forecasting for operations everette s. gardner, jr., ph.d. bauer college of business university of...
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Forecasting for Operations
Everette S. Gardner, Jr., Ph.D.Bauer College of Business
University of Houston
October 30, 2006
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Forecasting for Operations
• Operational systems typically include large numbers of time series. Problems in evaluating forecast accuracy:– Pooled data structures– Pooled averages– Choice of error statistic– Cumulating over lead times– Stability of error measures across origins– Method selection– Product hierarchies
• References– Tashman (IJF, 2000)– Fildes (Management Science, 1989; IJF, 1992)
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Forecasting for Operations
• We can bypass many of these problems by judging the impact of forecasting in financial or operational terms:– Customer service – Inventory investment– Purchasing workload– Capacity requirements– Production scheduling efficiency
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Forecasting for OperationsCase Studies:
• Customer service– U.S. Navy distribution system
• Inventory investment– Manufacturer of snack foods
• Purchasing workload– Manufacturer/distributor of water filtration
systems
• Capacity requirements– Distributor of cleaning supplies
• Production scheduling efficiency– Manufacturer of cookware
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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
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U. S. Navy distribution system
• Problem– 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 about half of the
series
• Solution– Automatic forecasting with the damped trend
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Origins of the damped trend
• Reference– Gardner & McKenzie, Management Science,
1985
• Operational requirement– Automatic forecasting system for military repair
and maintenance parts
• Theory– Lewandowski, IJF, 1982 (M1-Competition)
Trend extrapolation should become moreconservative as the forecast horizon increases.
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The damped trend
1) Error = Actual demand – Forecast
2) Level= Forecast + Weight1(Error)
3) Trend = (Previous trend) + Weight2(Error)
4) Forecast for t+1= Level + Trend
5) Forecast for t+2 = Level + Trend + 2 Trend
. .
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Automatic forecastingwith the damped trend
• Constant-level data– Forecasts emulate simple smoothing
• Consistent trend– Forecasts emulate Holt’s linear trend
• Erratic trend– Forecasts are damped
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Automatic forecastingwith the damped trend
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In constant-level data, the forecasts emulate simple exponential smoothing:
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Automatic forecastingwith the damped trendIn data with a consistent trend and little noise, the forecasts emulate Holt’s linear trend:
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Automatic forecastingwith the damped trendWhen the trend is erratic, the forecasts are damped:
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50 Saturation level
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Automatic forecastingwith the damped trendThe damping effect increases with the level of noise in the data:
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Saturation level
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U. S. Navy distribution system
• Research design 1– Random sample (5,000 items) selected.– Models tested:
• Random walk benchmark• Simple, linear-trend, and damped-trend
smoothing– Error measures
Mean absolute percentage error (MAPE)Geometric root mean squared error (GRMSE)
• Results 1– Damped trend was clear winner.– Impact on backorder delay unknown.
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U. S. Navy distribution system
• Research design 2– Error measures were discarded and monthly
inventory values were computed:• EOQ• Standard deviation of forecast error• Safety stock• Steady-state estimate of average backorder
delay
• Results 2– Again, damped trend was clear winner.– Management was not convinced and requested
more evidence.
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U. S. Navy distribution system• Research design 3
– 6-year simulation of inventory performance• Actual daily demand history used.• Stock levels updated after each transaction.• Reorders placed using actual leadtimes from
the past.• Forecasts, EOQs, and safety stocks updated
monthly.• Backorder delays summarized monthly
• Results 3– Again, damped trend was 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 backordersU.S. Navy distribution system
Damped trend
Simple smoothing
Linear trend
Random walk
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370 380 390 400 410 420 430
Inventory investment (millions)
Ba
ck
ord
er
da
ys
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Snack-food manufacturer• Company
– Manufacturer of 80 snack foods– Food inventories managed by commodity
trading rules– No formal decision rules for packaging
inventories– Subjective forecasting
• Problem– Excess stocks of packaging materials– Difficult to set a target value for inventory
investment on the balance sheet
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$0
$500,000
$1,000,000
$1,500,000
$2,000,000
$2,500,000
Packaging material inventory vs. sales
Monthly, 11-oz. corn chips
Inventory
Sales
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Snack-food manufacturerSolution
– 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 performance11-oz. corn chips
$200,000
$250,000
$300,000
$350,000
$400,000
$450,000
$500,000
Actual
Forecast
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Investment analysis11-oz. Corn chips
Forecast annual usage $4,138,770
Economic order quantity $318,367
Standard deviation of forecast errors $34,140
Nbr. shortages
per 1,000 Probability Safety Order Maximum
order cycles of shortage stock quantity investment
100.0000 0.1000 $43,758 $318,367 $362,12550.0000 0.0500 $56,167 $318,367 $374,5341.0000 0.0010 $105,510 $318,367 $423,8770.0100 0.0000 $145,601 $318,367 $463,9680.0001 0.0000 $177,496 $318,367 $495,863
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Safety stocks vs. shortages11-oz. Corn chips
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
0 10 20 30 40 50 60 70 80 90 100
Shortages per 1,000 order cycles
Saf
ety
stoc
k
Target
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Safety stocks vs. forecast errors 11-oz. Corn chips
($200,000)
($150,000)
($100,000)
($50,000)
$0
$50,000
$100,000
$150,000
$200,000
Safety stock
Forecast errors
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$0
$500,000
$1,000,000
$1,500,000
$2,000,000
$2,500,000
Target inventory vs. salesMonthly, 11-oz. corn chips
Actual Inventory
Sales
Target inventory
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Target inventory analysis
Actual inventory based on subjective decisions
$ 182.6 million
Target inventory based on the damped trend and EOQ/Safety stocks
$ 135.0 million
Projected savings $ 47.2 million
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Auto parts distributor• Company
– 24 distribution centers– 350 company-owned stores, 1,600 affiliated stores– Millions of time series
• Forecasting system– Trigg & Leach adaptive exponential smoothing:
Parameter = |Smoothed error/Smoothed MAD|– Every demand series treated as multiplicative
seasonal: Actual demand / index = Adjusted demand– Predetermined group seasonal indices used for
most series
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Auto parts distributor• Forecasting system (continued)
– For intermittent series, multiplicative seasonal adjustment is infeasible. Company solution:
• Add a large constant before seasonal adjustment
• Remove the constant afterward
• Inventory control system– EOQ– Safety stocks
• Based on MAD• Set to meet target probability of shortage
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Auto parts distributor
• Problems– Samples showed that seasonal adjustment
inflated the variance of most demand series– Inflated variances led to purchases much larger
than true requirements
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Auto parts distributor:Example of inflated variance
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80 Original data
Company seas. adjustment
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Auto parts distributor
• Proposals to management– Replace adaptive smoothing with simple
smoothing– Replace MAD with RMSE– Forecast intermittent series with intermittent
methods– Test series for seasonality– Use additive seasonal adjustment
• Actual demand – index = Adjusted demand– Develop tradeoff curves between inventory
investment and customer service
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Auto parts distributor• Instructions from management
– Fix seasonal adjustment first– Minimize sample sizes– Minimize implementation programming
• Research plan– Stratified random sample of 691 series from four
distribution centers– Seasonal identification based on variance
reduction– Additive seasonal adjustment
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Auto parts distributorSeasonal adjustment of continuous data
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80 Original data
Company seas. adjustment
Additive seas. adjustment
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Auto parts distributorSeasonal adjustment of intermittent data
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180Original dataCompany seas. adjustmentAdditive seas. adjustment
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Auto parts distributor:Estimated savings
Safety stock 95% confidence limitsInventory reduction lower upperFlorida
Fast-movers 16% 14% 18%Temperature control 22% 16% 28%
MinnesotaFast-movers 18% 15% 20%Temperature control 43% 33% 52%
MissouriFast-movers 17% 15% 19%Temperature control 19% 11% 27%
CaliforniaFast-movers 19% 16% 21%Temperature control 20% 13% 27%
Total percentage 19% 17% 21%Total dollars (millions) $5.1 $4.7 $5.4
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Auto parts distributor• Sensitivity analysis
– Simple smoothing produced significantly smaller safety stocks than adaptive smoothing
– Periodic refitting of the simple smoothing model did not improve results
– Replacement of the MAD with the RMSE made little difference in safety stocks
– Autocorrelation analysis was no better than the simple variance test for seasonal identification
– Croston’s method for intermittent data was no better than simple smoothing
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Auto parts distributor• Lessons
– It is dangerous to ignore seasonality testing in inventory series
– It is dangerous to assume that every seasonal time series is multiplicative
– Group seasonal indices can perform poorly in noisy data
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Cookware manufacturer
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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Number of production set-ups per month(Exponential smoothing implemented in May)
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Cookware manufacturer
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Production runs by color, before and after exponential smoothing
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Conclusions• Judge forecast accuracy in financial or
operational terms– Customer service – Inventory investment on the balance sheet– Purchasing workload– Capacity requirements
• Benchmark forecast accuracy with exponential smoothing