1 Forecasting for Operations Everette S. Gardner, Jr.

2 Forecasting for operations  Research themes  The damped trend  Case studies 1.Supply chain costs: Specialty chemicals 2.Manufacturing inventory investment: Snack foods 3.Purchasing workload: Water treatment systems  Consequences of forecast errors  How to evaluate forecast performance

3 Research themes  Intermittent demand  Distribution inventory management  Biased forecasting  Bullwhip effect  Sensitivity of costs to forecast errors

4 Intermittent demand  Empirical research is mixed - not clear that intermittent methods can beat SES  No underlying model exists for the Croston method or any of its variants (Shenstone & Hyndman, IJF, 2005)  Why not remove zeroes by aggregation? (Nikolopoulos et al.,JORS, 2011)

5 Distribution inventory management  The damped trend gives better inventory performance than other exponential smoothing methods (Gardner, MS, 1990)  Marginal improvements in forecast accuracy produce much larger improvements in inventory costs (Syntetos et al., IJF, 2010)

6 Biased forecasting  Effects (Sanders & Graman, Omega,2009)  Costs are more sensitive to bias than variance  Over-forecasting produces lower costs than unbiased forecasting in an MRP environment  Objections  Conclusions depend on assumptions  Safety stock is always a better option than adding bias to the forecasts

7 The bullwhip effect  Definition  Tendency of demand variability to increase as one moves up a supply chain  Caused by lead times and forecast errors  Is the bullwhip effect inevitable?  Yes – But it can be reduced with centralized demand information (Chen et al., MS, 2000)  No – Bullwhip effect is due to poor research design (Fildes & Kingsman, JORS, 2010)

8 Sensitivity of costs to forecast error  Fildes and Kingsman (JORS, 2011)  Research design  MRP simulation  Distinguishes between noise and specification error  Demand processes are experimental factors  Conclusions  Cost increases exponentially with demand uncertainty  Cost benefits of improved forecasting are greater than the effects of choosing inventory decision rules

9 Performance of the damped trend  “The damped trend is a well established forecasting method that should improve accuracy in practical applications.” (Armstrong, IJF, 2006)  “The damped trend can reasonably claim to be a benchmark forecasting method for all others to beat.” (Fildes et al., JORS, 2008)

10 Why the damped trend works  Rationale The damped trend has an underlying random coefficient state space (RCSS) model that adapts to changes in trend (McKenzie & Gardner, IJF, 2011)  Practice Fitting the damped trend is a means of automatic method selection from numerous special cases (Gardner & McKenzie, JORS, 2011)

11 SSOE state space models  {A t } are i.i.d. binary random variates  White noise innovation processes ε and are different  Parameters h and h* are related but usually different

12 Runs of linear trends in the RCSS model  With a strong trend, {A t } will consist of long runs of 1s with occasional 0s.  With a weak trend, {A t } will consist of long runs of 0s with occasional 1s.  In between, we get a mixture of models on shorter time scales, i.e. damping.

13 Advantages of the RCSS model  Allows both smooth and sudden changes in trend.  is a measure of the persistence of the linear trend. The mean run length is thus  RCSS prediction intervals are much wider than those of constant coefficient models. and

14 Method% Damped trend 43.0 Holt 10.0 SES w/ damped drift 24.8 SES w/ drift2.4 SES0.8 RW w/ damped drift7.8 RW w/ drift2.5 RW0.0 Modified exp. trend8.3 Linear trend0.1 Simple average0.3 Methods automatically identified in the M3 time series

15 Case 1: Chemicals supply chain  Scope  4 plants: N. and S. America, Europe, Asia  10 component chemicals, 25 products  400 customers, 250,000 tons of annual production  Production and transportation plans based on  Damped trend  Optimization  Simulation

16 Examples of chemicals demand series

17 Scaled errors  Average forecast error measures are misleading  Drastic changes in scale  Some observations near zero  Alternative - Scaled errors (Hyndman & Koehler, 2006)  Based on in-sample, one-step errors from the naïve method  If scaled error is less than 1, we beat the naïve method

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19 Proportions of total demand for 25 time series

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21 Monthly demand forecasts Damped trend MIP: Minimize total supply chain cost Monthly production schedule MIP: Disaggregate monthly schedule Detailed weekly schedule Simulation: daily mfg. & shipments Inv. on hand Inv. in transit Backorders Actual demand Supply chain model

22 Top-level mixed integer program (MIP)  Objective: Minimize total supply chain costs, including  Inventory carrying  Production  Transportation  Import tariffs

23 Top-level MIP continued  Data requirements  Demand forecasts  Pending orders  Shipments in transit  Inventory levels  Machine and storage capacity  Business rules for  Production run lengths  Transportation modes

24 Monthly demand forecasts Damped trend MIP: Minimize total supply chain cost Monthly production schedule MIP: Disaggregate monthly schedule Detailed weekly schedule Simulation: daily mfg. & shipments Inv. on hand Inv. in transit Backorders Actual demand Supply chain model

25 Second-level MIP  Disaggregates top-level schedule  Weekly schedule for each machine at each plant  12-week horizon  Data requirements  Forecasts  Week-ending inventories  Pending orders  Scheduled in and out bound shipments  Bootstrap safety stocks (Snyder et al., IJF, 2002)

26 Monthly demand forecasts Damped trend MIP: Minimize total supply chain cost Monthly production schedule MIP: Disaggregate monthly schedule Detailed weekly schedule Simulation: daily mfg. & shipments Inv. on hand Inv. in transit Backorders Actual demand Supply chain model

27 Simulation model  Executes manufacturing plans on a daily basis using actual demand history  Feeds production, inventories, backorders, and shipments to the MIP models  Sources of uncertainty  Demand  Transportation lead times  Machine breakdowns

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30 Case 2: Snack-food manufacturer  Scope  82 snack foods  Food stocks managed by commodity traders  Packaging materials managed with subjective forecasts and EOQ/safety stock inventory rules  Problems  Excess stocks of perishable packaging materials  Difficult to predict inventory on the balance sheet

31 11-Oz. corn chips Monthly packaging inventory and usage Actual Inventory from subjective forecasts Monthly Usage Month

32 Snack-food manufacturer  Solution  Automatic forecasting with the damped trend  Retain EOQ/safety stock inventory rules

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

34 Investment analysis: 11-oz. corn chips

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

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

37 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

38 Forecasting regional demand  Forecast total unit demand with the damped trend  Forecast regional percentages with simple exponential smoothing

39 Regional sales percentages: Corn chips

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41 Case 3: Water treatment company  Scope  Assembly of systems and distribution of supplies  Annual sales = $16 million  Inventory = $6 million (23,000 SKUs)  Inventory system  Reorder monthly to maintain 3 months of stock  Numerous subjective adjustments  Forecasting system  6-month weighted moving average  Numerous subjective adjustments

42 Problems  Forecasts vs. reality  Annual forecasts on stock records = $29 million  Annual sales = $16 million  Purchasing workload  76,000 purchase orders per year  Messy stock records  Dead stock  Substitute items not linked to primary items

43 Water treatment company: Inventory status

44 Solutions  Forecast demand with the damped trend  Develop a decision rule for what to stock  Use the forecasts to do an ABC classification  Replace the monthly ordering policy with a hybrid inventory control system:  Class A JIT  Class B EOQ/safety stock  Class C Annual buys

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46 What to stock?  Cost to stock Average inventory balance x holding rate + Number of stock orders x transportation cost  Cost to not stock Nbr. of customer orders x drop-ship transportation cost

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

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

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

50 Consequences of forecast errors  Limited capacity creates interactions amongst products:  Under-forecasting  Chain reaction of backorders  Premium transportation  Over-forecasting  Excess stocks  Chain reaction of backorders (limited capacity put to wrong use)  Premium transportation

51 Consequences of forecast errors (cont.)  Errors often reverse themselves before system has fully responded to  Backorders, or  Excess stocks

52 How to evaluate forecast performance  Operational measures  Backorder delay time  Percent of time in stock  Percent of orders filled immediately  Number of purchase orders or production setups  Financial measures  Manufacturing, distribution, and supply chain costs  Value of backorders  Inventory investment on the balance sheet

53 Future research  Research is needed:  In real operating systems Gardner & Makridakis (IJF,1988)  On the benefits of improved forecasting Fildes & Kingsman (JORS, 2010)  On the relationship between forecast accuracy and operational performance Syntetos et al. (IJF, 2010)

54 Presentation and papers available at