Forecasting for Operations

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Forecasting for Operations

• Everette S. Gardner, Jr.

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Forecasting for operations

• Research themes
• The damped trend
• Case studies
• Supply chain costs Specialty chemicals
• Manufacturing inventory investment Snack foods
• Purchasing workload Water treatment systems
• Consequences of forecast errors
• How to evaluate forecast performance

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Research themes

• Intermittent demand
• Distribution inventory management
• Biased forecasting
• Bullwhip effect
• Sensitivity of costs to forecast errors

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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)

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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)

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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

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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)

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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

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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)

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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)

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SSOE state space models

• At are i.i.d. binary random variates
• White noise innovation processes e and are
  different
• Parameters h and h are related but usually
  different

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Runs of linear trends in the RCSS model

• With a strong trend, At will consist of long
  runs of 1s with occasional 0s.
  
• With a weak trend, At 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.

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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
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Methods automatically identified in the M3 time
series
Method
Damped trend 43.0
Holt 10.0
SES w/ damped drift 24.8
SES w/ drift 2.4
SES 0.8
RW w/ damped drift 7.8
RW w/ drift 2.5
RW 0.0
Modified exp. trend 8.3
Linear trend 0.1
Simple average 0.3
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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

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Examples of chemicals demand series
1
2
3
4
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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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Proportions of total demand for 25 time series
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Supply chain model
Damped trend
Actual demand
Simulation daily mfg. shipments
Monthly demand forecasts
MIP Minimize total supply chain cost
Inv. on hand Inv. in transit Backorders
Monthly production schedule
MIP Disaggregate monthly schedule
Detailed weekly schedule
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Top-level mixed integer program (MIP)

• Objective Minimize total supply chain costs,
  including
• Inventory carrying
• Production
• Transportation
• Import tariffs

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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

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

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

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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

• Solution
• Automatic forecasting with the damped trend
• Retain EOQ/safety stock inventory rules

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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 stock 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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Forecasting regional demand

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

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Regional sales percentages Corn chips
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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

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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

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Water treatment company
Inventory status
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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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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

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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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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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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

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Consequences of forecast errors (cont.)

• Errors often reverse themselves before system has
  fully responded to
• Backorders, or
• Excess stocks

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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

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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)

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Presentation and papers available at
www.bauer.uh.edu/gardner