Forecasting for Operations

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					Forecasting for Operations
Everette S. Gardner, Jr.




                             1
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




2
Research themes
     Intermittent demand
     Distribution inventory management
     Biased forecasting
     Bullwhip effect
     Sensitivity of costs to forecast errors




3
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)




4
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)




5
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




6
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)



7
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




8
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)



9
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)


10
yt   t 1  At bt 1  vt




                              SSOE state space models
          Constant coefficient               Random coefficient
          yt   t 1  bt 1   t         yt   t 1  At bt 1  vt
           t   t 1  bt 1  h1 t      t   t 1  At bt 1  h* vt
                                                                       1

           bt   bt 1  h2 t              bt  At bt 1  h* vt
                                                              2

                 {At} are i.i.d. binary random variates
                 White noise innovation processes ε and v are different
                 Parameters h and h* are related but usually different


       11
Runs of linear trends in the RCSS model

      bt  At bt 1  h* vt
                       2

      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.


12
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
       /(1   ) and P( At  1)  

      RCSS prediction intervals are much wider
       than those of constant coefficient models.


13
     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

14
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




15
     Examples of chemicals demand series

            1                   2




             3                  4




16
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




17
                  Mean absolute scaled error
                        Horizons 1-6

     1.4                All products
                        Critical products
     1.2

     1.0

     0.8

     0.6

     0.4

     0.2

     0.0
           Holt         SES           Damped


18
       Proportions of total demand
           for 25 time series

               4%   4%


     20%




     23%
                             26%


19
                  Mean absolute scaled error
                        Horizons 1-6

     1.4                All products
                        Critical products
     1.2

     1.0

     0.8

     0.6

     0.4

     0.2

     0.0
           Holt         SES           Damped



20
                 Supply chain model

     Damped
      trend                       Actual demand




      Monthly          MIP:            Inv. on hand
                                                         Simulation:
      demand         Minimize          Inv. in transit
                                                         daily mfg. &
     forecasts     total supply        Backorders
                                                          shipments
                    chain cost




                    Monthly                 MIP:          Detailed
                   production           Disaggregate       weekly
                    schedule              monthly         schedule
                                          schedule




21
Top-level mixed integer program (MIP)
      Objective: Minimize total supply chain costs,
       including
           Inventory carrying
           Production
           Transportation
           Import tariffs




22
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




23
                 Supply chain model

     Damped
      trend                       Actual demand




      Monthly          MIP:            Inv. on hand
                                                         Simulation:
      demand         Minimize          Inv. in transit
                                                         daily mfg. &
     forecasts     total supply        Backorders
                                                          shipments
                    chain cost




                    Monthly                 MIP:          Detailed
                   production           Disaggregate       weekly
                    schedule              monthly         schedule
                                          schedule




24
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)




25
                 Supply chain model

     Damped
      trend                       Actual demand




      Monthly          MIP:            Inv. on hand
                                                         Simulation:
      demand         Minimize          Inv. in transit
                                                         daily mfg. &
     forecasts     total supply        Backorders
                                                          shipments
                    chain cost




                    Monthly                 MIP:          Detailed
                   production           Disaggregate       weekly
                    schedule              monthly         schedule
                                          schedule




26
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




27
                    250,000
                                                       Cost vs. weighted lateness
                                                             (tons x days)
                                            Holt

                    200,000
Weighted lateness




                                SES
                    150,000



                    100,000

                                 Damped
                                  trend
                     50,000



                         0
                          114     115        116     117      118     119         120   121
                                        Total supply chain cost (Millions of $)

28
                           30%
                                               Cost vs. percentage of backorders

                                                   Holt
                           25%
Percentage of backorders




                                   SES
                           20%


                           15%

                                   Damped
                           10%      trend


                           5%


                           0%
                             114         115       116       117      118       119       120   121
                                                Total supply chain cost (millions of $)

        29
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




30
                11-Oz. corn chips
      Monthly packaging inventory and usage
$2,500,000
                      Actual Inventory
                      from subjective
$2,000,000               forecasts


$1,500,000

$1,000,000

  $500,000

         $0

                      Month
                                         Monthly Usage

 31
Snack-food manufacturer
      Solution
         Automatic forecasting with the damped trend

         Retain EOQ/safety stock inventory rules




32
                Damped-trend performance
                     11-oz. corn chips
     $500,000

                      Outlier            Actual
                                         Forecast
     $450,000



     $400,000



     $350,000



     $300,000



     $250,000



     $200,000



33
Investment analysis: 11-oz. corn chips
     Forecast annual usage (000s)            $4,138
     Economic order quantity                  $318
     Standard deviation of forecast errors      $34

      Probability     Safety   Order Maximum
      of shortage     stock   quantity investment
          0.1             $44    $318       $362
          0.05            $56    $318       $375
         0.001           $106    $318       $424
       0.00001           $146    $318       $464
      0.0000001          $177    $318       $496

34
                              Safety stocks vs. shortages
                                           11-oz. corn chips
               $200,000

               $180,000
                                Target
               $160,000

               $140,000
Safety stock




               $120,000

               $100,000

                $80,000

                $60,000

                $40,000

                $20,000

                    $0
                          0     10   20      30    40   50    60    70       80   90   100

                                          Shortages per 1,000 order cycles
35
            Safety stock vs. forecast errors
                     11-oz. corn chips
     $200,000
                        Safety stock
     $150,000

     $100,000

      $50,000

            $0

      ($50,000)         Forecast errors
     ($100,000)

     ($150,000)

     ($200,000)


36
               11-Oz. corn chips
     Target vs. actual packaging inventory
     $2,500,000
                                  Actual Inventory
                                  from subjective
                                  Actual Inventory
     $2,000,000                      forecasts
                                  from subjective
                                     forecasts

     $1,500,000


     $1,000,000


       $500,000


             $0
              Target maximum
             inventory based on
                damped trend      Month
                                                     Monthly Usage

37
Forecasting regional demand
      Forecast total unit demand with the damped
       trend
      Forecast regional percentages with simple
       exponential smoothing




38
Regional sales percentages: Corn chips
     50%

             South
     40%


     30%     East

             North
     20%

                 West
     10%


     0%
           Mar     Jun   Sep   Dec   Mar   Jun   Sep   Dec


39
                Packaging inventory (millions of $):
                           82 products


                183
     200
     180
                                        135
     160
     140
     120
     100
      80
      60
      40
      20
       0
           Actual                 Target


40
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


41
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



42
              Water treatment company:
                  Inventory status

     7,526 with no hits                 2,200 obsolete
        in 12 months                          9%         2,928 substitute
             33%                                              items
                                                               13%




                                                             4,202 with
                                                            inadequate
                   6,336 active items                     demand to stock
                          27%                                   18%




43
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




44
             Water treatment supplies:
                 One-step MASE

     1.2
     1.0
     0.8
     0.6
     0.4
     0.2
     0.0
           Moving      Moving    Damped trend
           average    average +
                      subjective
                     adjustments



45
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




46
     ABC classification based on
     damped-trend forecasts

      Class    Sales forecast    System      Items   Dollars

       A         > $36,000         JIT        3%      75%

       B      $600 - $35,999      EOQ        49%      18%
       C          < $600        Annual buy   48%       7%




47
             Annual purchasing workload
               Total savings = 58,000 orders (76%)


               Monthly ordering
 40,000
               ABC system
 35,000

 30,000

 25,000
                                      EOQ
 20,000
                                      EOQ
 15,000
                                                     Annual
 10,000              JIT                              buys
                      JIT
     5,000

        0
                A                 B              C



48
               Inventory investment
               Total savings = $591,000 (15%)

                             Monthly ordering
3,000,000                    ABC system

2,500,000             JIT


2,000,000
                                    EOQ
1,500,000
                                    EOQ
1,000,000           JIT                             Annual
                                                     buys
     500,000

          0
                A              B                C
49
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



50
Consequences of forecast errors (cont.)
      Errors often reverse themselves before system
       has fully responded to
          Backorders, or
          Excess stocks




51
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




52
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)




53
      Presentation and papers
            available at
     www.bauer.uh.edu/gardner




54

				
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