Managing Customer Relationships Through Price and Service QualityAgendaAgendaIntroductionGeneral contextAgendaService quality encountered and expectedInteractions modelRate of the interaction with the customerDynamic of customer-company interactionsResultsAgendaAggregate customer behaviorMarkov process representationState transition probabilitySystem behavior in steady stateCustomer response to a change in the service qualityNumerical experimentIntuitive explanationCustomer response to a change in the company pricing policyNumerical experimentIntuitive explanationAgendaProblem descriptionSolving and interpretationConclusionManaging Customer Relationships Through Price and Service Quality By: Gabriel BitranPaulo Rocha e OliveraAriel SchilkrutPresenter: Adrien de Chaisemartin04/22/2004This 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 descriptionz Individual customer behaviorz Aggregate customer behavior| System behavior in steady state| Profit optimizationAgenda| Problem raised by the paper| Model descriptionz Individual customer behaviorz Aggregate customer behavior| System behavior in steady state| Profit optimizationIntroduction| Imagine that you are a computer hotline…z People call you when they have questions about their computersz They pay for this service| You want to increase your profit, which parameters can you adjust?z Price of the service z Number of people who answer the questions (“service quality”)| How do you play on these parameters? z Decreasing price and increasing service quality can augment the number of customer and increase my profit| But…z More customers can lead to more delays and thus more customers who defectz Lower price can lead to less profitsGeneral context | Subscription-based, capacity-constrained service| Customers choose the depth of their relationship with the company based on their level of satisfaction| Pricing and service quality affect this level of satisfaction| The intuitive reasoning: | But sometimes:Service qualityPricingCustomer base and profitService qualityCustomer basePriceprofitComplex relationship between pricing, service quality and profitabilityAgenda| Problem raised by the paper| Model descriptionz Individual customer behaviorz Aggregate customer behavior| System behavior in steady state| Profit optimizationService quality encountered and expectedi1Customers interact with the company whenever they choose to do so evolves with:(1 )x is a random variable with distribution F(x| )kkkk kkkkwww wwFαα−=+−=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)suppRate of the interaction with the customer()i()iCustomers use the service at the rate : (level of satisfaction, )Utility of customer: ( ( ) ) ( )Customers will renew their subscription when:() () 0 with () ()uuuspvpcwTpcwp cwcxdFxηηηηυη η−+⎡⎤−− −> =⎣⎦i()i()()i()i()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: ; , , ( )su u ssuwbppF T p cw pbbppF bbηηυηηηη∞⎡⎤⋅= − − −⎣⎦=⋅= <∫Dynamic of customer-company interactions(See Figure 2 on page 10 of the Bitran, et al. paper)Results***Monotonocity of customer's usage rate: with with c with Monotonocity of the customer's utupwηηη2/2/2/***ility: b with and b with c b with The company can use as a concrete and manageableusppww2/2/2/*measure of customer utility bAgenda| Problem raised by the paper| Model descriptionz Individual customer behaviorz Aggregate customer behavior| System behavior in steady state| Profit optimizationAggregate customer behavior*min*max max minCustomers stay with the company if b bThat corresponds to with b ( ) bWe can construct a Markov process where each state is described by the number of previous interactions and thww w≥≤= [][][][]max 1 1 2e 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 thsswwululu=∪∪[]e k th interaction, ;iiwlu∈Markov process representation(See Figure 3 on page 14 of the Bitran, et al. paper)State transition probability| Recall that:| In term of probability:Where F is the true distribution of the company service quality| If we assume that is uniformly distributed in [li; ui] then:w1(1 )kkk kkww wαα−=+−ii1(1 ) (1 )Pr( | ) Prkkkkkkkxyxywxwy w Fαααα+⎛⎞⎛⎞−− −−≤== ≤ =⎜⎟⎜⎟⎝⎠⎝⎠ii11(1 ) (1 )Pr( | )iiiiiuujk jkkkkij j j ikklluy lypl w u w I F dy F dyαααα+∆⎡⎤−− −−⎛⎞⎛⎞=≤≤ ∈= −⎢⎥⎜⎟⎜⎟⎢⎥⎝⎠⎝⎠⎣⎦∫∫System behavior in steady state| 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 companyii{}11 *min:with : ( )ikkkjiji i iiI IpIIIwIbwbλλ−−∈⎡⎤⎡ ⎤==∈∈→≥⎣⎦⎣ ⎦∑ Customer response to a change in the service quality ,kjj,kjLet the total service demand rate: with WBUT...There is no such rule for the total number of customers N( ie: N calculated with N= )kiikλλλλλη=∑∑2/Numerical experiment(See Figure 4 on page 18 of the Bitran, et al. paper)Intuitive explanation| As the service quality decreases, the probability that the customer leaves the company increases. At the same time his number of interactions decreases| Let’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 increaseE (length of stay)=E (total number of interaction) x (Average interval between interaction)Decrease with a lower service quality Increase with a lower service qualityCustomer response to a change in the company pricing policymax and affect directly which in turn affects .For a higher price,