Combining Managerial Insights with Predictive Models when ...IBM DemandTec, Dunnhumby’s KSS...
Transcript of Combining Managerial Insights with Predictive Models when ...IBM DemandTec, Dunnhumby’s KSS...
Combining Managerial Insights with Predictive Models when Setting Optimal Prices A l a n L . M o n t g o m e r y P r o f e s s o r o f M a r ke t i n g , C a r n e g i e M e l l o n U n i v e r s i t y V i s i t i n g P r o f e s s o r, H K U E - m a i l : a l a n m o n t g o m e r y @ c m u . e d u A l l R i g h t s R e s e r v e d , © 2 0 1 8 A l a n M o n t g o m e r y
D o n o t d i s t r i b u t e o r r e p r o d u c e w i t h o u t A l a n M o n t g o m e r y ’s P e r m i s s i o n
Research Goal Apopularfeatureofbothoptimalpricingsolutionsinbothindustryandacademicsistoimplementbusinessruleswhichimposeconstraintsontheoptimalpricingsolution.
Theseconstraintsreflectpriorinformationonthepartoftheuseraboutthepricingsolution.However,currentapproachestreatthisinformationinanad-hocmanner.
Thisresearchshowshowbusinessrulescanbeformulatedaspriorinformationtoyieldbetterpricingdecisions.
2
Example Why did Amazon charge $2m for textbook?
3
Example What is the optimal price for “Asparagus Water”?
4
Broader Research Question
HowtocombineDataScience/MLwithHuman/Expert/ManagerialIntuition/Judgment?◦ Onlyusethedata(objectivebutinefficient)◦ Onlyusemanagerialinsight(subjectivebutexplainable)◦ Usedataunlessconflictswithmanagerialinsight◦ Usemanagerialinsightunlessitconflictswithdata◦ Combinebothtogether(weighteachappropriately)
5
Outline Currentpracticeofpriceoptimization Businessrulesaspriorinformation Creatinginformativepriorsfrombusinessrules EmpiricalExample
6
Current State of Price Optimization
7
8
Optimal Product Pricing Profits:
Optimalpricingrule:
Wherepriceelasticitymeasuresdemandresponsivenesstopricechanges:
*
1p cβ
β=
+
%%
q p qp q p
β ∂ Δ= ≈∂ Δ
( )p c qΠ = −
9
10
Optimal Product Line Pricing TotalProfits:
Optimalpricingrule:
Wherecrosspriceelasticitiesmeasurecompetitiveeffects:
*
1ii
i iii j ji j i
j i
p cs s
ββ µ β
≠
=+ +∑
% ,%
i i iij
i i j
q p qp q p
β ∂ Δ= ≈∂ Δ
1( )
M
i i iip c q
=
Π = −∑
, i i i ii i
i j jj
p c p qsp p q
µ −= =∑
11
Price Optimization in Practice Hugegrowthofpriceoptimizationinpracticeforbothretailersandmanufacturers:◦ IBMDemandTec,Dunnhumby’sKSSRetail,Oracle,PROS,SAPKhimetrics,Vendavo,VistaarTechnologies,andZilliant
GartnerMarketscope(2010)statesthat“priceoptimizationtechnologywillhaveamoredirectimpactonincreasingrevenueormarginsthananyotherCRMtechnology”.◦ TheYankeeGroupestimatedthatmorethanonebilliondollarswouldbespentonthesesystemsin2007
2012Gartnerstudy(Fletcher2012)showedgainsof2to4%ofrevenuefromusingthesesystems.◦ Anecdotalreportssuggestincreasesingrossmarginsintherangeof2-8%,retailerstypicallyhavegrossmarginsofabout25%andhaveannualrevenuesof$2.5trillion.
◦ Suggestsbenefitforretailersalonewouldbebetween$12.5band$50bannually.
Germannetal(2014)findretailersbenefitfromdeployingcustomeranalyticsmorethanfirmsinmostinudstries◦ CompredwithMediaEntertainment,Energy,Insurance,Telecom,Hospitality,Banking
12
Traditional Modeling Process Themulti-productpricingdecisionprocess:
Demand Estimation Price Optimization quantity sold
past prices estimates (elasticities)
optimal prices are constrained or ignore business rules as non-binding
Demand Model linear, log-log, log-linear, etc Estimation:
ols, mle, bayesian, etc
maxp profit(p|q) s.t. fi(p|q) ≤ 0 Impose constraints post hoc
13
Business Rules as Prior Information
14
Business Rules Currentpricingsolutionsfrequentlyimplementconstraintsthatreflect“businessrules”,whichcodifymanagerknowledge:◦ Allowednumberandfrequencyofmarkdowns(e.g.,atleastaweekbetweentwoconsecutivemarkdowns)
◦ Min-maxdiscountlevelsormaximumlifetimediscount◦ Minimumnumberofweeksbeforeaninitialmarkdowncanoccur◦ Typesofmarkdownsallowed(e.g.,10%,25%,…)orthepermissiblesetofprices
◦ The“family”ofitemsthatmustbemarkeddowntogether
Source:ElmaghrabyandKeskinocak(2003;ManagementScience)
15
Why use business rules? Answer:to“improve”thepricingsolutionandfindabetteronethanwouldbeaffordedwithouttheseconstraints Examples:◦ Strategicdecision(ElmaghrabyandKeskinocak2003)◦ Ensuredesiredpositioningoftheproduct(Hawtin2002)
16
DemandTec’s Rule Relaxation Approach 1. Grouppriceadvanceordeclinerules.Theusersetsamaximum
weightedgrouppriceadvanceordeclineto10%.
2. Sizepricingrules.Theusergoeswiththedefaultthatlargeritemscostlessperequivalentunitthansmalleridenticalitems.
3. Brandpricingrules.Forsoftdrinks,theuserdesignatesthepriceofbrandAisneverlessthanthepriceofbrandB.ForjuicestheuserdesignatesthatbrandCisalwaysgreaterthanBrandD.
4. Unitpricingrules.Theusergoeswiththedefaultthattheoverallpriceoflargeritemsisgreaterthantheoverallpriceofsmalleridenticalitems.
5. Competitionrules.Theuserdesignatesthatallpricesmustbeatleast10%lessthanthepricesofthesameitemssoldbycompetitorXandarewithin2%ofthepricesofthesameitemssoldbycompetitorY.
6. Linepricerules.Theuserdesignatesthatdifferentflavorsofthesameitemarepricedthesame.
Source:Nealetal.(2010),Patent#7617119 17
Examples of Business Rules in Academic Research ◦ CorstjensandDoyle(1981)useconstraintstorepresentstorecapacity,availabilityandcontrol
◦ Montgomery(1997)constrainstheoptimalpricesubjecttoanaveragepriceand/ortotalrevenueconstraint
◦ SubramanianandSherali(2010)ensurethatnewsolutiondoesnotdeviatetoofarfromcurrent
◦ DengandYano(2006)boundpricerangestoensurereasonablesolutions◦ BitranandModschein(1997)andFengandGallego(1995)allowonlyafixednumberofpricechanges
◦ GallegoandvanRyzin(1994)priceshavetobechosenfromadiscretesetofpossibleprices
◦ ReibsteinandGatignon(1984)pricesofsmallersizescannotbegreaterthanthepriceoflargersizes
◦ Cohenetal(2015)usesrulestoavoidpromotionwearout,9¢priceendings,andconstraintsonthenumberandtimingofpromotions.
18
Conjecture Businessrulesandtheconstraintsonthepricingsolutiontheyimplyareaverypopularfeatureofcurrentpricingsolutions Theproblemisthatthisisanon-Bayesiansolutionsinceconstraintsrepresentaprioriinformationaboutthesolution(eithertocompensateformodelweaknessesortodirectinformationaboutthesolution) Abetterapproach(fromadecisiontheoreticstandpoint)istofollowaconsistentlyBayesianframeworkifwetrulywishtohaveanoptimaldecision.
19
Business Rules constitute Prior Information Anystatementsorconstraintsonoptimalpricesimplicitlyconstitutepriorbeliefs◦ Themanagerholdsthesebeliefsevenbeforelookingatthedata
Optimalpricesarefunctionsofpriceelasticities Therefore,manager’spriorbeliefsaboutoptimalpricesimplypriorsontheparameterspace
PriorbeliefsshouldberepresentedaspriorinformationifwefollowBayesianprinciples Therefore,businessrulesshouldbeemployedapriori
20
Example Considerthefollowingsituation:◦ Apricingmanagerreceivestheoutputfromapricingoptimizationsolution,andthenremarksthatthissolutiondoesn’tlookright—theoptimalpriceshouldnotbemorethan5%higher.
Therearetwopossibilities:◦ Thepricingmanagerhasindependentinformationfromthedata/model(e.g.,wasnotinvolvedintheanalysis)andistryingtocombinetwosourcesofinformation
◦ Thepricingmanagerhasdependentinformationfromthedata/modelandistryingtoinfluencetheposteriorsolutiontoconformtohispriorbeliefs.However,thenaturalsequenceisinverted–posterior/dataàprior
21
Proposed Modeling Process Themulti-productpricingdecisionprocess:
Demand Estimation Price Optimization quantity sold
past prices estimates (elasticities)
optimal prices use prior knowledge efficiently
Demand Model parametric or nonparametric Estimation: bayesian
maxp profit(p|q) No need to impose constraints since all rules already reflected in estimates
22
prior information from business
rules
Creating Informative Priors from Business Rules
23
Practical Problem Bayesianmodelsforceanalyststoformulatepriorsintermsofconjugate(ornon-conjugate)priorsontheparameterswhichrepresentallknowninformation. Themanagerinthepreviouscasepossessesanassessmentaboutoptimalprice—amarginalpropertyofthemodel—nottheparametersofthemodel. Ourproposalistoinferapriorfromthemarginaldistributionbyinvertingthemanager’sassessmentabouttheoptimalpriceintoanimpliedprior.
24
Log-Linear Demand Example Supposequantitydemandfollowsalog-linearmodel,whereqisquantityandpisprice:
Theoptimalprice(conditioneduponparameter)andthecost(c):
Andwehaveabusinessrule:
2log( ) log( ) , ~ (0, )q p Nα β ε ε σ= + +
p* = f (β ) = β
1+ βc
c ≤ p* ≤ τ
25
Change of Variable Solution Moregenerallywecanthinkofouroptimalpriceasafunctionofthepriceelasticity:
Wecantransformbetweentheoptimalpricespaceandthepriceelasticityspaceusinginversefunctions:
Theimpliedpriorcanbecomputedfromachangeofvariablesapproach,whichgivesthedistributionofoptimalprices:
( ) ( )* , where 1 1
p c f c fβ ββ ββ β
= ⋅ = ⋅ =+ +
( )* *
1 1* , where
1p p xf f xc c p x
β − −⎛ ⎞= = =⎜ ⎟ − −⎝ ⎠
* 1 * 2* 1
* * * 2( )( )p
p df p cp p p f pc dp c p c pβ β
−−⎛ ⎞⎛ ⎞ ⎛ ⎞
= ⋅ = ⋅⎜ ⎟⎜ ⎟ ⎜ ⎟− −⎝ ⎠ ⎝ ⎠⎝ ⎠
26
Decision Rules BayesianRulemaximizestheposteriorexpectationofprofits.
Thetraditionalapproach:
ThedifferencebetweenthetwoistheBayesianruleisunconstrained–italreadyincorporatestheinformation,whilethetraditionalapproachintroducestheruleposthoc.
Caution:Pricesusedinthreedistinctcontexts:◦ Observations(Data),OptimalPrice(Distribution),PricefromDecisionRule(Point)
!p = min argmax
pE π p,β( ) | D⎡⎣ ⎤⎦ ,τ⎛
⎝⎜⎞⎠⎟
!p = argmax
pE π p,β( ) | D ,R : p* ∈(c,τ )⎡⎣ ⎤⎦
27
-6 -5 -4 -3 -2 -1 0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Price Elasticity Posterior Distribution
Beta
Density
Bayes
Traditional
28
1.2 1.4 1.6 1.8 2.0
01
23
4
Optimal Price Posterior Distribution
Price
Density
Bayes
Traditional
29
Example Results: Elasticity and Optimal Price Estimates
Rule Price Elasticity Optimal Price Traditional -3.00 (1.00) 1.67
Bayesian -3.29 (0.79) 1.49 (0.18)
Weak Prior on Elasticity, optimal price < $2.00
30
Example Results: Elasticity and Optimal Price Estimates
Rule Price Elasticity Optimal Price Traditional -3.00 (0.71) 1.50
Bayesian -3.57 (0.43) 1.40 (0.06)
Strong Prior on Elasticity, optimal price < $1.50
31
Example 2: Optimal Price Prior with 3 Rules 1) Range ($2.99,$4.99), 2) 9¢ endings, 3) Near $3.19
32
Example 2: Optimal Price Prior with 3 Rules 1) Range ($2.99,$4.99), 2) 9¢ endings, 3) Near $3.19
33
Example 2: Optimal Price Prior with 3 Rules 1) 9¢ endings, 2) Near $2.99, 3) Range ($2.99,$4.99)
34
Example 2: Optimal Price Prior with 3 Rules 1) 9¢ endings, 2) Near $2.99, 3) Range ($2.99,$4.99)
35
Summary Thetraditionalapproachsplitstheproblemintoanestimationandinferencescheme.◦ Businessrulesareusedinanex-postmanner,andiftheyarenotbindingtheyareignored.
TheinferentialapproachisBayesianduringestimation.◦ Heretheoptimalpriceisconstrainedbuttheparameterestimatesarenotchanged.
TheBayesianDecisionTheoreticapproachcombinesestimationandinferenceintoasingletask.◦ Theestimatesfrombothareconsistentandefficient.Informationfrombusinessrulesareusedaprioriandoptimalpricesareunconstrained.
Substantialandpracticaldifferencesamongsttheapproaches.
36
Empirical Example
37
Multivariate Pricing Problem SystemofdemandequationsoverMproducts:
Themanagerwishestooptimizetotalprofitswhenfacedwithknownvariablescosts:
Optimalpricemarginssolvethefirstordercondition: Π = ( pi − ci )E qi⎡⎣ ⎤⎦
i∑
m = −diag(w) ′B( )−1w = −diag(r) ′B( )−1
r
ln(qit ) =α i + ηij
j=1
N
∑ pjt + ξi fit +ψ idit + ε it , ε it ~ N (0,σ i2 )
38
Business Rules Individualpricebounds◦ Optimalpricesarewithin20%ofcurrentprices◦ Alternative:pricesabovecostandlowerthancostx150%
Enforceprice-qualitytiers◦ High-qualitytieraregreaterthannationalbrandprices◦ Nationalbrandpricesaregreaterthanstorebrandprices
p0i
* ≤ pi* ≤ p1i
*{ }
max pA
*( ) ≤ min pB*( ),max pB
*( ) ≤ min pC*( )
39
Posterior Price Coefficients
40
Optimal Prices Tier Product Traditional Bayesian Change
Premium TropPrem64 .0526(.0033)
.0515(.0046)
-2.1%
National TropReg64 .0408(.0027)
.0379(.0033)
-7.1%
National MinMaid64 .0409(.0028)
.0360(.0029)
-12.0%
Store Dom64 .0321(.0022)
.0276(.0029)
-14.0%
TotalProfits: $11,074(2,372)
$7,073(1,135)
-36.1%
41
Findings Treatingbusinessrulesaspriorinformationhasahugeimpacton◦ Parameterestimates◦ Optimalprices◦ Expectedprofitability
42
Conclusions
43
Conclusion Currentoptimalpricingpractitionersandresearchersareintroducinginformationinanadhocmannerbyrelyingupon“businessrules”orconstraints. AnappropriateBayesianmethodiscorrectandefficientandshouldavoidadhoc“corrections”totheposterior.
Thisapproachiseasyandcouldleadtobetterdecisionsupportsystemsthatreflect“expert”knowledgeefficiently.
44
Further Results WehaveembeddedtheoptimizationproblemwithinaMCMCalgorithm,whichgivesageneralapproachforoptimizationunderuncertainty◦ Werelaxthecertaintyofthebusinessrules(perhapsthedatacaninformwhetherthebusinessruleiscorrect)
◦ Sometimesbusinessrulesareusedtotestthemodel(e.g.,ifthemodelgivesstrangesolutionsthenitiswrong)
◦ Relaxtheassumptionaboutfunctionalformandcanlearnitfromthedatausingnonparametrictechniques
45