Forecasting for Operations

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Forecasting for Operations

• Dr. Everette S. Gardner, Jr.

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Forecasting for operations

• Why we should forecast with models
• The importance of forecasting
• Exponential smoothing in a nutshell
• Case studies
• Customer service U.S. Navy distribution system
• Inventory investment Mfg. of snack foods
• Inventory investment Auto parts distributor
• Purchasing workload Mfg. of water filtration
  systems
• Recommendations How to improve forecast
  accuracy

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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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The Importance of Forecasting

• Forecasts determine
• Master schedules
• Economic order quantities
• Safety stocks
• JIT requirements to both internal and external
  suppliers

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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

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Exponential smoothing methods

• Forecasts are based on weighted moving averages
  of
• Level
• Trend
• Seasonality
• Averages give more weight to recent data

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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

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Exponential smoothing at work

• A depth charge has a magnificent laxative
  effect on a submariner.
• Lt. Sheldon H. Kinney,
• Commander,
• USS Bronstein (DE 189)

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Forecast profiles from exponential smoothing

• Additive
  Multiplicative
• 
  Nonseasonal Seasonality Seasonality
• Constant
• Level
• Linear
• Trend
• Exponential
• Trend
• Damped
• Trend

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Automatic Forecasting with the damped trend
In constant-level data, the forecasts emulate
simple exponential smoothing
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Automatic Forecasting with the damped trend
In data with consistent growth and little noise,
the forecasts usually follow a linear trend
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Automatic Forecasting with the damped trend
When the trend is erratic, the forecasts are
damped
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Automatic Forecasting with the damped trend
The damping effect increases with noise in the
data
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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

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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

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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

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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

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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

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

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11-Oz. corn chipsMonthly packaging inventory and
usage
Actual Inventory from subjective forecasts
Month
Monthly Usage
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Snack-food manufacturer (cont.)

• Solution
• Automatic forecasting with the damped trend
• Replenishment by economic order quantity
• Safety stocks set to meet target probability of
  shortage

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Damped-trend performance
11-oz. corn chips
Outlier
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Investment analysis 11-oz. corn chips
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Safety stocks vs. shortages
11-oz. corn chips
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Safety stocks vs. forecast errors
11-oz. corn chips
Safety stock
Forecast errors
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11-Oz. corn chipsTarget vs. actual packaging
inventory
Actual Inventory from subjective forecasts
Actual Inventory from subjective forecasts
Target maximum inventory based on damped trend
Month
Monthly Usage
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How to forecast regional demand

• Forecast total units with the damped trend
• Forecast regional percentages with simple
  exponential smoothing

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Damped-trend performance
11-oz. corn chips
Outlier
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Regional sales percentages Corn chips
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Case 3 Auto parts distributor

• Scope
• 24 distribution centers
• 350 company-owned stores, 1,600 affiliated stores
• Millions of time series
• Independent marketing, finance, and operations
  forecasts
• Inventory system
• Standard EOQ/safety stock
• Operations forecasting system
• Multiplicative seasonal adjustment for all time
  series
• Simple exponential smoothing of
  seasonally-adjusted data

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Forecast profiles from exponential smoothing

• Additive Multiplicative
• 
  Nonseasonal Seasonality Seasonality
• Constant
• Level
• Linear
• Trend
• Exponential
• Trend
• Damped
• Trend

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Seasonal adjustment procedures

• Multiplicative
• Range of seasonal fluctuation grows with the data
• Seasonal index is a ratio
• Seasonally adjusted data Actual sales / Index
• Additive
• Range of seasonal fluctuation is constant
• Seasonal index is stated in units
• Seasonally adjusted data Actual sales index

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Auto parts distributor (cont.)

• Multiplicative seasonality is infeasible for data
  with zeroes
• Company solution for data with zeroes
• Add a large constant to each months sales before
  seasonal adjustment
• Subtract the constant afterward

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Auto parts distributor (cont.)

• Effects of company seasonal adjustment procedure
• Many non-seasonal time series were adjusted
• Variance of seasonally-adjusted data was almost
  always greater than original data
• Inflated variance led to
• Excess safety stocks
• Purchases much larger than true requirements
• Frequent subjective adjustments of forecasts

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Auto parts distributor
Example of inflated variance
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Auto parts distributor (cont.)

• Proposals to Management
• Test for seasonality before adjustment
• Use additive seasonal adjustment, which works
  regardless of zeroes in the data
• Actual data index Adjusted data
• Develop tradeoff curves between inventory
  investment and customer service

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Auto parts distributor
Seasonal adjustment comparisons no zeroes
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Auto parts distributor
Seasonal adjustment comparisons With zeroes
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Auto parts distributorEstimated savings
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Case 4 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

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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

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Solutions

• Develop a decision rule for what to stock
• Forecast demand for all items with the damped
  trend
• 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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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.

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Water filtration company
Inventory status
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ABC classification based ondamped-trend
forecasts
Class Sales forecast System Items Dollars
A gt 36,000 JIT 3 75
B 600 - 35,999 EOQ 49 18
C lt 600 Annual buy 48 7
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The hybrid inventory control system
Control System Inventory Class Production Schedule Lead-time Behavior
JIT A, B Level Certain
MRP A, B Variable Reliable
EOQ / Safety stock A, B Variable Variable
Annual buy C Any Any
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Annual purchasing workload Total savings 58,000
orders (76)
EOQ
JIT
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Inventory investment Total savings 591,000
(15)
EOQ
JIT
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Conclusions

• Test all demand series for seasonality
• For series that pass the test, compare additive
  and multiplicative seasonal adjustment
• Forecast at the highest possible level of
  aggregation
• For total units, forecast with the damped trend
  model

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Conclusions (cont.)

• Break down total forecasts with simple smoothing
  applied to category percentages
• Regions
• Pack sizes
• Colors
• Benchmark the forecasts with a random walk
• Get operations and marketing together and
  produce one corporate forecast

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Conclusions (cont.)

• Judge forecast accuracy in financial and
  operational terms
• Customer service measures
• Backorder delay time
• Percent of time in stock
• Probability of stockout
• Dollars backordered
• Inventory investment on the balance sheet
• Purchasing workload or production setups

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www.bauer.uh.edu/gardner