INSEADIoana Popescu

DPRM3

DYNAMIC PRICING & REVENUE MANAGEMENT

Professor  Ioana Popescu

Session 3: Demand estimation.   Static pricing with constraints.

• Demand estimation: transaction data & survey methods• Static price optimization with budget constraints. • Consumer perception of price

© I.Popescu 2010 DPRM 3

DPRM Overview

Basic Frameworks and tools Industry To do

1. Introduction to revenue management

2. Multi‐pricing in segmented markets Entertainment Poll 1

Demand Estimation & Pricing

3. Static pricing with constraints Adwords/Congestion Group 1

4. Dynamic pricing: markdowns  Retail/Consumer Goods      Strategy

5. Benefit assessment Fashion

Revenue Management

6. Managing risks Airlines/Hotels Poll 2

7. Multi‐resource management Media/Clouds Poll 3

8. RM for price takers Leasing/Transport Group 2

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

This week

The DPRM Process

4. Manage Price

Decisions

5. ManageInventory/Availability

2. Design product line 3. Forecast

demand

1. Segmentthe market

Today

our focus

© I.Popescu 2010 DPRM 3

Some background

• Demand modeling, estimation and forecasting is one of the most important implementation challenges in DPRM practice. Major development and operational time and effort are spent on demand forecasting and estimation

• Industry studies suggest a 20% reduction in forecast error can translate into a 1% incremental increase in revenue (Poelt AGIFORS 1998)

• “Forecasting” often connotes a single‐number, but in DPRM we need entire demand functions, plus information on the degree of demand uncertainty (demand distributions) to make good decisions

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Demand modeling & forecasting within RM 

Forecasting moduleBookingsNo-shows

CancellationsRatings (media)Fares (airlines)

Groups utilizationPrice sensitivity

Transactiondata

Optimization moduleAllocationsBid Prices

Overbooking LimitsMarkdownsPromotions

User interface

Marketdata

Productsdata

Pricingdata

Reservation/salessystem

Manager Analyst Analyst

Un

con

stra

inin

g

Methods for estimating the price‐response function

Sales Data 3rd party data

Surveys/ Experiments

Experts judgements

POS data, loyaltlyprogram data, clickstream data

Panels (ACNielsen)

MIDS (mkt info data tapes – airlines)

Questionnaires, Live experiments

Conjoint

Company experts, Salesforce

Price response estimation methods

INSEADIoana Popescu

DPRM3

Source : Simon-Kucher & Partners

Classification of estimation methods

Internal External

Historical data

Company experts

Sales force

Individual customers

Many customers (>30 per segment)

In-dept interviews 0 + + +

Expert judgment workshops

+ + +

Focus Groups 0

Structured questionnaire

+ + +

Statistical analysis

+ + 0

Choice modeling + +

In-market tests 0 + +

Met

hods

Sources

Dire

ctio

nal

Qua

ntita

tive

+ + = Great …+ = Medium …0 = Limited …approach to gain

insights for identifying profit

opportunity

EDM case – managing an advertising budget

Half the money I spend on advertising is wasted. The trouble is I don’t know which half.

John Wanamaker, retail store owner

INSEADIoana Popescu

DPRM3

Search advertising

Traffic Estimator Data (see EDM.xls file)

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Estimation based on transaction data: EDM

Max CPCb

CPC   C(b)CPD   X(b)

Profit

Σ X(b)*conv.rate* Conv. profit before advertising  ‐ X(b) *C(b)Maximize:

Estimate:

Constraint: Total Cost = Σ X(b)*C(b) ≤ Budget

Decide (for each keyword):

© Prof. Ioana Popescu

Step 1: EDM Data analysis

• Use Google Traffic Estimator data to estimate cost (CPC) & demand (CPD) based on max_CPC bid for each keyword

Wheelchair Rental CPC estimation

y = 0.8424x + 0.011 R2 = 0.999

$-

$0.20

$0.40

$0.60

$0.80

$1.00

$- $0.20 $0.40 $0.60 $0.80 $1.00 $1.20

max CPC

estim

ated

CPC

Wheelchair Rental CPD estimation

y = 14.794x + 3.3162 R2 = 0.9693

0

5

10

15

20

$- $0.50 $1.00 $1.50

max CPC

estim

ated

CPD

INSEADIoana Popescu

DPRM3

© Prof. Ioana Popescu

Step 2: EDM constrained optimization model

• Data :  – volume X(b) &  cost C(b) from traffic estimator data analysis

– conversion rates from historical data

– budget

• Objective:

maximize profit = Σi X(bi)*conv.ratei* $100  ‐ X(bi) *C(bi)

• Decision variables:  b1, b2, b3 [max_CPC for each keyword i ]

• Constraints: Σi X(bi)*C(bi)  ≤ $10 [Total Cost ≤ Budget]

© Prof. Ioana Popescu

EDM summary of historical data

Term Clicks Total Cost CPC Conversions Conversion % Cost Per Conversionrent wheelchair 1024 826.35 0.81$ 11 1.07% 75.12$ rent wheelchairs 2880 2761.94 0.96$ 36 1.25% 76.72$ rental wheelchair 816 730.73 0.90$ 9 1.10% 81.19$ rental wheelchairs 953 946.66 0.99$ 9 0.94% 105.18$ wheelchair rental 5311 4190.64 0.79$ 78 1.47% 53.73$

10984 9456.32 0.86$ 143 1.30% 66.13$

INSEADIoana Popescu

DPRM3

EDM: Multi‐Pricing with Constraints

STEP 1: Forecast demand (CPD) and cost (CPC) based on max_CPC bid for each keyword– build parametric models (data analysis → regression)– non‐parametric models works w/o constraints

STEP 2: Using the forecasted models, set up an optimization model (Solver) to determine bids for each keyword to optimize total profits subject to budget   constraints 

© I.Popescu 2010 DPRM 3

Estimation based on wtp data

• Vertigo

• Kilimanjaro

• London Congestion Charge

INSEADIoana Popescu

DPRM3

Pricing a Kilimanjaro hike

• Data analysis: estimate a demand model based on your data

• Optimization: find the price that maximizes revenue/profit

© I.Popescu 2010 DPRM 3

Parametric estimate based on linear demand (Kili P5)

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Parametric estimate based on linear demand (Kili P5)

Linear demand: d(p)=a‐bpMaximize: Revenue = p (30.55 – 0.0114 p)   ⇒ p*= 1334  

(vs. 900 empirical)

© I.Popescu 2010 DPRM 3

Parametric estimate: log‐linear demand (Kili P3)

Log‐linear demand: d(p)= exp(a‐bp)Maximize: Revenue rate= p * exp(– 0.001p)   ⇒ p*=$ 970

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Parametric estimate based on linear demand (Kili P3)

Linear demand: d(p)=a‐bpMaximize: Revenue rate= p (0.8896 – 0.0005 p)   ⇒ p*= 873  

(vs. 500 empirical)

W illingness to pa y dis tribution

y = -0.0005x + 0.8869R2 = 0.7042

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 500 1000 1500 2000 2500 3000

p r ice

% w

ho b

uy

Revenue

0

2000

4000

6000

8000

10000

12000

14000

16000

0 500 1000 1500 2000 2500 3000price

© I.Popescu 2010 DPRM 3

Parametric estimate: log‐linear demand (Kili P3)

Log‐linear demand: d(p)= exp(a‐bp)Maximize: Revenue rate= p * exp(– 0.0017 p)   ⇒ p*=$ 571

Log-linear wtp model

y = 1.4323e-0.0017x

R2 = 0.9406

0

0.2

0.4

0.6

0.8

1

1.2

0 500 1000 1500 2000 2500 3000price

% w

ho b

uy

Log-linear Demand

y = -0.0017x + 4.0228R2 = 0.9406

-1-0.5

00.5

11.5

22.5

33.5

4

0 500 1000 1500 2000 2500 3000

price

ln(d

eman

d)

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Graphical comparison

|ε|Quan

tity

|ε |

PriceQ

uan

tity

|ε|Quan

tityd=a-bp d=aebpd=apb

PricePrice

Linear Log-linearIso-elastic

a-bp a p−ε a exp(- b p)

log (D) = log(N) – b plog(D) = log(N) – ε log(p)D= N(1‐bp)

© I.Popescu 2010DPRM

Multi‐Pricing with Constraints –Generic Procedure

STEP 1: Forecast price‐response for each segment/product:– parametric model (regression ‐‐ using transaction or survey data)– non‐parametric (ok for setting a single price, or many prices w/o constraints)

STEP 2: Using the forecasts, set up a (usually non‐linear) optimization model (Solver) to determine optimal prices subject to various resource constraints (e.g. budget: EDM, LCC; capacity: Vertigo)

STEP 3: Set prices for each segment according to the model predictions             (the logic:  balance marginal revenues/profits per constrained resource unit)

STEP 4: If changing prices is feasible, go back periodically to STEP 1

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

London Congestion Charge

Revenue - Parametric versus nonParametric estimates

-200,000-100,000

-100,000200,000300,000400,000500,000600,000700,000800,000900,000

1,000,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Parametric Nonparametric

Parametric estimate ‐‐ uniform wtp

               y = ‐0.0942x + 1.2924           R2 = 0.9323

0.00

0.25

0.50

0.75

1.00

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

w

1‐F(w)

D(p)=N(1.29‐0.09p)

Objectives:1. max revenue2. minimize emissions s.t. revenue ≥ 500,000

R(p)=p N(1.29‐0.09p)

Speed(p)       =  30‐.0625*D(p)/1000

Emissions(p)= 616.6‐16.7*speed (if <25)235.7‐1.4*speed (if >25)

© I.Popescu 2010 DPRM 3

Parametric vs. nonparametric estimates

• Parametric estimate

– Assume demand model defined by a modest number of parameters

– Estimate the parameters from data

• Demand is linear: D(p) = a ‐ bp

• Demand is N(μ , σ)– Pros: Concise description; can extrapolate beyond observed history; optimization

– Cons: Makes assumptions on form of response that may not be valid

• Nonparametric estimate

– Use the raw data directly to estimate demand without making assumptions on the functional form of the relationships

• Empirical histogram of demand volume

• Empirical histogram of reservation prices

– Pros: No assumptions; uses values actually observed

– Cons: Subject to “noise” in data; can’t extrapolate beyond history; hard to optimize

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Two broad strategies for estimation/forecasting• Bottom‐Up Forecasting

– Start with forming detailed models (“sub‐forecasts”)

• Individual customers; Segments; Locations; Channels

– Aggregate these sub‐forecasts into an overall forecast of demand

– Good at capturing detailed demand effects like difference in preferences across 

segments, locations and channels

• Top‐Down Forecasting

– Start with high‐level model of aggregate demand (“super‐forecast”)

– Disaggregate this super‐forecast to form estimates of demand by channel, product, 

location, etc.

– Good at capturing aggregate demand effects like seasonality, trends, etc.

Often in practice both strategies are used simultaneously

© I.Popescu 2010 DPRM 3

Extensions: Multi‐product demand & choice• So far customers faced a binary choice: to buy or not to buy. • What if they have multiple alternatives?

• Examples:– Multiple versions of a product (Vertigo part 3)

– Competing products/brands

– Choice of time periods

• Two approaches:

1. Multi‐product demand functionsThis can be estimated by regressing demand of each product against the 

price of both products 1 and 2 (multiple regression) 

D1(p) = a1 – b11 p1 + b12 p2 D2(p) = a2 + b21 p1 ‐ b22 p2

2. Discrete choice models based on utility max (multinomial logit ‐‐MNL)

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Resto menu prices

Menu A: €25 Menu B: € 35 Menu C: €40

© I.Popescu 2010 DPRM 3

Extremeness Aversion

Extremeness aversion (or Goldilocks pricing) : Add a high‐end version to your product line: people will trade‐up

Examples: restaurant menus, Carrefour champagne, electronics

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Online ad for the Economist a few years ago

• The Economist annual subscription options:

‐ Economist.com website only: $59‐ Print edition only: $125‐ Print edition PLUS website access: $125

16%0%84%

68%

32%

Asymmetric dominanceSegmentation: create value or the perception of value

© I.Popescu 2010 DPRM 3

Customer perception of prices

– Choice: extremeness aversion & asymmetric dominance– Framing & anchoring

– Reference prices & Endogenous expectations

– Fairness : prospect theory & dual entitlement

INSEADIoana Popescu

DPRM3

© I.Popescu 2010 DPRM 3

Summary  – session 3

• Need to estimate parametric price response models (regression vs. raw/non‐parametric models) as input for price  optimization (solver)

• Demand / price‐response estimation sources:

– Transaction data (most reliable)– Survey (willingness to pay, choice) data

• Different models will give different results: decision support only

• Combine data with judgment:– Understand consumer behavior (more to come)

© I.Popescu 2010 DPRM 3

Next time: markdown management  

• The Retailer simulation (see website) 

– read the case + task  (in the course‐pack)– Understand the data file

– Play with the simulation ‐‐ available on all INSEAD desktops 

– Prepare a group  strategy

• Think how you would assess revenue impact (Bloomingdales)

• Groups will compete in class – there will be a Prize!

• Winner will present strategy to the class 

• The simulation might not work on your laptop (see web for details …)