Forecasting short term trucking rates

Xiwen Bai

Advised by Dr. Chris Caplice

22 May 2018

2

IntroductionMOTIVATION

Transportation Trucking Forecasting

$1.5trillionspentin2015onlogisticsandtransportation

8%ofUSGDP

Upto50%oftotallogisticscostsaretransportationcost

Emphasizeonleanproductionandinventoryminimization

LifebloodoftheUSeconomy

Earned $726.4billionrevenuein2015

Represents81.5%ofUSfreighttransportationrevenue

Transportationbudgetplanning

Economicsorderquantity

Inventoryreplenishment

Facilitylocation

3

IntroductionOBJECTIVE&SCOPE

Ø Objective:• Todevelopaforecastingmodelthatpredictsbothcontractandspotratesfordryvanonindividuallanesforthenextsevendays

Ø Scope:• Onehigh-volumetruckload(TL)laneasasamplelaneforforecasts

Ø ContractvsSpotmarket:• Contract:stabilityforshippers,lessflexibility• Spot:moreflexibility,higherratevolatility

4

Trends in truck rate forecasting research

Ø Contractratesmorefrequentlystudiedthanspotrates

Ø Methodologyevolvement

Approximated

rate function

Regressionbasedmethod

Machinelearning

TL:distanceLTL:distance

weight

Market-Lane-specificvariable:

Origin/destinationTenderrejection

EconomicsofscaleFreightclass

NotoftenusedintruckingExceptBudak,etal.(2017)

5

Research Gaps

Ø Moststudiesusinglinearregressionmethods

Ø Spotmarketrateshavebeenlessstudied

Ø Nostudyconsideringinteractions betweenspotandcontractrates,betweenratesforaparticularlaneanditsadjacentroutes,orbetweenratesandvolumes.

6

Methodology

• NAR:Nonlinearautoregressive(NAR)

• NARX:NonlinearautoregressivewitheXogenous inputs

NeuralNetwork

• ARIMA:Autoregressiveintegratedmovingaverage

TimeSeriesModels

• Whentoupdatemodelwithnewinformation

Modelupdate

7

MethodologyFORECASTINGMODELS:NEURALNETWORK&ARIMA

!" = $% + $'!"(' + ⋯+ $*!"(* + +" + ,'+"(' + ⋯+ ,-+"(-

! " + 1 = & ! " , … ! " − *+ + 1 ; - " , - " − 1 ,…- " − *. + 1

Ø NAR&NARXmodels• Hybridofneuralnetworkandtimeseriesmodels

Ø ARIMAmodel

ModelStructure

𝑢(𝑡) isexogenousinput;dy andduarememorydelays

Ø Abilitytofindcomplexandnonlinearassociationsbetweentheparameters

Ø Highertoleranceforerrors,robusttonoise

Ø Lessconcernedwithmulticollinearityissue

Ø Noneedforerrordistributionassumption

NeuralNetworkAdvantage

8

MethodologyMODELUPDATEWITHNEWINFORMATION

9

MethodologyDATA

Ø GeorgiaCentral(GA_C)toFloridaCentral(FL_C)dailyspotandcontractcostpermileoveraone-yearperiod(1Apr2016to31Mar2017);

Ø Training:Validation:Testset=70:15:15

LHDVODpairMap(Contract)

15,019 54,443

Avgvolume

Origdest

Destination

origin

2016Population

590,000to1,340,000

1,340,000to3,070,000

3,070,000to5,590,000

5,590,000to9,000,000

9,000,000to39,700,000

MapbasedonLngandLatandLat.ForpaneLat:ColorshowssumofAvgvolume.DetailsareshownforODPair.ForpaneLat

(2):ColorshowsdetailsaboutOrigdest.Mapcoloringshows2017PopulationbyState.ThedataisfilteredonAvgvolumeand

Ratetype.TheAvgvolumefilterrangesfrom15000to54443andkeepsNullvalues.TheRatetypefilterkeepsC.

0

1

2

3

4

5

6

Apr-16 Jul-16 Oct-16 Jan-17

Costperm

ile

CCPM

S-CPM

10

MethodologyINPUTDECISIONVARIABLESANALYSIS

Autocorrelationandcross-correlationsbetweenGA_CtoFL_Ccontractrates andothervariables

Numberoflags

[Contract,Contract]

[Contract,Spot]

[Contract,ContractGA_C|FL_N]

[Contract,ContractGA_C|FL_S]

[Contract,ContractGA_C|SC_C]

[Contract,Volume]

0 1 0.25 0.05 0.5 0.08 -0.411 0.38 0.11 -0.11 0.23 0.12 -0.032 0.22 0.1 -0.05 0.16 0.13 0.233 0.04 0.13 -0.07 0.13 0.03 0.334 0.01 0.17 0.03 0.1 0.16 0.155 0.12 0.19 0.12 0.22 0.08 -0.056 0.21 0.16 0.02 0.26 0.07 -0.327 0.42 0.14 0.05 0.4 0.06 -0.34

Numberoflags [Spot,Spot] [Spot,

Contract][Spot,Volume]

0 1 0.25 -0.181 0.3 0.21 -0.092 0.28 0.23 -0.013 0.3 0.11 0.044 0.23 0.13 0.025 0.27 0.06 0.056 0.26 0.12 -0.087 0.23 0.14 -0.16

Autocorrelationandcross-correlationsbetweenGA_CtoFL_Cspotrates andothervariables

11

Results and discussionsNARRESULTSFORSPOTRATES

Feedback delays (𝑑&) Hidden nodes (𝑁() MSE for validation set7 4 0.4948 2 0.5079 5 0.54310 2 0.52711 3 0.52612 4 0.53913 2 0.55814 2 0.5440.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

MSE

Noofhiddennodes

MSEforthevalidationsetwithdifferentnumbersofhiddennodes(Nh)(dy=7)

NARmodelresultsforspotrateswithdifferentfeedbackdelays(dy)

Thesamemodelforeachdu andNh isrun10timestogetstableresults.MSEsaretheaveragevaluesof10runs.

12

Results and discussionsNARXRESULTSFORSPOTRATESWITHCONTRACTRATESASINPUTS

Inputdelays(𝑑)) Hiddennodes(𝑁() MSEforvalidationset1 6 0.5442 5 0.5133 4 0.5114 2 0.5525 3 0.5016 2 0.5307 2 0.559

Note:dy=7.Thesamemodelforeachdu andNh isrun10timestogetstableresults.MSEsaretheaveragevaluesof10runs.

13

Results and discussionsMODELUPDATEWITHNEWINFORMATIONFORSPOTRATES

Ø Updatedmodelsdonotperformbetterthantheoriginalmodelinmostcases.

Ø Reason:parameters(numbersofhiddennodesandfeedbackdelays)trainedintheoriginalmodelnotstableduetohighlevelofvolatilityandnoiseintheoriginaldata

-120%

-80%

-40%

0%

40%

80%

1 2 3 4 5 6

%M

SEre

duction

Periodahead

ErrorreductionfromnewrollingwindowmodelErrorreductionfromnewcumulativemodel

MSEreductionsbyupdatingmodelswithnewinformationforspotrates

14

Results and discussionsNARANDNARXRESULTSFORCONTRACTRATES

Inputvariables Inputdelay(𝑑))

Hiddennodes(𝑁()

MSEforvalidationset

CR 7 3 0.00239

CR,SR 7 3 0.00235CR,GA_C|FL_S 7 1 0.00205CR,Volume 7 2 0.00192CR,SR,GA_C|FL_S 7 2 0.00226CR,SR,Volume 7 1 0.00210CR,GA_C|FL_S,Volume 7 4 0.00211CR,SR,GA_C|FL_S,Volume 7 1 0.00200

Note:Feedbackdelay(dy)issetto7forallcases.CR standsforspotrates,SR forspotrates,GA_C|FL_SforcontractratesonGA_C|FL_S.Thesamemodelforeachdu andNh isrun10timestogetstableresults.MSEsaretheaveragedvaluesof10runs.

15

Results and discussionsMODELUPDATEWITHNEWINFORMATIONFORCONTRACTRATES

Ø Updatedmodelperformsbetterthantheoriginalmodelfrom3-periodaheadonwards

Ø Rollingwindowmodelperformsbetterthanthecumulativemodel

MSEreductionsbyupdatingmodelswithnewinformationforcontractrates

-50%

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

1 2 3 4 5 6

%M

SEre

duction

Periodahead

ErrorreductionfromnewrollingwindowmodelErrorreductionfromnewcumulativemodel

16

Results and discussionsRMSECOMPARISONBETWEENNAR(X)ANDARIMA

Ratetype Modeltype Bestmodel RMSEfor7days(rollingforecast)

SpotNAR(X) NARwith𝑑&=7 0.56511ARIMA ARIMA(6,0,2) 0.60167

%Difference -6%

ContractNAR(X) NARXwith𝑑&=7,𝑑)=7 0.03286ARIMA ARIMA(7,0,1) 0.03082

%Difference 7%

Note:%Differenceiscalculatedas(RMSENAR(X)- RMSEARIMA)/RMSEARIMA ,asawaytomeasurerelativeperformanceoftwotypesofmodels.

17

ConclusionKEYFINDINGS

Spotrate:NARvsARIMAContractrate:NARvsARIMA1

2

3

4

5

Contractrate:Addingvolume,ratesonadjacentroutes,retrainingofthemodelincreasesthemodel’sperformance

Muchhigheraccuracyandlessforecastingvariabilityforcontractthanspotrates

Noshort-terminformationtransmissionbetweenspotandcontractrates

Spotrate:Additionalinformation,suchaspastvaluesofcontractratesModelupdatewithnewinformationdoesnotimproveforecastingaccuracy

18

Forecastingguidelineforpractitioners

• howtoselectinputvariables• whatmodeltouse• whentoupdatemodelwithnewinformation• whatforecastingerrorexpectedfrommodel

Aidsupplychaindecisionmaking

• Transportationbudgetplanning• Economicsorderquantity• Vehiclerouting• Facilitylocation

ConclusionCONTRIBUTION

1 2

19

Thank You!