managing customer relationships through price & service quality customer choice models -...

Managing Customer Relationships Through Price and Service Quality

By: Gabriel BitranPaulo Rocha e OliveraAriel Schilkrut

Presenter: Adrien de Chaisemartin

04/22/2004

This summary presentation is based on: Bitran, Gabriel, P. Rocha e Oliveira, and A. Schilkrut. "Managing Customer Relationships Through Price and Service Quality." MIT Sloan School of Management, 2003.

Agenda

Problem raised by the paper

Model descriptionIndividual customer behaviorAggregate customer behavior

System behavior in steady state

Profit optimization

Introduction

Imagine that you are a computer hotline…People call you when they have questions about their computersThey pay for this service

You want to increase your profit, which parameters can you adjust?Price of the service Number of people who answer the questions (“service quality”)

How do you play on these parameters? Decreasing price and increasing service quality can augment the number of customer and increase my profit

But…More customers can lead to more delays and thus more customers who defectLower price can lead to less profits

General context

Subscription-based, capacity-constrained serviceCustomers choose the depth of their relationship with the company based on their level of satisfactionPricing and service quality affect this level of satisfactionThe intuitive reasoning:

But sometimes:

Service qualityPricing

Customer base and profit

Service quality Customer base

Price profit

Complex relationship between pricing, service quality and profitability

Agenda




Profit optimization

Service quality encountered and expected

1

Customers interact with the company whenever they choose to do so evolves with:

(1 )

x is a random variable with distribution

F(x| )

k

k k k k k

kk

ww w w

w F

α α −= + −

=

Interactions model

[ ] subscription fee to have access to the service

during a period pT; (p+1) T usage fee. To be paid each time the service is used

(See Figure 1 on page 9 of the Bitran, et al. paper)

s

u

p

p

Rate of the interaction with the customer

( ) ( )

Customers use the service at the rate : (level of satisfaction, )Utility of customer: ( ( ) ) ( )

Customers will renew their subscription when:

( ) ( ) 0 with ( ) ( )

u

u

u s

pv p c w

T p c w p c w c x dF x

η ηη

η υ η η

− +

⎡ ⎤− − − > =⎣ ⎦ ( )

( ) ( ) ( )

( )

0

*

* *min

|

We can then define b, the expected net utility per unit of time:

; , , ( ) ( ) ( )

The customer will choose arg max( )

And he will defect whenever: ; , , ( )

s u u s

s u

w

b p p F T p c w p

b

b p p F b b

η η υ η η

η

η

∞

⎡ ⎤⋅ = − − −⎣ ⎦=

⋅ = <

∫

Dynamic of customer-company interactions


Results

*

*

*

M onotonocity of customer's usage rate: with

with c with

M onotonocity of the customer's ut

up

w

η

η

η

*

*

*

ility: b with and

b with c b with

The company can use as a concrete and manageable

u sp p

w

w*

measure of customer utility b

Agenda




Profit optimization

Aggregate customer behavior

*min

*max max min

Customers stay with the company if b bThat corresponds to with b ( ) b

We can construct a Markov process where each state is described by the number of previous interactions and th

w w w≥

≤ =

[ ] [ ] [ ] [ ]max 1 1 2

e customer's current level of satisfaction represented by .To discretize the set of level of satisfaction we use:I= 0; 0; ; ... ;

The states of theMarkov process are (i,k) where after th

s s

w

w u l u l u= ∪ ∪

[ ]e k th interaction, ;i iw l u∈

Markov process representation


State transition probability

Recall that:

In term of probability:

Where F is the true distribution of the company service qualityIf we assume that is uniformly distributed in [li; ui] then:w

1(1 )k k k k kw w wα α −= + −

1(1 ) (1 )Pr( | ) Pr k k

k k kk k

x y x yw x w y w Fα αα α

+⎛ ⎞ ⎛ ⎞− − − −

≤ = = ≤ =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

11

(1 ) (1 )Pr( | )

i i

i

i i

u uj k j kk

k kij j j ik kl l

u y l yp l w u w I F dy F dy

α αα α

+ ∆

⎡ ⎤− − − −⎛ ⎞ ⎛ ⎞= ≤ ≤ ∈ = −⎢ ⎥⎜ ⎟ ⎜ ⎟

⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦∫ ∫


Now that we know how the customers react to the decisions of thecompany, we can calculate the number of customers who pay the subscription fee and the service demand rate from customers to the company

{ }1 1 *min

:

with : ( )i

k k kj ij i i i

i I I

p I I I w I b w bλ λ− −

∈

⎡ ⎤ ⎡ ⎤= = ∈ ∈ → ≥⎣ ⎦ ⎣ ⎦∑

Customer response to a change in the service quality

,

kj

j,k j

Let the total service demand rate:

with W

BUT...There is no such rule for the total number of customers N

( ie: N calculated with N= )

ki

i kλ λ λ

λ

λη

= ∑

∑

Numerical experiment


Intuitive explanation

As the service quality decreases, the probability that the customer leaves the company increases. At the same time his number of interactions decreasesLet’s study the effects of this on the length of stay:

The length of stay can thus increase with the decrease of service quality and thus make the number of customer increase

E (length of stay)=E (total number of interaction) x (Average interval between interaction)

Decrease with a lower service quality Increase with a lower service quality

Customer response to a change in the company pricing policy

max and affect directly which in turn affects .For a higher price, customers expect a better service

Consequently: with and

BUT...There is no such rule for the total number of custom

u s

u s

p p w

p p

λ

λ

ers N

Numerical experiment


Intuitive explanation

Based on the monotonicity of η*, the increase of pu will produce an increase in the time between customer interactionsBut at the same time, the increase of pu will make the criteria for staying in the company more strict and thus the number of interactions will decreaseThere is therefore no direct relation between the length of stay and pu, and consequently, no direct relation between N and pu

On the other hand : swith pN

Agenda




Profit optimization

Problem description

Revenue:

Cost:

Thus we have the following nonlinear program to solve:

Such that:

u sR p Npλ= +

( , )C Wλ

max ( , )u sp Np C Wλ λΠ = + −( , , )( , , )

0

u s

u s

g p p WN h p p WW

λ =

=

≥

Solving and interpretation

Using the Lagrange multipliers we obtain the equations:

(See equations 12, 13, and 14 on page 14 of the Bitran, et al. paper)

Those equations equate marginal revenue with marginal costsEach of them can be decomposed into several intuitive parts

Conclusion

This paper gives the analytical tools to understand the complex relation between pricing policy, service quality and customer base and behaviorThe main originality of this paper is the introduction of this factor of relation depth: ηPrincipal criticism: the paper does not take into account the fact that there is a difference between subscribing to the whole period and subscribing for one interaction. At the end of each period, even if the customer had been satisfied enough to make another interaction, he could decide that overall the service is not good enough to pay for another whole period

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