothing at work “A depth charge has a magnificent laxative effect on a submariner.” Lt. Sheldon H. Kinney, Commander, USS Bronstein (DE 189)

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

11 Automatic Forecasting with the damped trend In constant-level data, the forecasts emulate simple exponential smoothing:

12 In data with consistent growth and little noise, the forecasts usually follow a linear trend: Automatic Forecasting with the damped trend

13 Automatic Forecasting with the damped trend When the trend is erratic, the forecasts are damped:

14 Automatic Forecasting with the damped trend The damping effect increases with noise in the data:

15 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

16  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.)

17 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

18 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

19 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

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

21 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

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

23 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

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

25 Investment analysis: 11-oz. corn chips

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

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

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

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

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

31 Regional sales percentages: Corn chips

32 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

33 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

34 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

35 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

36 Water filtration company: Inventory status

37 ABC classification based on damped-trend forecasts for the next year ClassSales forecastSystemItemsDollars A> $36,000JIT3%75% B$600 - $35,999EOQ49%18% C< $600Annual buy48%7%

38 Inventory control system recommendations Control System Inventory Class Production Schedule Lead-time Behavior JITA, BLevelCertain MRPA, BVariableReliable EOQ / Safety stockA, BVariable Annual buyCAny

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

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

41 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

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