A Quality Value Chain Network: Linking SupplyChain Quality to Customer Lifetime Value*

Qiuping YuKelley School of Business, Indiana University, qiupyu@indiana.edu

Masha ShunkoFoster School of Business, University of Washington, mshunko@uw.edu

Shawn MankadJohnson Graduate School of Management, Cornell University, spm263@cornell.edu

We create a quality value chain network concept to analyze the impact of supply chain quality (SCQ) on

the customer lifetime value (CLV). We apply our framework to a rich dataset from a major restaurant

chain utilizing text analysis of the complaints to measure SCQ, a two-stage least squares (2SLS) model with

instruments to assess the impact of SCQ on customer experience, and a structural model of consumer pur-

chasing behavior to eventually link customer experience to CLV. Note that we consider not only the impact

of customer experience at the focal store but also that from adjacent stores on CLV. Considering such net-

work effect significantly improves the model performance in predicting customer behavior and quantification

of financial returns. We identify the profile of the most valuable customers and provide insights on which

SCQ issues the supply chain should focus on, and which restaurants should be prioritized for supply chain

improvements.

1. Introduction

According to the Forrester report on customer life-cycle marketing, 72% of surveyed companies

list customer experience improvement as their number one priority (Forrester 2016). Customer

experience improvements, ranging from improving general product and service delivery to providing

customized campaigns and services for individual customers, can lead to increased customer loyalty

and higher revenues. According to a McKinsey & Company study (Shital Chheda and Roggenhofer

2017), a successful improvement has to focus not only on the front-end touch-points but also on

back-end operations and processes to be sustainable. One of the earlier conceptual frameworks in

the literature that links internal operational processes to customer satisfaction, loyalty and thus

profitability is the service profit chain framework proposed by Heskett and Schlesinger (1997). This

framework focuses on a firm’s internal service attributes such as employee quality and satisfaction.

Anderson and Mittal (2000) extend this chain framework to include both product and service

attributes, which they refer to as a satisfaction profit chain.

The idea of a profit chain was originally developed within the boundaries of one firm. In practice,

firms rarely operate in isolation, and many firms rely on their supply chain to provide products

* This paper is supported by the National Science Foundation under Grant No. 1633158

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or services. In many cases, firms may carry a brand name (e.g., Starbucks, McDonalds) such that

customer experience provided by one firm may affect customer perception of the quality of another

firm that carries the same brand name (see Figure 1). We enrich the classic profit chain concept

through two dimensions: (1) We extend the service profit chain upstream to include the supply

chain attributes that may have a direct impact on the product/service attributes that, in turn, have

their impact on customer experience; and (2) We include customer experience at all firms that carry

the same brand name to address potential competition and/or reputation spillover effects. Several

profit chain studies have included multiple firms or outlets in the profit chain framework (Bowman

and Narayandas 2004, Loveman 1998). To the best of our knowledge, however, our framework is

broader than the previous works on the profit chain and appears to be the first that considers all of

the stages in the supply chain and includes manufacturers, distributors, and a network of retailers

and their individual end consumers. Our study is also more granular than the previous value chain

studies and appears to be the first value chain study that differentiates the impact of customer

experience on their purchasing behavior at the individual customer level. Moreover, unlike most

of the value chain studies, we consider not only customers’ current purchasing behavior but also

their future purchasing behavior by measuring customer lifetime value (CLV). From the application

perspective, our paper appears to be the first comprehensive value chain study using field data

from a major fast food restaurant chain. It generates numerous unique managerial insights as we

elaborate below.

The extended profit chain framework, which we refer to as the quality value chain network,

can be used to create value from the individual firm’s perspective, the brand’s perspective, and

the supply chain orchestrator’s perspective. Given that supply chain operations are not directly

observable to customers, we propose a two-phase methodology to link the supply chain quality to

the CLV (see Figure 1). In the first phase, we identify how the supply chain can create value for

customers by improving supply chain quality, which can lead to an improved customer experience.

In the second phase, we identify how increased customer experience at all firms within the brand

creates future value for all supply chain players by increasing CLV. This methodology provides

numerous managerial insights. For the firms, it identifies customers who have the highest response

to customer experience improvement, allowing the firms to target their campaigns. For the supply

chain, it identifies which supply chain quality issues have the biggest impact on customer experience

and, thus, on the CLV, allowing supply chain management to focus on the most critical issues.

Meanwhile, we identify firms that have the highest response to customer experience improvements,

allowing the supply chain to create tailored supply chain management strategies that lead to

profit maximization via prioritizing the right firms with the right customers and the right network

features. A recent McKinsey & Company study (Maynes and Rawson 2016) notes that many

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Figure 1: The supply chain network under consideration consists of multiple firms that carry thesame brand name such that operations of one firm may affect the customer behavior at anotherfirm through brand reputation.

customer experience initiatives fail due to companies’ inability to link particular initiatives to

generated value and to a lack of focus on the initiatives that bring the highest return. Our framework

and two-phase methodology, as described above, help to address these common practical issues in

the industry.

We apply our methodology to a large dataset from the fast-food industry, namely, a national

restaurant chain that operates multiple franchises in different locations that carry the same brand

name. In the first phase, our focus is on how supply chain can create valuable customer experi-

ence. Customer experience is affected by multiple dimensions; in our application, an important

determinant of customer experience is the quality of served food. Kim et al. (2009) studied the

impact of various product and service components on customer satisfaction in dining facilities at

public universities using web surveys of students and found that food quality was the most impor-

tant predictor of customer satisfaction and of intent to return. Hwang and Zhao (2010) made

similar observations and identified food quality and taste as one of the main drivers of customer

satisfaction.

Because food quality depends largely on the management of supply chain quality (e.g., quality

and timeliness of delivered ingredients), we analyze the impact of different dimensions of supply

chain quality on customer experience to inform the firm as to which aspects of supply chain quality

are critical to improving customer experience. In our data sample, all restaurants are serviced by

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the same distributor and the same set of suppliers; hence, the quality of the distributor (e.g., dis-

tributor’s overall fill rate) is fixed at the distributor level. The quality of the distributor-restaurant

link, however, may differ for each restaurant as it depends on many factors, (e.g., distributor’s

prioritization rules, relationship between the distributor and the restaurant, the distance between

the distributor and the restaurant, experience of the restaurant manager). Thus, we consider the

supply chain quality from each restaurant’s perspective.

We conduct a text analysis of the complaints filed by restaurants against their distributors and

suppliers to extract information about supply chain quality. Through manual examination of a

training set of complaints, we identify three main supply issues — Freshness, Packaging, and

Delivery — and their associated keywords. We then use the Latent Dirichlet Allocation topic

model to refine the keywords and to categorize our complaints according to these three issues. We

then evaluate how each of these issues affects customers’ experience in the downstream restaurants,

using a linear regression model that accounts for the potential endogeneity issues. Our results show

that issues related to Freshness have the largest impact on customer experience among all supply

chain issues. In particular, we find that reducing one complaint related to Freshness per month can

improve the customer experience score by about 0.44 (on a scale from 0 to 10). In our application,

most complaints related to Freshness are associated with over-ripeness of products and come from

one supplier, proposing an immediate managerial action to improve handling and reduce lead time

on products from the particular supplier.

In the second phase, we explore how customer experience with a network of restaurants affects

CLV at a focal restaurant. Note that customers’ decision to stay engaged with a restaurant that they

visited may depend not only on their experience at this focal restaurant but also on the reputation

of the brand and/or customer experiences at other locations that carry the same brand name. For

example, customers may be more likely not to come back to the visited restaurant if the overall

customer experience of the adjacent outlets of the same brand is higher; hence, customers may

prefer to go to a better location. We refer to this phenomenon as the competition effect. In contrast,

given that all of the restaurants share the same brand name, good overall customer experience of

adjacent restaurants may improve the reputation of the brand and customers will be more likely to

keep coming to the visited focal restaurant. We refer to this effect as the reputation spillover effect.

We combine the two effects into the network effect. If better overall customer experience at adjacent

restaurants reduces customers’ churn rate at the focal restaurant, the network effect is positive,

and the reputation spillover effect dominates. Otherwise, the network effect is negative, and the

competition effect dominates. Customers’ perception of the quality of the neighboring restaurants

may be acquired through one or both of the following channels: word-of-mouth through friends and

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family, or personal experience (e.g., personal visits to the adjacent stores). We build our model in

a way that allows us to separate the network effects by channel.

In our setting, restaurants have a non-contractual relationship with their customers. Thus,

restaurants cannot directly observe whether customers have churned, i.e., stopped engaging with

the restaurants, nor can restaurants observe the latent arrival process of the churned customers,

had they not churned. To uncover the latent information about customers’ churn rate and arrival

process and, thus, to measure CLV, we propose a latent attrition model that is a variation of the

BG/NBD model (Fader et al. 2005a). Our latent attribution model extends the BG/NBD model

to account for the impact of customer experience reported in all of the restaurants in the network

in regard to customers’ purchasing decisions. We show that both customer experience at the focal

store and the perceived neighbor quality have a significant impact on customers’ purchasing deci-

sions. Incorporating the perceived neighbor quality in the model significantly improves the model

performance, both in its goodness-of-fit and forecasting accuracy. We show that better overall

perceived neighbor quality reduces customers’ churn rate at the focal store regardless of whether

the customers have visited the adjacent stores, which implies that the network effect is positive

and that the reputation spillover effect dominates the competition effect. We also show that the

reputation spillover effect is even stronger relative to the competition effect for customers who have

visited the neighbor stores than for those who have not.

Through counterfactual studies, we demonstrate how each individual restaurant and the supply

chain orchestrator can use our two-phase methodology and results to prioritize investment in

customer experience and supply chain improvements to maximize their return on investment (ROI).

Note that, for each individual customer, our latent attribution model in the second phase allows us

to quantify the exact incremental number of future transactions that the customer can generate at

the focal store if her experience at the focal store improves. We show that the incremental number

of future transactions is the highest among the customers whose last visit to the restaurant was

neither too long ago nor too recent and whose number of total transactions with the firm is neither

too high nor too low. Hence, firms should focus their customer experience improvement initiatives

(e.g., targeted campaigns) on the customers who fit the profile above. From the supply chain

orchestrator’s perspective, we note that improving the supply chain quality for a focal restaurant

not only generates additional number of transactions at the focal restaurant, but may also lead

to more sales at the adjacent stores due to the network effect. The supply chain orchestrator thus

should prioritize the supply chain improvement for the store that can generate the largest total

incremental number of transactions in the entire network of restaurants. In particular, we show that

the supply chain orchestrator should prioritize the restaurants that have high quality neighbors and

a high percentage of customers with the profile identified above. It is worth noting that a recent

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Forbes report suggests personalization of service as one of the top ten trends in improving customer

experience in 2017 (Hyken 2016). The results of our study help companies to design personalized

marketing or operational campaigns in both business-to-business (B2B) and business-to-customer

(B2C) settings, as we describe above.

2. Literature Review

We study the impact of supply chain quality on customer experience and consequently, on the

CLV accounting for the network effect among multiple firms. To this end, our research is related to

several streams of literature: quality and profitability, customer lifetime value, quality competition,

and supply chain quality.

Quality and Profitability. Heskett and Schlesinger (1997) developed the service profit chain

framework that established a chained relationship between service quality, customer satisfaction,

customer loyalty, and eventually, financial growth and profitability. The satisfaction profit chain

framework extends the service profit chain by including performance attributes beyond service

attributes (Anderson and Mittal 2000). Empirical studies that support each of these links are seen

in the literature. We refer interested readers to Zeithaml (2000) and, more recently to Kumar et al.

(2013) for an extensive review. A number of recent empirical works in the operations management

literature also have examined the impact of quality on customer behavior or sales (Aksin et al.

2013, Batt and Terwiesch 2015, Cachon et al. 2013, Kesavan et al. 2014, Lu et al. 2013, Musalem

et al. 2016, Tan and Netessine 2014, Yu et al. 2017), and the impact of loyalty on growth in the app

economy (Mendelson and Moon 2017). For the link between customer satisfaction and behavior,

although there are several studies that report a significant positive relationship (Bolton 1998), some

studies show that satisfaction has no significant impact on customer loyalty (Verhoef 2003). Based

on the reality of marketplace practices, the link between satisfaction and profitability also seems to

be weak (Kumar et al. 2013). Most of the research in this stream, however, does not differentiate

the impact of customer satisfaction across different customers, which could lead to large variance

and a seemingly weak overall relationship between customer satisfaction and profitability. Kumar

et al. (2013) explicitly call for research that systemically explores how customer satisfaction or,

more broadly, experience affects profitability differently for different customers, which will allow

firms to focus on customers who have the highest response to experience and, thus, improve the

return on investment.

Our paper research fills this gap by investigating how customer experience affects CLV differ-

ently for customers with different transaction patterns. Not only does our approach appear to be

much more granular in capturing the heterogeneous impact of customer experience across different

customers compared to the previous works in profit chains, but our framework also is broader

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and appears to be the first to consider all of the stages in the supply chain, including suppliers,

distributors, and a network of retailers and their end consumers. From the application perspective,

our work appears to be the first comprehensive value chain network study that uses field data from

a major fast-food restaurant chain. It generates numerous unique managerial insights.

Customer Lifetime Value. The CLV metric is a forward-looking metric that takes into account

the dynamic nature of customer behavior and allows firms to develop personalized strategies for cus-

tomers of different transaction patterns to maximize return on investment. It is generally acknowl-

edged that CLV is a preferred metric to measure customers value to the firm as compared to other

metrics (such as past profitability or customer churn rate) (Kumar and Reinartz 2016). Multiple

approaches for calculating CLV have been proposed. We focus on the ones for non-contractual

settings, as it is for our application, whereby the firm does not directly observe the times when

customers churn. One of the earliest models known as the Pareto/NBD model of Schmittlein et al.

(1987) serves as a building block for many follow-up models. To simplify the model estimation,

Fader et al. (2005a) proposed the BG/NBD model, which allows customers to become inactive only

immediately after a purchasing transaction rather than at any point in time (as it is in Schmit-

tlein et al. (1987)). This simplification significantly reduces the computational time required for

estimation. One of the limitations of these frequently used latent attrition models, including the

Pareto/NBD and BG/NBD models, is the lack of accounting for the impact of attributes, such as

quality or customer experience, on CLV.

Ho et al. (2006) extend the above latent attrition models by proposing an analytical model

that accounts for the impact of customer satisfaction in CLV in non-contractual settings. Aflaki

and Popescu (2014) also explore the impact of service quality on CLV analytically. The authors,

however, focus on a contractual setting and incorporate observations from behavioral theories in

their model. Afeche et al. (2015) extend the works above by considering the capacity constraint

whereby the service quality is a function of the allocated capacity. While all of the works above

are analytical, Braun et al. (2015) extend the BG/NBD model in an empirical study in which

they explore how service quality affects CLV, using data from an online marketplace for freelance

writing services. The service quality in their study is measured by a panel of reviewers hired by

the firm. In our application, however, we focus on customer experience as reported by customers

themselves via an online consumer survey. According to Parasuraman et al. (1985), there is a sig-

nificant gap between self-reported customer experience and quality metrics estimated internally by

the firm. In the customer relationship management literature, service quality is generally consid-

ered an antecedent of customer satisfaction or experience (Cronin Jr and Taylor 1992). The link

between customer experience and purchase intention is often much stronger than that between

service quality and purchase intention. This may explain why including the service quality does not

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significantly improve the goodness of fit of the model or its forecasting accuracy compared to the

base model without service quality in Braun et al. (2015), while it does significantly improve the

model performance by including customer experience in our case. Knox and van Oest (2014) study

the impact of customer complaints and firm recoveries on customer future purchasing behavior

using data from an Internet and catalog retailer. The analysis in both Braun et al. (2015) and Knox

and van Oest (2014) is limited to one firm. We take one step further by exploring how customer

experience in a network of firms affects CLV at the focal store, for which we explicitly account

for the potential competition and reputation spillover effect across different firms in the network.

Our results show that it is important to include the network effect in the customer purchasing

model, as it significantly improves the model performance in terms of both its goodness of fit and

its forecasting accuracy. We show that the reputation spillover effect dominates the competition

effect among the firms in the same neighborhood that share the same brand name. By accounting

for such network effect, we can quantify the total ROI from improving the supply chain quality

of a focal firm in a more holistic manner. In particular, we can quantify not only the associated

incremental value generated at the focal firm, but also the significant amount of incremental value

generated at the adjacent firms through the network effect. Without accounting for the network

effect, the supply chain orchestrator would have underestimated the ROI from improving the sup-

ply chain quality of a focal firm. To this end, our work is also related to the literature on quality

competition.

Quality Competition. There has been a stream of analytical papers (Aksoy-Pierson et al. 2013,

Allon and Federgruen 2009, Cachon and Harker 2002, Cohen and Whang 1997, Gans 2002) that

explore the impact of quality competition on customer behavior and equilibrium outcomes. More

recently, there is an emerging body of empirical research on quality competition. For example, Allon

et al. (2011) empirically study how waiting time performance affects different firms’ market shares

and price decisions using firm level data from the hamburger drive-through fast-food industry.

The authors show that, in the fast-food industry, customers trade off price and waiting time and

attribute a very high cost to the time that they spend waiting. Moving beyond waiting time as

a proxy for service quality, Guajardo et al. (2015) empirically study how service and product

attributes affect customer demand in the presence of competition using product-level monthly sales

data from the US automobile industry. One of their main findings is that service attributes, which

jointly determine service quality, become more important in determining consumer demand when

products exhibit lower quality. Buell et al. (2016) empirically examine the relationship between

the level of service quality competition and customer defection rates, using customer level data

from the retail banking sector over a five-year period. They find that the level of service quality

competition affects customer defection from an incumbent firm to a competitor, and that the

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impact is moderated by whether the incumbent firm has a high or low service quality position in

the market. Note that none of the works above considered the impact of quality on customers’

future behavior or account for the potential different impact of quality across different customers

at an individual customer level. We fill this gap and contribute to this stream of literature by

looking at a network of firms that can jointly affect CLV. Our approach not only allows each firm

to identify the customers with the highest future incremental value from their improved experience

in a B2C setting but also allows the supply chain orchestrator to identify the firms that generate

the highest return on investment from their supply chain quality improvement in a B2B setting.

Supply Chain Quality. There are multiple approaches and frameworks for assessing the per-

formance of supply chains. Kaynak and Hartley (2008) summarize the literature on quality mea-

surement and frameworks within the supply chain context. In our study, we focus on the attributes

that have a direct impact on the availability and taste of the menu items at the restaurant: fresh-

ness of delivered products, timeliness of delivery, and packaging. Coyle et al. (2008) list on-time

delivery and quality of delivered goods as the top two supply chain performance attributes used

in real industry practice. Our attributes also are among the top attributes identified for supplier

quality in Bowman and Narayandas (2004) and Lehmann and O’shaughnessy (1974). It is worth

noting that Bowman and Narayandas (2004) adapt the service profit chain framework in the B2B

market. The authors explore how vendor effort affects vendor quality and, thus, business buyers’

satisfaction, and eventually, vendor’s profitability from its business buyers.

We enrich this framework by extending it to include individual end consumers. Moreover, in

our analysis, we systematically identify the causal relationship between supply chain quality and

customer experience, using novel instrumental variables, while the links in Bowman and Narayandas

(2004) are demonstrated mostly through correlations. Beyond the profit chain framework, there

is a substantial body of analytical research that explores the impact of supplier quality measured

by various metrics (i.e., inventory availability, delivery time, and product quality) on customer

behavior or aggregated demand (Cachon and Lariviere 2001, Cohen and Whang 1997, Gans 2002,

Olsen and Parker 2008). There also are recent empirical studies that explore the impact of supplier

quality on a firm’s behavior in B2B settings with a focus on inventory availability, e.g., Craig et al.

(2016).

3. Empirical Setting and Data Description

We describe our framework while applying it to a nationwide restaurant chain in the United States

that operates multiple franchise outlets that carry the same brand name. Each outlet operates as

an independent firm. The dataset acquired through the Wharton Customer Analytics Initiative

(WCAI) captures customer transaction data, customer responses to the satisfaction survey and

supply chain data.

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3.1. Customer Transaction and Survey Data

Recall that the main objective of our study is to explore the impact of supply chain quality on

customer experience and thus eventually on CLV. To eliminate the potential effects of confounding

variables and to control for factors that are external to supply chain quality or customer experience,

but may affect customers’ purchasing behavior, we focus on four ZIP-code areas that have the high-

est number of restaurants that carry the brand name and that have similar demographic profiles.

Thus, selection of the sample will control for, among other variables, market heterogeneity, which

could confound our analysis due to different levels of brand presence, and customers’ heterogeneity

due to different demographics. All four ZIP-code areas are in the same city and include in total

36 restaurants that carry the brand name of interest in these areas. To better measure customer

experience in the restaurants, we select 28 restaurants that have at least 50 completed customer

surveys.1 These restaurants received, on average, 265 survey responses (full summary statistics are

provided in Table 2).

For customers who pay with a credit card or have a loyalty account, we observe customers’ trans-

actions over time through their unique customer ID and we limit our attention to such customers.

To this end, we sampled 3,000 such customers in total from the selected restaurants. For each

selected customer, we then extract all of their transactions at any restaurant that carry the same

brand name even if it is outside of the 28 selected restaurants. For each transaction, we observe

the corresponding transaction ID, customer ID, restaurant ID, transaction time, and transaction

amount. Among the selected restaurants, on average, customers make 2.2 visits to one restaurant

during the observation window of July 1, 2013 to July 2, 2015 with the number of visits ranging

from 1 to 75.

All customers are invited to complete an online customer satisfaction survey following each

purchasing transaction in return for a free treat. The survey consists of questions regarding cus-

tomer experience at the restaurant, which includes items about overall experience/satisfaction and

detailed questions about such concerns as satisfaction with food quality, speed of service, cleanli-

ness, etc. For each question, the customers rank their experience from 0 (not at all satisfied) to 10

(very satisfied). For each completed survey, in addition to customers’ responses to the questions

above, we also observe the time when the survey was filled and restaurant ID with which the survey

is affiliated.

In this study, we use the answers to the question “How likely are you to recommend this restau-

rant?” to determine customer experience at restaurants. This question is considered to be of great

importance in determining the overall perceived quality in the service and retail industry, and is

1 We explore the robustness of our main insights to this sample selection procedure in Section 6.

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used in practice to determine the Net Promoter Score (NPS). Notably, NPS is known to be a

good predictor of revenue (Reichheld 2003). In addition, we analyze the answers to the questions

“Please rate the following: Cleanliness” and “Please rate the following: Comfort and Atmosphere”

for controls. Summary statistics of the survey data are provided in Table 2.

3.2. Supply Chain Data

All restaurants in our selected sample are serviced by one distributor that procures from 26 suppli-

ers. This supply chain structure allows us to focus on the supply chain quality from the restaurants’

perspective. Although while the quality at the distributor level is fixed, the quality received by

each restaurant from the distributor varies and we capture this variation at the restaurant level.

There are many dimensions to quality in fast-food restaurants that affect customer experience.

The quality of the ingredients for the items listed on the menu is one of the important factors (Min

and Min 2011), and it depends on the quality of the supply chain that supports the restaurant.

As explained earlier, we measure the supply chain quality from the restaurants’ perspective, which

varies over time and across restaurants. When restaurants incur problems with their deliveries

and/or supplies, they file complaints with the call center of the supply chain orchestrator. Com-

plaints serve as a mechanism to get replacement and/or credit for damaged or unusable supplies.

The call center records the complaint, investigates, and assigns the complaint to a responsible

party.

Using analysis of complaints’ texts, we identify the main quality issues that appear frequently

in the complaints. To identify the main issues involved and to categorize the complaints by these

issues, we first manually go through a training set of complaints and identify the main supply

chain issues (Freshness, Packaging, and Delivery) and their associated keywords. For example, the

complaint “Store received 1 case of Chips that has all bags open at the top seals,” indicates that the

restaurant has encountered a problem with Packaging and that the words “bag” and “seals” may

be associated with the Packaging topic. We then use a form of probabilistic topic modeling based

on the Latent Dirichlet Allocation model (LDA), which is a hierarchical Bayesian model developed

in computer science of how content is structured within text (Blei 2012), to refine our topic and

keyword associations and to categorize all complaints. The main idea of this method is as follows:

Each complaint is modeled as a collection of words drawn from different topic distributions, whereby

the proportion of each topic that comprises a review is given by P(topic|complaint). Each topic is

defined as a multinomial distribution over the observed set of words within all complaints, which

is given by P(word|topic) (Blei 2012). The goal of LDA is to infer both probability distributions,

modeled as latent variables, from the observed word counts in each complaint.

Recently the LDA model has been successfully used in business applications to assess product

quality from user-generated content on websites (Abrahams et al. 2015, Tirunillai and Tellis 2014).

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In contrast to these prior works, we estimate the LDA model after specifying an informative prior

distribution of keywords for each topic, which allows us to pre-specify topics of interest, thus

integrating managerial intuition with statistical modeling of the text. To form the prior we manually

went through a training set of complaints and identified main topics and associated keywords – an

approach that has been successfully used in previous text mining works (see, for example, Hu and

Liu (2004) and Wallach et al. (2009)). To the best of our knowledge, this is the first application

of such analysis in supply chain management literature, and one of the first applications in the

management literature. In Appendix A Table 7 we summarize the words by topic included in the

prior and the updated list of words by topic after applying the LDA model.

In general, each complaint may include multiple topics. For example: “Case was dented and

crushed. As per caller the case was on the bottom of cases. Cucumbers are broken,” mentions

keywords associated with Freshness and with Packaging issues. To associate each complaint

with one main topic, we assign the complaints to the most likely topic using the estimate of

P(topic|complaint). In the example above, the complaint is classified as Packaging issue, which is

the main quality problem. In our application, complaints are logged by trained call center employ-

ees, and we find that most complaints are short (an average of 24 words, 151 characters) and

focused, making association with one issue fairly straight-forward.

We validate our seeded LDA approach using three quality metrics: the average topic coherence

(Mimno et al. 2011), Hellinger distance (Blei and Lafferty 2009), and entropy (Hall et al. 2008).

Please see Appendix C for detailed definition of the metrics. Table 1 shows that the seeded LDA

method is preferred to the standard LDA topic model with uninformed prior according to all three

quality metrics (higher values are preferred for coherence and Hellinger distance measures, and

lower values are preferred for the entropy measure).

Method Topic Coherence Hellinger Distance Entropy

Seeded LDA -1206.724 0.627 3.525

LDA with Uninformed Prior -1387.492 0.555 3.769

Table 1: Quality metrics for the topic modeling show that the seeded LDA results are preferableto topic modeling with an uninformed prior.

After each complaint is associated with one issue, we count the number of complaints per issue

for each restaurant and use these counts as measures of supply chain quality. In Table 2, we present

the descriptive statistics of all variables included in the supply chain analysis. We include the age

of the restaurant calculated in days from opening until the end of the observation window, and the

distance from the restaurant to its distributor (in miles), which we will use later for controls. To

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compute the distance between a given restaurant and its distributor, we first find their geographic

coordinates using Google Maps Geolocation API based on the provided addresses. We then use the

coordinates to find the driving distance between the restaurant and its distributor using Google

Maps Distance Matrix API. We assume that the distances are symmetrical between restaurants

(i.e., the distance between A and B is the same as between B and A). We compute the distances

between restaurants, using the same approach. We use the distances to identify restaurants that

are within a close proximity (specified by parameter d) from a focal restaurant in our second phase

analysis.

Statistic N Mean St. Dev. Min Max

Average score for “Recommend Restaurant”1 28 8.762 0.541 7.305 9.732

Average score for “Cleanliness/Comfort”2 28 9.090 0.410 8.138 9.759

Total number of surveys filled 28 264.536 243.929 53 878

Complaints regarding Freshness issues3 28 5.786 13.815 0 57

Complaints regarding Packaging issues3 28 2.786 3.881 0 14

Complaints regarding Delivery issues3 28 0.357 0.989 0 5

Distance from restaurant to distributor (miles) 28 131.021 25.624 39.900 138.000

Restaurant age (days) 28 3,848 2,095 765 7,759

Table 2: Restaurant-level summary statistics for the selected sample. Notes: 1For each restaurant computethe average score for the “Recommend Restaurant” question, then report the descriptive statistics across restaurants; 2For eachrestaurant compute the average score for the “Cleanliness” question and “Comfort Atmosphere” question, take the average of thetwo, then report the descriptive statistics across restaurants; 3For each restaurant, compute the total number of complaints ona specific topic per restaurant over the whole observation time window, then report the descriptive statistics across restaurants.

4. Model

Given that supply chain quality is not directly observable to customers, to link supply chain quality

to CLV, we conduct the analysis in two phases. In the first phase, we explore how supply chain

quality affects customer experience at the downstream restaurants using a linear regression model.

In the second phase, we propose a latent attrition model to capture how customers experience the

focal restaurant and how the average customer experience reported for the adjacent restaurants

affects CLV at the focal restaurant.

4.1. Impact of Supply Chain Quality on Customer Experience

In this section, we first describe our variables and present a regression model to identify which

operational and supply chain characteristics drive customer experience at restaurants. We then

discuss potential endogeneity issues and present a two-stage least squares (2SLS) approach with

instrumental variables to address such issues.

14

4.1.1. Variables and Linear Model Our dependent variable is the level of customer expe-

rience provided at the restaurant. To capture customer experience at the restaurant, we use the

responses to the “How likely are you to recommend this restaurant?” question from the customer

surveys – RECOMMENDjl. In particular, for each restaurant j, we compute a rolling average2

from the time l to time l+ τ . We set the time window length to τ = 84.3 We average the responses

over a time window to capture potential delay between the occurrence of an issue at the restaurants

and customer survey completion. We regress RECOMMENDjl on the following time-variant

characteristics of the restaurants. First, we include three variables counting the number of com-

plaints placed by restaurant j on day l on one of three supply chain issues identified through text

analysis (COMPLFreshjl , COMPLPackagejl , and COMPLDeliveryjl ). To control for the general quality

level of the restaurant due to factors other than supply chain quality, we add the average score

given to the restaurant on Cleanliness and Comfort in the customer survey (AV GCLEANjl) to

the model specification.4 For example, this control variable should capture whether restaurants

have more experienced or more talented managers, which may affect the frequency of complaints

and the quality of the relationship between the distributor/suppliers and the restaurant. Similarly,

restaurants may have better staff, which creates a better atmosphere for customers and hence,

influences their customer experience, and so on, which should be controlled for by AV GCLEANjl.

We also combine other controls in vector Cj : To control for potential demographic and socioeco-

nomic differences between restaurants’ locations, we control for the ZIP code where the restaurant

is located; in addition, we control for the restaurant’s age in days from opening until the end of

the observation window rescaled by 1/1000.

RECOMMENDj,l+τ = β0 +βFreshCOMPLFreshjl +βDeliveryCOMPLDeliveryjl +

βPackagingCOMPLPackagingjl +βAbilityAV GCLEANjl +

βControlsCj + εjl. (1)

4.1.2. 2SLS Model Using an OLS model as specified above may lead to biased estimators

due to potential endogeneity issues. Although supply chain quality can affect customer experi-

ence, such customer experience also may directly affect the number of supply chain complaints

2 Note that we use the average response to the question “How likely are you to recommend this restaurant?” ratherthan does the Net Promoter Score to measure customer experience. This is because we find that the continuousaverage metric significantly better predicts customers’ future purchasing behavior than the Net Promoter Score basedon our second phase analysis, which is consistent with the results in Pingitore et al. (2007).

3 To select the time window τ , we ran the model with different rolling horizons ranging from 1 day to 98 in incrementsof 7 days, and selected the final model based on the best fit according to the adjusted R-squared measure.

4 In a study of students’ preference of fast food restaurants by (Knutson 2000), cleanliness was ranked as the numberone driving force of students’ choice.

15

filed by the restaurants. This can comprise the three variables that count the number of supply

chain complaints in (1) endogenous variables. For example, high customer experience may lead

to higher sales at the restaurant level. This implies that the restaurant may have more money to

invest in better management that collaborates better with the supply chain members and causes

supply chain quality to increase. Although we intend to control for this problem by including the

proxy for quality of management using the AV GCLEANjl variable, we are uncertain whether

AV GCLEANjl can fully capture the management capability of the restaurants. Meanwhile, low

customer experience leads to frustrated customers who complain more to the restaurants, which

may trigger higher number of complaints in the supply chain. Although we observe that very few

supply chain complaints (2%) in our data mention that they originate from the customers, we

cannot fully exclude the associated potential endogeneity issues. To this end, it is worth noting

that, our results based on the Wu-Hausman test reject the hypothesis that the three counts of

supply chain complaints are exogenous variables with p < 0.01.

To address the above endogeneity issues, we use a 2SLS approach with three instrumental vari-

ables. To be valid instrument variables, they have to satisfy two conditions: relevance (correlated

with the endogenous variable, i.e., number of complaints) and exclusion (it uncorrelated with the

error term) (Wooldridge 2001). To this end, we use the following three instrumental variables: the

distance from the distributor to the restaurant (DISTj), the adoption of the point-of-sale (POS)

system at the restaurants, captured with a binary variable (POSjl), and the number of restaurants

serviced by the distributor (STORENUMl).

(1) The distance from the distributor to the restaurant (DISTj): Note that, if a restaurant

is located far from the distributor, it can be scheduled last on the route and hence, may incur

frequent delivery delays, or the boxes to the restaurant may have a higher risk of getting damaged

because they are stuck at the bottom of the delivery truck. As a result, the distance from the

distributor is likely to be correlated with the number of supply chain complaints and thus satisfies

the relevance condition. Because the distance between the restaurant and its distributor should

have no direct impact on customer experience, the exclusion condition is satisfied. (2) The adoption

of the point-of-sale (POS) system at the restaurants captured with a binary variable (POSjl): Note

that POSjl = 1 if the POS has been implemented at restaurant j at time l, and 0 otherwise. The

POS system makes the customer transaction data readily available and the data are shared at

all stages involved in the supply chain in our application. Thus, the adoption of the POS system

helps to better inform the supply chain partners about the consumer demand so that they can

better plan their supplies. This establishes the relevance of POSjl. However, because POS has no

impact on the customer interaction process, POS implementation should have no direct impact

on customer experience and, thus satisfy the exclusion condition. (3) The number of restaurants

16

serviced by distributor (STORENUMl): Although there is only one distributor in our selected

sample, this number changes over time. Because the distributor has to deal with more restaurants,

the supply chain quality may suffer from such issues as slower processing of orders or availability.

This, however, should have no direct impact on customer experience. To further validate the three

instruments proposed above, we confirm that the instruments pass the relevance condition using

the F-tests which indicates that they are not weak instruments. We also provide evidence that

the three instruments satisfy the exclusion condition using an F-test with the instruments on the

residuals from the final model. Full results from the first stage and the detailed results of the two

tests mentioned above are presented in Appendix D.

In the first stage of the 2SLS approach, we estimate the endogenous independent variables

COMPLcat

jl for cat∈ Fresh,Package,Delivery using the instruments defined above and control

variables Cj . In the second stage, we replace the observed counts of complaints in (1) with the

predicted number of complaints obtained from Stage 1. We then estimate the model specified in

(1) with robust errors (Wooldridge 2001).

4.2. Impact of Customer Experience on Customer Purchasing Behavior

In this section, we propose a latent attrition model to study the impact of customer experience on

customers’ future purchasing behavior and describe our estimation strategy.

4.2.1. Customer Purchasing Behavior Model To standardize notation, we use j ∈

1,2, ..., J to index the restaurants. Customers of a given restaurant j are indexed by i ∈

1,2, ...,Nj. Customer i’s transactions at a restaurant j are indexed by k ∈ 1,2, ...,Kij and tijk

represents the time of transaction k made by customer i in restaurant j. Customers have a non-

contractual relationship with the restaurants. Although customer i is active with a restaurant, he

or she makes transactions according to a Poisson process with rate λi. We allow the arrival rate λi

to vary across different customers. To account for such heterogeneity, we let the arrival rate follow

a gamma distribution. In particular, λi is a realization of λ∼Gamma(aλ, bλ), where aλ and bλ are

the shape and rate parameters of the gamma distribution, respectively.

After each transaction, a customer may decide to stop visiting the restaurant and become per-

manently inactive, i.e. churn. We denote customer i’s probability of churning after his or her kth

transaction at restaurant j with pijk, given by

pijk = 1− exp(−θiyijk). (2)

θi captures customers’ specific heterogeneity due to the unobservable variables beyond the factors

in yijk, (e.g., customers may react to the same experience differently, customers may see different

value in the brand). We let θ∼Gamma(aθ, bθ), where aθ and bθ are the shape and rate parameters

17

of the gamma distribution, respectively. We assume that θ and λ are independent. yijk is a function

of factors that may affect customers’ churn rate. Customers’ probability of churning at a restaurant

may depend not only on their experience with the focal restaurant but also on the perceived quality

of the adjacent restaurants. For example, if the perceived quality of the adjacent restaurants is

high, customers may become more likely to churn at the focal restaurant and to decide to visit the

adjacent restaurants instead. We refer to such effect as the competition effect. Because all of the

restaurants in our application share the same brand name, good perceived quality of the adjacent

restaurants may improve the quality reputation of the brand and thus reduce customers’ churn

rate at the focal restaurant. We refer to such effect as the reputation spillover effect. We define

the network effect as the combined competition and reputation spillover effects. To operationalize

the impact of customer experience at the focal restaurant and the network effect on their churn

rates at the focal restaurant, we let qijk denote customer i’s experience at restaurant j by the end

of his or her kth transaction there. We define qdjk as the average perceived quality of the adjacent

restaurants, which are within d miles from the focal restaurant j, at the time of transaction k. Note

that customers’ perception of the adjacent restaurant’s quality can be acquired through word-of-

mouth or/and personal experience with visiting a neighboring restaurant. Thus, the network effect

for customers who have visited the adjacent restaurants may be different from that for customers

who have not visited any of the adjacent restaurants. To this end, we let the binary variable δdijk

indicate whether or not customer i has visited any of the restaurants adjacent to restaurant j by

the time of transaction k. In particular, we have δdijk = 1 if the customer has visited any of the

adjacent restaurants, and 0 otherwise. Finally, customers’ churn rate also may be different across

different ZIP codes due to such factors as different customer demographics, strength of the brand

in the area, or competition from other brands. We let Zipj be a vector of dummies that indicates

the ZIP code where restaurant j is located.

To capture all of the factors above, we let yijk be given as follows

log(yijk) = αFQqijk +αNQqdjk +αdδ

dijk +αintq

djkδ

dijk +αZIP ·Zipj, (3)

Note that including the interaction term qdjkδdijk in (3) allows us to differentiate the network effect

through the two different channels (i.e., word-of-mouth and personal visits) noted above. In par-

ticular, the coefficient αNQ captures the network effect through the word-of-mouth channel, while

αint quantifies the additional network effect through the channel of customers’ personal visits.

Finally, it is important to note that, by including the ZIP code level fixed effect and explicitly

characterizing individual customers’ heterogeneity, our model allows us to elicit the causal impact

of customer experience at the focal store and the network effect on their purchasing behavior in a

clean manner.

18

4.2.2. Estimation Strategy We use the maximum likelihood estimation method to estimate

the parameters in the customer purchasing model described above. We construct the likelihood

function as follows: (1) We first compute the likelihood of observing the sequence of transactions for

each given customer at a given restaurant; (2) we then compute the likelihood for all the customers

of each given focal restaurant; and (3) finally, we compute the total likelihood function for all the

selected restaurants in the given market.

Before we derive the likelihood function, we first describe how we construct the key variables (i.e.,

qijk and qdjk) in the purchasing behavior model. Recall that qijk represents customer i’s experience

at restaurant j at the time of transaction k. Similar to our analysis in the first phase, we use cus-

tomers’ response to the question “How likely are you to recommend this restaurant?” to measure

customer experience. To this end, it is important to note that, although we can link customers’

surveys to a particular restaurant, we cannot link customers’ surveys to the corresponding transac-

tions. Moreover, most of the customers’ do not complete surveys for all of their transactions. Thus,

instead of measuring customer experience at the transactional level, we do so at the restaurant

level. In particular, we let qj indicate the average recommendation score collected from all surveys

completed for restaurant j and set qijk = qj. We include surveys collected over the full observation

period to measure customer experience for the following two reasons: (1) our results show that

the average recommendation scores are stationary over time for all the selected restaurants based

on the augmented Dickey-Fuller (ADF) test; and that (2) this allows us to include more surveys

to measure customer experience, which can potentially reduce the bias introduced by a low num-

ber of completed surveys. To explore the robustness of our main insights to our measurement of

customer experience, we consider an alternative model whereby we measure customer experience

using completed surveys up to the time of the their last transaction, in Section 6.

We next construct the variable qdjk, which is the average perceived customer experience across all

of the adjacent restaurants within distance d from restaurant j. We index the focal restaurant j’s

adjacent restaurants as jm with m∈ 1,2, ..,Mdj , where Md

j is the total number of adjacent restau-

rants for the focal restaurant j within distance d. We let qjm be the average recommendation score

collected from all surveys for the adjacent restaurant jm. To this end, we have qdjk = 1

Mdj

Mdj∑

m=1

qjm .

Based on our conversation with the managers at the restaurant chain, we let the distance threshold

d= 1 mile in our estimation. To demonstrate the robustness of our main insights to our choice of

the value for d, we explore several alternative models with different values for d (d ∈ 1,1.5,2).

Our results show that, although the main insights are consistent across all these models, the model

with d= 1 best explains the data based on the Akaike information criterion (AIC; Burnham and

Anderson (2003)). Hence, we focus on the case with d= 1 throughout the paper.

19

We are now ready to construct the likelihood function. Consider customer i who had Kij transac-

tions at restaurant j in the period (0, T ] with the transactions occurring at tij = (tij1, tij2, ..., tijKij ).

Meanwhile, his or her corresponding visiting trajectory to other restaurants is characterized by

δdij = (δdij1, ..., δdijKij

). His or her experience at the focal restaurant and the perceived quality of

the adjacent restaurants during the past Kij transactions are given by qij = (qij1, ..., qijKij ) and

qdj = (qdj1, ...., q

djKij

), respectively. We let Lij be the likelihood of observing the sequence of trans-

actions of customer i at restaurant j starting at the moment tij1. To this end, we have

Lij(Kij , tij ,δdij,qij, q

dj ,ZIPj , T |αFQ, αNQ, αd, αint,αZIP , λi, θi)

= λKij−1i exp

(−λi(tijKij − tij1)

)(Kij−1∏m=1

(1− pijm)

)(pijKij + (1− pijkij ) exp

(−λi(T − tijKij )

)). (4)

Then, for a randomly chosen customer, we compute the corresponding expected likelihood function

by taking expectation of the likelihood function defined in (4) over the random variables λ and θ.

This is characterized in the following lemma (all proofs and derivations are provided in Appendix

B).

Lemma 1. The expected likelihood function for a randomly chosen customer is given by

Eλ,θ[Lij(Kij, tij ,δdij ,qij, q

dj ,ZIPj, T |αFQ, αNQ, αd, αint,αZIP , λi, θi)]

=Γ(aλ+Kij−1)

Γ(aλ)

baλλ(

bλ+tijKij−tij1

)aλ+Kij−1

(bθ

bθ+Yi,j,Kij−1

)aθ(

1−(bθ+Yi,j,Kij−1

bθ+YijKij

)aθ (1−

(bλ+tijKij

−tij1bλ+T−tij1

)aλ+Kij−1))

, (5)

where YijK =∑k=K

k=1 yijk.

Finally, we denote the total likelihood function across all customers and restaurants in the

chosen neighborhood as LL(ω), with ω being the set of parameters to be estimated, given by

ω= (αFQ, αNQ, αd, αint,αZIP , aλ, bλ, aθ, bθ). We then have

LL(ω) =J∑j=1

Nj∑i=1

log(Eλ,θ[Lij]). (6)

We then estimate the parameters ω = (αFQ, αNQ, αd, αint,αZIP , aλ, bλ, aθ, bθ) by maximizing the

likelihood function given in (6) using the nonlinear optimization solver Knitro in matlab. To con-

struct the confidence interval for each parameter, we use the non-replacement sub-sampling; see

Horowitz et al. (2001).

5. Estimation Results

In this section, we summarize the results from both phases of our framework. First, we identify

which supply chain issues are most important for determining customer experience at the restau-

rants. Next, we show the impact of customer experience on customer future purchasing behavior.

20

5.1. Impact of Supply Chain Quality on Customer Experience

We present the estimation results from the first phase of our analysis in Table 3.

The four estimation results differ in how the idiosyncratic noise is modeled, which can affect

the statistical validity of the overall estimation (Arora 1973). Specifically, the error structure in

the first model includes a component specific to restaurants (εjl = ζjl + ξj), whereas the second

model includes a temporal component (εjl = ζjl+ ξl). Each error specification induces a correlation

structure, so that every pair of observations from the same group (either by restaurant or time) are

correlated. The third model, which is the most conservative, computes standard errors using the

so-called “sandwich covariance” estimator (Fitzmaurice et al. 2012), which produces statistically

consistent standard errors even in the presence of autocorrelation and heteroskedasticity. Finally,

the last column shows results from a standard linear model. The results across the three 2SLS

models are consistent both in terms of the signs and the magnitudes of the estimates. To this end,

we show that supply chain issues related to Freshness of products and ingredients have a significant

impact on the customer experience, as they directly affect the availability and taste of menu items.

Moreover, we show that reducing one complaint per month can improve customer experience at the

restaurant by 13.052/30 = 0.44. The supply chain quality issues related to Packaging and Delivery,

however, do not seem to affect customer experience at the restaurant significantly. This result is

intuitive: Freshness issues have a direct impact on the taste of final product served to the customers

and, hence, have a higher impact on the customer experience at the store.

Our approach of classifying the complaints using text analysis and including separate categories

in the model can help management to identify which supply chain issues need to be addressed

first and to quantify the impact of such issues on customer experience. Once the issue is identified,

the company may dig deeper into this particular category. In our application, for example, 79% of

the Freshness complaints are associated with one supplier, and 65% of the Freshness complaints

are associated with over-ripening of fruits and vegetables. The supply chain can work with the

particular supplier and focus on remedial actions to prevent over-ripening, such as improving

forecasting and decreasing the lead time.

This modeling phase allows us to quantify the impact of supply chain issues on customer expe-

rience. The next phase identifies how valuable is customer experience improvement is for different

customers with different transaction patterns.

5.2. Impact of Customer Experience on Customer Purchasing Behavior

The novel and unique feature of our customer purchasing behavior model is that we account for

the impact not only of customer experience in the focal restaurant but also of the the network

effect on customers’ purchasing decisions. We refer to the full model described in Section 4.2 as the

21

Dependent variable: RECOMMENDjl

2SLS

(EX)

2SLS

(Time)

2SLS

(Robust SE)OLS

(1) (2) (3) (4)

Freshness complaints −16.841∗∗∗ −13.528∗∗∗ −13.052∗ −0.167∗∗∗

(1.298) (2.592) (7.691) (0.036)

Packaging complaints −3.254 −11.172 −9.007 −0.080

(2.459) (11.990) (18.167) (0.054)

Delivery complaints 1.024 3.317 −4.941 0.018

(0.729) (3.582) (37.723) (0.167)

Manager Ability 1.268∗∗∗ 1.280∗∗∗ 1.285∗∗∗ 1.241∗∗∗

(0.008) (0.016) (0.026) (0.006)

ZIP Code 1 −0.348∗∗∗ −0.338∗∗∗ −0.346∗∗∗ −0.231∗∗∗

(0.100) (0.024) (0.047) (0.011)

ZIP Code 2 −0.161∗ −0.165∗∗∗ −0.174∗∗∗ −0.218∗∗∗

(0.095) (0.021) (0.049) (0.010)

ZIP Code 3 −0.175∗ −0.133∗∗∗ −0.144∗ −0.046∗∗∗

(0.099) (0.047) (0.082) (0.011)

Restaurant Age 0.012 0.009∗∗ 0.010 −0.011∗∗∗

(0.017) (0.004) (0.008) (0.002)

Constant −2.512∗∗∗ −2.549∗∗∗ −2.670∗∗∗ −2.359∗∗∗

(0.108) (0.163) (0.228) (0.051)

Observations 20,233 20,233 20,233 20,233

R2 0.602 0.411 0.587 0.729

Adjusted R2 0.602 0.389 0.587 0.729

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Table 3: Impact of supply chain quality on customer experience.

network effect model. To assess the value of including customer experience at the focal restaurant

and that at the neighboring restaurants, in characterizing customers’ purchasing behavior, we also

consider the following two models: (1) the model whereby we do not account for the impact of

customer experience in any restaurants, which we refer to as the benchmark model ; and (2) the

22

model whereby we account only for the impact of customer experience at the focal restaurant but

not the network effect, which we refer to as the focal experience model. We report the estimation

results of all three models in Table 4.5

Description Notation Benchmark Focal Experience Network Effect

Model Model Model

Shape parameter of λ aλ 0.35 0.32 0.33

(0.33,0.37) (0.30,0.35) (0.31,0,35)

Rate parameter of λ bλ 1.22 1.17 1.18

(1.15,1.29) (1.10,1.24) (1.12,1.24)

Shape parameter of θ aθ 0.85 0.89 0.92

(0.82,0.88) (0.85,0.92) (0.88,0.95)

Rate parameter of θ bθ 0.73 0.01 0.00

(0.63,0.78) (0.00,0.01) (0.00,0.00)

Effect of focal customer experience αFQ −0.58 −0.62

(-0.65,-0.52) (-0.71,-0.56)

Effect of neighborhood customer experience αNQ −0.38

(-0.48,-0.25)

Effect of visiting at least one adjacent αd 4.54

restaurant (2.87,8.13)

Interaction effect αint −0.57

(-0.99,-0.38)

Fixed effect of ZIP Code 2 νZip2 0.10 0.38 0.59

(0.04,0.16) (0.31,0.45) (0.48,0.68)

Fixed effect of ZIP Code 3a νZip3 0.06 0.32 0.40

(0.01,0.12) (0.26,0.39) (0.34,0.47)

Table 4: Estimation results for the customer purchasing behavior models: Estimates of the param-eters and the corresponding 95% confidence intervals.

a Because ZIP Codes 1 and 4 were statistically similar, we eliminated the control for the fourth ZIP Code.

Note that aλ/bλ represents the average weekly rate of transactions, which is around 0.3 trans-

actions per week across all models. Most managerially relevant parameters are αFQ, αNQ, αint

and αd, and the results are consistent across the three models. As one would expect, αFQ has a

negative sign, implying that better customer experience at the focal restaurant reduces customers’

probability of churning. Interestingly, αNQ also has a negative sign. It implies that better customer

experience at the adjacent restaurants of the same brand does not lure away customers from the

5 Note that in all three models reported in Table 4, we omit ZIP Code 4 as a control. However, it is important to notethat we also have considered the models whereby we include ZIP Code 4 along with ZIP Codes 2 and 3 as controls.Our results show that the coefficient for ZIP Code 4 is not significantly different from 0 in all of the three modelsand that including ZIP Code 4 as a control does not improve the goodness of fit of these models. Thus, to improvethe estimation efficiency of the models, we focus on the ones for which we omit ZIP Code 4 as a control.

23

focal restaurant but, instead, enhances the focal restaurant’s ability to keep customers. This may

be because good overall customer experience offered by the adjacent restaurants leads to a good

reputation of the brand in the area and hence, reassures customers of their restaurant choice.

This result indicates that the reputation spillover effect dominates the competition effect. More-

over, negative αint implies that better overall customer experience of adjacent restaurants reduces

customers’ churn rate at the focal restaurant even more for customers who have visited adjacent

restaurants compared to those who have not. This shows that the reputation spillover effect can be

enhanced through customers’ personal visits to the adjacent restaurants. Note that the parameter

αNQ captures the network effect through the channel of word-of-mouth, while the parameter αint

measures the additional network effect through personal visits to the adjacent stores. Finally, as

expected, we have αd > 0, which indicates that customers who have visited adjacent restaurants

have a higher churn rate at the focal restaurant as compared to those who have not. This may be

because customers who explore multiple stores have more options and thus tend to be less loyal to

the focal store.

Model assessment and selection In this section, we compare the three customer purchasing

behavior models identified above, based on the AIC, and the prediction accuracy of the model.

We normalize the AIC of the Benchmark Model to 0 and report the AIC of all models relative to

the benchmark model in Table 5. The model with the lowest AIC best explains the data. Thus,

our results show that the network effect model best explains the data among all the three models,

while the benchmark model is the worst in explaining the observed customer purchasing behavior.

This indicates that both customer experience at the focal restaurant and the network effect are

informative additions to the benchmark model and help to explain the data significantly better.

We next assess the predictive accuracy of the various models that we consider. Following Braun

et al. (2015), we use the probability that a customer will make 0 transactions in the focal restau-

rant in the next t† weeks after the observation period T (conditional on his or her transaction

history) as our variable of interest. We denote it as P (X(t†) = 0|Kij, tij ,δdij ,qij , q

dj ,Zipj, T ), where

(Kij, tij ,δdij ,qij , q

dj ,Zipj, T ) characterizes the corresponding past transaction pattern and experi-

ence. We derive its expression in Appendix B, see (23).

To evaluate the prediction accuracy of our models, we divide the data into two subsets, with one

for training the model and the other for testing. In particular, the testing subset includes all of the

transactions in the last eight weeks of our observation window (from April 27, 2015 to June 22,

2015), while we use the remaining data to train our model. We first estimate our models by using

the training data. Using these estimates, for any given customer in the training set, we can compute

his or her predicted probability of making 0 transactions in the future eight weeks based on his

24

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Observed Probability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1P

red

icte

d A

ve

rag

e P

rob

ab

ility

Figure 2: Probability of making 0 transactionsin the future eight weeks.

Models AIC RMSE MAE

Benchmark Model 0 0.112 0.080

Focal Experience Model -12.0 0.120 0.079

Network Effect Model -16.4 0.090 0.059

Table 5: Model selection measures

or her transaction history. We next compute the corresponding observed probability of making 0

transactions in the future eight weeks using the testing data. To do so, we first divide the customers

into 15 groups based on their predicted probability of making 0 transactions in the future eight

weeks. In particular, group g includes all customers with the predicted probability from (g−1)/15

to g/15, for g = 1,2, · · · ,15. For each group, we calculate the observed average probability of

making 0 transactions in the future eight weeks using the testing data. We then compare the

observed average probability to the average predicted probability of making zero transaction in the

future eight weeks for all the 15 groups. We measure the prediction accuracy our model in terms

of such probability using the following two commonly used metrics: mean-absolute error (MAE)

and root-mean-square error (RMSE). We report the results in Table 5.

Based on both RMSE and MAE, we observe that the network effect model predicts customers’

future purchasing behavior the most accurately among all the three models, which is consistent with

our modeling choice according to AIC. In Figure 2, we demonstrate how accurately the network

effect model can predict the probability of making 0 transactions in the future eight weeks by

plotting the predicted probability against the observed probability.

The above analysis shows that accounting for the network effect is important for explaining and

predicting customers’ future purchasing behavior. The model with network effect performs signifi-

cantly better in terms of both its goodness of fit and prediction accuracy compared to the models

without the network effect. We also show that increasing customer experience at one restaurant

not only improves customers’ intent to stay at the focal restaurant, but also can potentially ben-

efit its adjacent restaurants through the network effect. With the improved forecasting accuracy

and the additional insights regarding the network effect, our model can help the supply chain and

25

firms’ managers to estimate financial return of the supply chain quality and customer experience

improvements more accurately, as it will become clear in Section 7.

6. Robustness Studies

To check robustness of our customer purchasing behavior estimation, we study several alternative

models below.

Rolling Average Recommendation Score. Recall that we measure customer experience at

a restaurant by using all of the surveys collected in the entire observation time horizon in our

main network effect model. Thus, customer experience at a restaurant is constant over time in

these models. To explore the robustness of our main insights to the above choice of customer

experience measurement, we consider an alternative network effect model whereby we measure

customer experience at a given time using the rolling average of the recommendation scores from

the surveys collected up to that time. We refer to this model as the rolling network effect model.

This model allows us to capture the variation of customer experience over time, if any. We find

that our main insights continue to hold based on this alternative model (see Table 6). However, it

does not explain the observed customer purchasing behavior as well compared to our main network

effect model based on the AIC score.

Customer-based Network. Recall that we define the network of restaurants based on geographic

proximity in our main network effect model. We next consider an alternative model whereby we

define the network of restaurants based on customers’ personal visits. In particular, for any given

customer, we find all restaurants that the customer visited (regardless of their location) and include

them in this customer’s personal network. The perceived customer experience of the “adjacent”

restaurants to the focal restaurant now becomes the average customer experience aggregated across

all restaurants except the focal one visited by the customer. We refer to this model as the customer-

based network effect model. Again, we find that the results of this alternative model are consistent

with our main insights (see Table 6). However, our main network effect model better explains the

observed customer purchasing behavior than does the customer-based network effect model based

on AIC.

Potential Sample Selection Issue. Among the restaurants in the four ZIP Codes areas we

focus on, we select the ones that collect at least 50 surveys in our observation window. To confirm

that our results are not subject to sampling bias due to the elimination of restaurants with a low

number of surveys, we estimate our network effect model using the data from only the two ZIP

codes (ZIP Codes 1 and 4) where we kept most of the restaurants. We eliminate only one restaurant

out of 10 in ZIP Code 1 and one out of eight restaurants in ZIP Code 4. For ease of reference, we

name this model as the subsample network effect model. Our main insights continue to hold based

26

Notation Rolling Network Customer-based Subsample Network

Effect Model Network Effect Model Effect Model

aλ 0.35 0.33 0.459

(0.33,0.37) (0.30,0.35) (0.414,0.507)

bλ 1.22 1.18 1.323

(1.16,1.28) (1.11,1.25) (1.218,1.466)

aθ 0.89 0.92 0.881

(0.85,0.92) (0.86,0.95) (0.852,0.912)

bθ 0.03 0.00 0.00

(0.00,0.75) (0.00,0.01) (0.00,0.00)

αFQ −0.19 −0.59 −0.492

(-0.23,-0.15) (-0.69,-0.54) (-0.556,-0.401)

αNQ −0.17 −0.11 −0.357

(-0.22,-0.10) (-0.21,-0.02) (-0.491,-0.229)

αd 1.83 0.66 8.271

(0.79,3.17) (-0.13,1.57) (-2.144,14.38)

αint −0.26 −1.013

(-0.42,-0.14) (-1.719,0.2)

νZip2 0.27 0.40

(0.17,0.35) (0.33,0.47)

νZip3 0.27 0.34

(0.22,0.36) (0.28,0.41)

νZip4 −0.053

(-0.135,0.038)

Table 6: Estimation results of all of the alternative network effect models that characterize theimpact of customer experience on customer purchasing behavior.

on this alternative model (see Table 6), which reduces the concern about the potential sample

selection issue.

7. Counterfactual Studies

We have characterized the mechanism by which the supply chain quality affects customer expe-

rience and, thus, customers’ purchasing behavior through the two-phase methodology presented

above. We next describe how individual restaurants and the supply chain orchestrator can use

our methodology and results to prioritize investment in customer experience and supply chain

improvements to maximize their ROI. For example, a firm may run a marketing campaign on a

constrained budget and has to choose which customers to include in the campaign to maximize the

ROI. Similarly, the supply chain orchestrator may not be able to make supply chain improvements

for all restaurants and will have to choose, for example, which restaurant to serve first or which

restaurants to serve with the freshest supplies to maximize the ROI.

At the individual restaurant level, improving customer experience may take the form of a targeted

marketing or service campaign (e.g., sending special offers or providing premium services to specific

27

customers). Assuming that the cost of an improvement is the same across customers (e.g., it costs

the same to send an offer to each customer), the ROI for a restaurant from improving the experience

of any given customer is proportional to the additional future revenue that the customer generates

at the restaurant due to her improved experience. Given that the transaction amount has little

variation across different transactions and customers in our application, the additional revenue

from a given customer at a restaurant and, hence, the CLV, is proportional to the future number

of transactions that the customer generates at the restaurant.

At the supply chain level, improving the supply chain quality for a given restaurant may take

the form of fixing a particular supply chain issue. For example, if a certain restaurant incurs

Packaging issues because their shipment is at the bottom of the truck due to the route schedule, the

supply chain orchestrator may reduce the risk of this problem by adding cushioning to the bottom

shipments. Assuming that the cost of fixing such a problem does not vary across restaurants, the

ROI for the supply chain orchestrator from improving the supply chain quality of a given restaurant

is proportional to the incremental number of future transactions generated in the entire network

of restaurants due to the supply chain improvement. Note that improving the supply chain quality

for one restaurant will not only generate additional transactions at the focal restaurant, it also

may generate more revenue for the adjacent stores due to the network effect. Our network effect

model allows us to quantify the number of incremental transactions generated through both the

focal restaurant and the other restaurants in the network.

7.1. Expected Incremental Number of Future Transactions

We next derive the expected incremental number of future transactions that we need for our

ROI approximation. Consider customer i who had Kij transactions at restaurant j during the

observation period [0, T ] with the transactions occurring at tij = (tij1, tij2, · · · , tijKij ). The factors

that may affect the customer’s churn rate at the end of each of the Kij past transactions are

captured by yij = (yij1, yij2, · · · , yijKij ). Recall that yij is a function of customer experience at

the focal restaurant qij , the perceived quality of the adjacent restaurants qdj , customers’ visiting

trajectory to the adjacent restaurants δdij , and the ZIP code controls Zipj, see (2). For convenience

of notations, we let YijKij =∑k=Kij

k=1 yijk. Customers’ past transaction pattern and corresponding

experience are fully captured by (Kij, tij ,δdij ,qij , q

dj ,Zipj, T ). We then characterize the conditional

probability that customer i is still active at restaurant j by the end of time period T, denoted as

PAijT , in Lemma 2.

28

Lemma 2. For customer i with a past transaction pattern and experience characterized by

(Kij, tij ,δdij ,qij , q

dj ,Zipj, T ), the probability that she is still active at restaurant j by the end of

time period T is given by

PAijT =

(1−

(bλ +T − tij1

bλ + tijKij − tij1

)aλ+Kij−1(

1−

(bθ +YijKijbθ+Yi,j,Kij−1

)aθ))−1

. (7)

Timeline

T- theendofobservation

period!"#$ !"#% … !"#& …' + t

Observed horizon Forecasted horizonof lengtht

Figure 3: Transactions sequence for a customer i in restaurant j.

Next we derive the expected number of transactions for customer i at restaurant j in the

future t† periods conditional on her past transaction pattern and experience, characterized by

(Kij, tij ,δdij ,qij , q

dj ,,Zipj, T ). We denote this as Xij(t

†). To visualize the sequence of the events,

we illustrate the timeline in Figure 3. For simplicity of notation, we use a † superscript to denote

measures associated with the forecasting horizon t†. In particular, we let y†ijk denote the function

of factors that may affect customer i’s churn rate at restaurant j at the time of the customer’s kth

transaction after the end of the observation period T . Note that y†ijk is identical to yijk given in

(2) with the modification that the subscript k in y†ijk refers to the kth transaction after the end of

the observation time period T rather than the kth transaction during the observation period [0, T ].

For ease of exposition, similar to Yijx defined above, we let Y †ijx =x∑k=1

y†ijk. The expected number of

future transactions for customer i after time T is characterized in Lemma 3, below. For simplicity,

we assume that customers’ future experience at the focal restaurant and the perceived quality

of the adjacent restaurants stays the same as that of the last transaction during the observation

period [0, T ], i.e., y†ijx = yijKij for x∈Z+.6

Lemma 3. For customer i whose past transaction pattern and experience are characterized by

(Kij, tij ,δdij ,qij , q

dj ,Zipj, T ), the expected number of transaction in the future t† periods is given by

E[Xij(t†)|Kij, tij ,δ

dij ,qij , q

dj ,Zipj, T ] = PA

ijT

∞∑x=1

(YijKij + bθ

YijKij +Y †ijx + bθ

)aθB

(t†

t†+ bλ +T − tij1;x,aλ +Kij − 1

),

(8)

6 Because our results show that the average recommendation scores are stationary over time for all selected restaurantsbased on the augmented Dickey-Fuller (ADF) test, this is a reasonable assumption for our application.

29

where B(

t†

t†+bλ+T−tij1;k,aλ +Kij − 1

)is the cumulative distribution function of the beta distribu-

tion with parameters k and aλ +Kij − 1 evaluated at t†

t†+bλ+T−tij1.

For the ROI approximation, we next derive the expected incremental number of future

transactions that a customer can generate at a focal restaurant as her experience at the

focal restaurant or that at the corresponding adjacent restaurant changes. Consider a hypo-

thetical customer i whose past transaction pattern and experience are characterized by

(Kij, tij ,δdij ,qij , q

dj ,Zipj, T ), as described above. We denote her incremental number of transac-

tions in the future t† periods at the focal restaurant j from improving her experience there by ∆qij

as GFQ(∆qij |Kij, tij ,δdij ,qij , q

dj ,Zipj, T ), where ∆qij represents the vector of changes to customer

i’s experience at the focal restaurant j over time and is given by ∆qij = (∆qij1,∆qij2, · · ·∆qijKij ).

We have

GFQ(∆qij |Kij, tij ,δdij ,qij , q

dj ,Zipj, T ) =

E[Xij(t†)|Kij, tij ,δ

dij ,qij , q

dj ,Zipj, T ]−E[Xij(t

†)|Kij, tij ,δdij ,qij −∆qij , q

dj ,Zipj, T ]. (9)

Similarly, we denote the incremental number of transactions that customer i generates in the future

t† periods at the focal restaurant j if the average perceived quality at the adjacent restaurants

increases by ∆qdj as GNQ(∆qij |Kij, tij ,δdij ,qij , q

dj ,Zipj, T ), where ∆qdj represents the vector of

changes in the average perceived customer experience of the adjacent restaurants over time given

by ∆qdj = (∆qj1,∆qj2, · · · ,∆qjKij ). We then have

GNQ(∆qij |Kij, tij ,δdij ,qij , q

dj ,Zipj, T ) =

E[Xij(t†)|Kij, tij ,δ

dij ,qij , q

dj ,Zipj, T ]−E[Xij(t

†)|Kij, tij ,δdij ,qij , q

dj −∆qdj ,Zipj, T ]. (10)

7.2. Counterfactual Results

We will now use the expected incremental number of future transactions in response to change

in customer experience derived above to (a) identify the customers who can generate the highest

incremental value due to their improved customer experience for the focal restaurant (thus, the

focal restaurant can target such customers with its marketing or service campaigns to maximize its

ROI) and (b) identify the restaurants that can deliver the highest incremental value for the entire

network of restaurants from a supply chain improvement (thus, the supply chain orchestrator can

select such restaurants to invest in first).

Identify customers with the highest incremental value. We start with the identification of

the customers who can generate the highest incremental value for a given restaurant. We consider an

observation window of 100 weeks, i.e., T = 100, and customers with the number of past transactions

30

from 0 to 60. Following the terminology used in the literature, we refer to the time of a customer’s

last transaction as her recency, while we refer to the customer’s total number of transactions as her

frequency. We focus on restaurants in ZIP code 4 and customers who have not visited any of the

corresponding adjacent restaurants.7 For any such customer with a given frequency and recency,

using (9), we can compute her incremental number of transactions in the future three years (156

weeks),8 when we improve the customer’s experience at the focal restaurant from 8 to 9, conditional

on the average perceived customer experience across the adjacent restaurants’ being 8.9 We present

our results using a two-dimensional contour plot, as seen Figure 4.

10 20 30 40 50 60 70 80 90 100

Recency: Time of Last Transaction (Week)

5

10

15

20

25

30

35

40

45

50

55

60

Fre

qu

en

cy: N

um

be

r o

f P

ast T

ran

sa

ctio

ns

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Figure 4: Iso-curves for incremental expected number of future transactions for customers in ZIPCode 4 who have not visited adjacent restaurants when customer experience of focal restaurantchanges from 8 to 9 and the network quality equals 8.

Each dot in Figure 4 represents a hypothetical customer with a particular frequency and recency.

All of the customers on a given iso-curve share the same expected incremental number of future

transactions at the focal restaurant, which is given in the color bar on the right side of the plot.

Note that, if a customer falls between two iso-curves, her incremental expected number of future

transactions falls between the values associated with the two corresponding iso-curves. For example,

the (red) dot represents a customer who visited the restaurant 28 times during the observation

7 The same logic applies to restaurants in other ZIP codes and customers who have visited the adjacent restaurants.

8 Based on our conversation with the managers, we choose to use the incremental number of transactions in the futurethree years instead of the classic discounted expected transactions (DET), proposed in Fader et al. (2005b), for betterforecasting reliability. Our qualitative insights, however, continue to hold if we use DET.

9 Note that we consider a customer experience of 8 points as a benchmark. This is because most of the restaurantsin our application have a customer experience score of 8 or above.

31

period of 100 weeks and whose last visit was in week 90.10 For such a customer, the expected

incremental number of future transactions at the focal restaurant over the next three years will

increase by 0.158 if her experience at the focal restaurant changes from 8 to 9. To this end, based

on the values associated with the iso-curves, the customers whose recency-and-frequency profile

are inside the lightest area (yellow regions) have the highest response to their customer experience

improvement at the focal restaurant. Hence, the focal restaurant should prioritize these customers

with their marketing efforts, e.g., sending targeted coupons and special offers to such customers.

To develop more intuition about the results presented in Figure 4, we next demonstrate how a

customer’s incremental value changes with her frequency conditional on recency. To this end, we

plot the incremental number of future transactions as a function of frequency (Kij) for two selected

recency values (tijKij = 80 and 95); see Figure 5. First, note the initial increasing trend that we

observe for both values of recency. Low frequency implies that the customer makes few transactions

with the firm and hence, the number of future transactions in the next three years is low. Even

if such a customer is exposed to increased customer experience, which will reduce the probability

of churning, the incremental number of transactions will be low. As the frequency increases, the

customer is likely to make more transactions in the next three years if she stays active, and, thus,

improvement in customer experience will lead to a higher incremental improvement in the number

of future transactions. Note now the decreasing trend that we observe on the curve with relatively

low recency (i.e., tijKij = 80). When the frequency is high, but the last visit was a long time ago

(in our case 20 weeks ago), it is likely that such a customer is no longer an active customer of

the restaurant, and, hence, a customer experience improvement will not lead to a high incremental

number of transactions. As frequency gets even higher, it is even more likely that the customer is

no longer active and, thus, we observe the decreasing trend. When the recency is high (tijKij = 95),

the customer is likely to be active with the restaurant regardless of her frequency. Hence, the

decreasing trend is not present. We observe a similar pattern regarding how customers’ incremental

value changes with respect to recency for fixed frequencies.

Identify restaurants with the highest incremental value. We next demonstrate how the

supply chain orchestrator can use our methodology and results to prioritize the supply chain

improvement across different restaurants to maximize its ROI. Note that improving customer expe-

rience at a focal restaurant not only generates an incremental number of future transactions at

the focal restaurant but also improves the revenue of the adjacent restaurants through the net-

work effect. In particular, the total incremental number of transactions generated in the network

10 Note that the average customer frequency that we observe in the data is 28 in our observation window of around100 weeks. Thus, we choose the frequency 28 for a representative customer.

32

0 10 20 30 40 50 60

Frequency: Number of Past Transactions

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Incre

me

nta

l F

utu

re N

um

be

r o

f T

ran

sa

ctio

ns

80

95

Time of Last Transaction (Week)

Figure 5: The expected incremental number of transactions in the next three years that customers,who have not visited any restaurants in the neighborhood of 1 mile, generate at a focal restaurantfrom ZIP Code 4, as their experience at the focal restaurant improves from 8 to 9, conditional onthe average perceived customer experience of the adjacent restaurants’ being 8.

of restaurants by improving customer experience at a focal restaurant is the sum of the incremen-

tal number of transactions generated at the focal restaurant and that generated at the adjacent

restaurants.

Recall that, for any given customer of a particular frequency and recency at a focal restaurant, we

can quantify the incremental number of future transactions that the customer generates at the focal

restaurant as her experience at the focal restaurant improves, using (9). We have demonstrated

our results in Figure 4. We can thus obtain the total incremental number of transactions generated

at a focal restaurant by summing over the incremental number of future transactions across all of

the customers at the focal restaurant.

We next quantify the total incremental number of future transactions generated at the adja-

cent restaurants by improving the focal restaurant’s customer experience. Mathematically, this is

equivalent to the total incremental number of future transactions generated at a focal restaurant

by improving the average customer experience of its adjacent restaurants, which we can quantify

by using (10). For each customer with given recency and frequency, we present the incremental

number of future transactions at the focal store as the perceived average customer experience of the

adjacent stores increases from 8 to 9 (conditional on customer experience of the focal store’s being

8), as seen in Figure 6. Note that Figure 6a shows the results for customers who have visited only

the focal restaurant but none of its adjacent restaurants, while Figure 6b shows the results for those

who have visited the focal restaurant and at least one of its adjacent restaurants. The incremental

33

value shown in Figure 6a is purely through the network effect due to word-of-mouth, while the

incremental value shown in Figure 6b is the total network effect through both the word-of-mouth

channel and customers’ personal experience channel.

Note a customer with 28 total transactions at the focal restaurant in the past 100 weeks and

who made her last transaction at the focal restaurant at Week 90 (indicated by the red dot). If the

customer has not visited any of the adjacent stores, she may generate 0.086 additional transactions

at the focal restaurant as the average perceived customer experience of the adjacent restaurants

improves from 8 to 9. As noted earlier, the network effect is even larger if the customer has visited

the adjacent restaurants. The corresponding additional transactions at the focal restaurant is 0.297,

which is 245 percent higher compared to the case when she has not visited any of the adjacent

restaurants. Our results above underscore the importance of accounting for the network effect for

the supply chain orchestrator. In particular, the supply chain orchestrator may underestimate the

ROI from improving a focal restaurant’s supply chain quality if orchestrator does not account for

the network effect.

10 20 30 40 50 60 70 80 90 100

Recency: Time of Last Transaction (Week)

5

10

15

20

25

30

35

40

45

50

55

60

Fre

quen

cy: N

umbe

r of

Pas

t Tra

nsac

tions

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

(a) For customers who have not visited neighbors

10 20 30 40 50 60 70 80 90 100

Recency: Time of Last Transaction (Week)

5

10

15

20

25

30

35

40

45

50

55

60

Fre

quen

cy: N

umbe

r of

Pas

t Tra

nsac

tions

0.05

0.1

0.15

0.2

0.25

0.3

(b) For customers who have visited neighbors

Figure 6: The expected number of future transactions for customers at a focal restaurant in ZIPCode 4 when the average customer experience of its adjacent restaurants increases from 8 to 9.

We have described how we quantify the total incremental value for the entire restaurant chain

through improving customer experience at a focal restaurant. To illustrate how this total incremen-

tal value changes with the perceived customer experience of the adjacent restaurants, we consider

the following hypothetical restaurant network. The network is comprised of two restaurants located

in ZIP Code 4. Each restaurant has only the other restaurant as its neighbor within 1 mile. We

assume that both restaurants have 5,000 customers who had 28 visits in the past 100 weeks and

made their last transaction at the 90th week. All of these customers have visited only one restaurant

by the end of the observation period. For ease of reference, we refer to one of the restaurants as

the focal restaurant and the other as the adjacent restaurant. For any fixed perceived customer

34

experience of the adjacent restaurant, we calculate the total incremental number of transactions

generated in the focal restaurant and that generated in the adjacent restaurant as customer expe-

rience at the focal restaurant improves from 8 to 9. In Figure 7, we present the total incremental

number of transactions generated at the focal restaurant, that generated at the adjacent restaurant,

and that generated in the entire network of restaurants as a function of the perceived customer

experience at the adjacent restaurant.

Figure 7 shows that improving customer experience at the focal restaurant generates not only

incremental number of transactions at the focal store itself, but also additional transactions for

the adjacent restaurant. Moreover, the incremental value for the focal restaurant and that for the

adjacent restaurant (from the improved customer experience at the focal restaurant) both increase

with the perceived customer experience of the adjacent restaurant due to the dominating reputation

spillover effect. Hence, firms should prioritize restaurants with adjacent restaurants that provide

higher customer experience.

0 1 2 3 4 5 6 7 8 9 10Customer Experience at Adjacent Restaurants

0

500

1000

1500

2000

2500

3000

3500

Incr

emen

tal N

umbe

r of F

utur

e Tr

ansa

ctio

ns

Expected total incremental number of transactions at the focal restaurant in the future 3 yearsExpected total incremental number of transactions at the adjacent restaurant in the future 3 yearsExpected total incremental number of transactions within the restaurant chain in the future 3 years

Figure 7: Total incremental number of transactions for the networks from ZIP Code 4 as customerexperience at the focal restaurant changes from 8 to 9.

We have demonstrated that, for a fixed ZIP Code market, the supply chain orchestrator should

prioritize serving the restaurant with adjacent restaurants of higher quality. We next show how

our model help the supply chain orchestrator to prioritize its service across different ZIP Code

markets.

We consider a second network which is identical to the network described above, with one

modification: Both restaurants in this network are located in ZIP Code 2 instead of ZIP Code 4.

We plot the total incremental number of future transactions (generated at the entire network of

35

the restaurants) as a function of the perceived customer experience at the adjacent restaurant (for

both networks) in Figure 8. Our results show that the ROI is higher from improving customer

experience at the focal restaurant from ZIP Code 4 than that from ZIP Code 2. This is because,

based on our estimation results in Section 5.2, customers of restaurants in ZIP Code 4 have a lower

churn rate compared to those of restaurants in ZIP Code 2 on average. Thus, our model also can

be used by the supply chain orchestrator to identify the right market to prioritize based on the

unobservable market characteristics.

0 1 2 3 4 5 6 7 8 9 10Customer Experience at Adjacent Restaurants

0

500

1000

1500

2000

2500

3000

3500

Incr

emen

tal N

umbe

r of

Fut

ure

Tra

nsac

tions Expected total incremental number of transactions within the restaurant chain in the future 3 years at Zip 4

Expected total incremental number of transactions within the restaurant chain in the future 3 years at Zip 2

Figure 8: Total incremental number of transactions for the two network described above when thecustomer experience at the focal restaurant changes from 8 to 9.

In summary, our counterfactual study demonstrates how a focal restaurant can use our model

to quantify the incremental value from improving an individual customer’s experience, and how

we can help the supply chain orchestrator to quantify the total incremental value by improving

a focal restaurant’s customer experience. Based on our results, we show that the focal restaurant

should prioritize customers whose last visit to the restaurant was neither too long ago nor too

recent and whose total number of past transactions with the restaurant is neither too high nor

too low, for its marketing campaign or premium services. Moreover, the supply chain orchestrator

should prioritize the restaurants with a high percentage of customers with the transaction pattern

characterized above and the restaurants with high quality neighbors.

36

8. Conclusion

In this study, we explore a quality value chain network which includes all of the stages in a supply

chain, namely, manufacturers, distributors, and a network of firms that share the same brand

and their individual end consumers. Compared to the classic profit chain concept proposed in

Heskett and Schlesinger (1997), we take a more holistic view in our framework by considering (1)

the impact of vertically-related supply chain partners on customer experience at the downstream

retailer firms, and (2) the impact from the horizontally-related firms through a common brand on

customer purchasing behavior at a focal firm. In particular, we develop a two-phase framework

and methodology to manage the quality value chain network. In the first phase, we identify the

operational factors (in our application, supply chain quality issues) that have the largest impact

on customer experience at the firms. In the second stage, we explore how customer experience at

a network of firms that share the same brand affects customer future purchasing behavior at a

focal firm. As a result, our framework provides insights regarding (1) which operational initiatives

need to be prioritized for improvement to have the largest impact on customer experience, (2)

improvement at which firms provide the largest ROI for the brand in the B2B setting, and (3)

which customers have the largest response to customer experience improvement and can be selected

for targeted campaigns in the B2C setting.

In our application to a major fast food restaurant chain, we identify three main supply chain

issues, i.e., Freshness, Packaging, and Delivery. Among these issues, Freshness has the largest

impact on customer experience at the restaurants. In particular, reducing one complaint related

to Freshness per month can improve customer experience score by 0.44 points out of 10. In regard

to how customer experience affects customer purchasing behavior, we show that it is important

to consider the network effect, which significantly improves the model performance both in terms

of goodness-of-fit and forecasting accuracy. We further show that the reputation spillover effect

among the adjacent stores dominates the competition effect. Namely, higher customer experience

offered by adjacent stores may improve customers’ loyalty to the focal restaurant instead of luring

away customers from the focal store.

Based on the mechanism that we established in regard to how customer experience affects her

purchasing behavior, we then conduct counterfactual analysis. For any given customer, we quantify

the incremental number of transactions that the customer will generate based on her past trans-

action patterns if the customer’s experience at the focal restaurant improves. We show that, to

optimize ROI, the firm should focus its customer experience improvement efforts on the customers

whose last visit for the restaurant was neither too long ago nor too recent and whose number of

total transactions with the firm is neither too high nor too low. At the restaurant level, the firm

should prioritize the supply chain improvement for the restaurants that have neighbors that offer

37

better customer experience and a high percentage of customers with the profile identified above.

It is worth mentioning that, ROI from supply chain improvement at a focal restaurant includes

both the incremental value generated directly at the focal restaurant and the increment value gen-

erated at its adjacent stores due to the network effect. We demonstrate that the incremental value

generated at the adjacent stores due to the network effect can be a significant portion of the total

incremental value generated within the entire restaurant chain. This implies that it is important

to consider the network effect to quantify the financial return more accurately and that the results

without the network effect can be considerably misleading.

Acknowledgments

The authors gratefully acknowledge WCAI and an anonymous data sponsor for providing the data and for

their tremendous support for this research.

References

Abrahams, Alan S, W. Fan, G. Alan Wang, Z. J. Zhang, J. Jiao. 2015. An integrated text analytic framework

for product defect discovery. Production and Operations Management 24(6) 975–990.

Afeche, Philipp, M. Araghi, O. Baron. 2015. Customer acquisition, retention, and queueing-related service

quality: Optimal advertising, staffing, and priorities for a call center .

Aflaki, Sam, I. Popescu. 2014. Managing retention in service relationships. Management Science 60(2)

415–433.

Aksin, Zeynep, B. Ata, S. M. Emadi, C.-L. Su. 2013. Structural estimation of callers’ delay sensitivity in

call centers. Management Science 59(12) 2727–2746.

Aksoy-Pierson, Margaret, G. Allon, A. Federgruen. 2013. Price competition under mixed multinomial logit

demand functions. Management Science 59(8) 1817–1835.

Allon, Gad, A. Federgruen. 2009. Competition in service industries with segmented markets. Management

Science 55(4) 619–634.

Allon, Gad, A. Federgruen, M. Pierson. 2011. How much is a reduction of your customers’ wait worth? an

empirical study of the fast-food drive-thru industry based on structural estimation methods. Manu-

facturing & Service Operations Management 13(4) 489–507.

Anderson, Eugene W, V. Mittal. 2000. Strengthening the satisfaction-profit chain. Journal of service research

3(2) 107–120.

Arora, Swarnjit. 1973. Error components regression models and their applications. Annals of Economic and

Social Measurement, Volume 2, number 4 . NBER, 451–461.

Batt, Robert J., C. Terwiesch. 2015. Waiting patiently: An empirical study of queue abandonment in an

emergency department. Manage. Sci. 61(1) 39–59.

38

Blei, David M. 2012. Probabilistic topic models. Communications of the ACM 55(4) 77–84.

Blei, David M, J. D. Lafferty. 2009. Topic models. Text mining: classification, clustering, and applications

10(71) 34.

Bolton, Ruth N. 1998. A dynamic model of the duration of the customer’s relationship with a continuous

service provider: The role of satisfaction. Marketing science 17(1) 45–65.

Bowman, Douglas, D. Narayandas. 2004. Linking customer management effort to customer profitability in

business markets. Journal of Marketing Research 41(4) 433–447.

Braun, Michael, D. A. Schweidel, E. Stein. 2015. Transaction attributes and customer valuation. Journal of

Marketing Research 52(6) 848–864.

Buell, Ryan W, D. Campbell, F. X. Frei. 2016. How do customers respond to increased service quality

competition? Manufacturing & Service Operations Management 18(4) 585–607.

Burnham, Kenneth P, D. R. Anderson. 2003. Model selection and multimodel inference: a practical

information-theoretic approach. Springer Science & Business Media.

Cachon, Gerard P, S. Gallino, M. Olivares. 2013. Does adding inventory increase sales? evidence of a scarcity

effect in us automobile dealerships. Columbia Business School Research Paper No. 13-60 .

Cachon, Gerard P, P. T. Harker. 2002. Competition and outsourcing with scale economies. Management

Science 48(10) 1314–1333.

Cachon, Gerard P, M. A. Lariviere. 2001. Turning the supply chain into a revenue chain. Harvard Business

Review March.

Cohen, Morris A, S. Whang. 1997. Competing in product and service: a product life-cycle model. Management

science 43(4) 535–545.

Coyle, John J, C. Langley, B. Gibson, R. Novack, E. Bardi. 2008. Supply Chain Management: A Logistics

Perspective. Cengage Learning. URL https://books.google.com/books?id=TbuZnzcXGysC.

Craig, Nathan, N. DeHoratius, A. Raman. 2016. The impact of supplier inventory service level on retailer

demand. Manufacturing & Service Operations Management 18(4) 461–474.

Cronin Jr, J Joseph, S. A. Taylor. 1992. Measuring service quality: a reexamination and extension. The

journal of marketing 56 55–68.

Fader, Peter S, B. G. Hardie, K. L. Lee. 2005a. Counting your customers the easy way: An alternative to

the Pareto/NBD model. Marketing Science 24 275–284.

Fader, Peter S, B. G. Hardie, K. L. Lee. 2005b. RFM and CLV: Using iso-value curves for customer base

analysis. Journal of Marketing Research 42(4) 415–430.

Fitzmaurice, Garrett M, N. M. Laird, J. H. Ware. 2012. Applied longitudinal analysis, vol. 998. John Wiley

& Sons.

39

Forrester. 2016. The Customer Life-Cycle Marketing Playbook For 2016. Tech. rep., Forrester.

Gans, Noah. 2002. Customer loyalty and supplier quality competition. Management Science 48(2) 207–221.

Guajardo, Jose A, M. A. Cohen, S. Netessine. 2015. Service competition and product quality in the us

automobile industry. Management Science 62(7) 1860–1877.

Hall, David, D. Jurafsky, C. D. Manning. 2008. Studying the history of ideas using topic models. Proceedings

of the conference on empirical methods in natural language processing . Association for Computational

Linguistics, 363–371.

Heskett, W. E. Sasser Jr., J., L. Schlesinger. 1997. The Service Profit Chain: How Leading Companies Link

Profit and Growth to Loyalty, Satisfaction, and Value. New York: Free Press.

Ho, Teck-Hua, Y.-H. Park, Y.-P. Zhou. 2006. Incorporating satisfaction into customer value analysis: Optimal

investment in lifetime value. Marketing Science 25(3) 260–277.

Horowitz, Joel L, J. Heckman, E. Leamer. 2001. Handbook of econometrics .

Hu, Minqing, B. Liu. 2004. Mining and summarizing customer reviews. Proceedings of the tenth ACM

SIGKDD international conference on Knowledge discovery and data mining . ACM, 168–177.

Hwang, Jinsoo, J. Zhao. 2010. Factors influencing customer satisfaction or dissatisfaction in the restaurant

business using answertree methodology. Journal of Quality Assurance in Hospitality & Tourism 11(2)

93–110.

Hyken, Shep. 2016. Ten Customer Service And Customer Experience Trends For 2017. Tech. rep., Forbes.

Kaynak, Hale, J. L. Hartley. 2008. A replication and extension of quality management into the supply chain.

Journal of Operations Management 26(4) 468 – 489. Special Issue: Research in Supply Chain Quality.

Kesavan, Saravanan, V. Deshpande, H. S. Lee. 2014. Increasing sales by managing congestion in self-service

environments: Evidence from a field experiment .

Kim, Woo Gon, C. Y. N. Ng, Y. soon Kim. 2009. Influence of institutional DINESERV on customer

satisfaction, return intention, and word-of-mouth. International Journal of Hospitality Management

28(1) 10 – 17.

Knox, George, R. van Oest. 2014. Customer complaints and recovery effectiveness: A customer base approach.

Journal of Marketing 78(5) 42–57.

Knutson, Bonnie J. 2000. College students and fast food. Cornell Hotel and Restaurant Administration

Quarterly 41(3) 68–74.

Kumar, V, I. Dalla Pozza, J. Ganesh. 2013. Revisiting the satisfaction–loyalty relationship: empirical gener-

alizations and directions for future research. Journal of Retailing 89(3) 246–262.

Kumar, V., W. Reinartz. 2016. Creating enduring customer value. Journal of Marketing 80(6) 36–68.

Lehmann, Donald R, J. O’shaughnessy. 1974. Difference in attribute importance for different industrial

products. The Journal of Marketing 36–42.

40

Loveman, Gary W. 1998. Employee satisfaction, customer loyalty, and financial performance: an empirical

examination of the service profit chain in retail banking. Journal of Service Research 1(1) 18–31.

Lu, Yina, A. Musalem, M. Olivares, A. Schilkrut. 2013. Measuring the effect of queues on customer purchases.

Management Science 59(8) 1743–1763.

Maynes, Joel, A. Rawson. 2016. Linking the customer experience to value. Tech. rep., McKinsey & Company.

Mendelson, Haim, K. Moon. 2017. Growth and customer loyalty: Evidence from the app economy. Stanford

University Graduate School of Business Working Paper .

Mimno, David, H. M. Wallach, E. Talley, M. Leenders, A. McCallum. 2011. Optimizing semantic coherence

in topic models. Proceedings of the Conference on Empirical Methods in Natural Language Processing .

Association for Computational Linguistics, 262–272.

Min, Hokey, H. Min. 2011. Benchmarking the service quality of fast-food restaurant franchises in the usa: A

longitudinal study. Benchmarking: An International Journal 18(2) 282–300.

Musalem, Andres, M. Olivares, A. Schilkrut. 2016. Retail in high definition: Monitoring customer assistance

through video analytics. Working Paper .

Olsen, Tava Lennon, R. P. Parker. 2008. Inventory management under market size dynamics. Management

Science 54(10) 1805–1821.

Parasuraman, Anantharanthan, V. A. Zeithaml, L. L. Berry. 1985. A conceptual model of service quality

and its implications for future research. the Journal of Marketing 41–50.

Pingitore, Gina, N. Morgan, L. Rego, A. Gigliotti, J. Meyers. 2007. The single-question trap: The net

promoter score has limitations in predicting financial performance. Marketing Research 19 9–13.

Reichheld, Frederick F. 2003. The one number you need to grow. Harvard business review 81(12) 46–55.

Schmittlein, David C, D. G. Morrison, R. Colombo. 1987. Counting your customers: Who-are they and what

will they do next? Management science 33(1) 1–24.

Shital Chheda, Ewan Duncan, S. Roggenhofer. 2017. Putting customer experience at the heart of next-

generation operating models. Tech. rep., McKinsey & Company.

Tan, Tom Fangyun, S. Netessine. 2014. When does the devil make work? an empirical study of the impact

of workload on worker productivity. Management Science 60(6) 1574–1593.

Tirunillai, Seshadri, G. J. Tellis. 2014. Mining marketing meaning from online chatter: Strategic brand

analysis of big data using latent dirichlet allocation. Journal of Marketing Research 51(4) 463–479.

Verhoef, Peter C. 2003. Understanding the effect of customer relationship management efforts on customer

retention and customer share development. Journal of marketing 67(4) 30–45.

Wallach, Hanna M, D. M. Mimno, A. McCallum. 2009. Rethinking lda: Why priors matter. Advances in

neural information processing systems. 1973–1981.

41

Wooldridge, Jeffrey M. 2001. Econometric Analysis of Cross Section and Panel Data, MIT Press Books,

vol. 1. The MIT Press.

Yu, Qiuping, G. Allon, A. Bassamboo. 2017. How do delay announcements shape customer behavior? An

empirical study. Management Science 63(1) 1–20.

Zeithaml, Valarie A. 2000. Service quality, profitability, and the economic worth of customers: what we know

and what we need to learn. Journal of the academy of marketing science 28(1) 67–85.

42

Appendix A: Supply Chain Data Analysis

Topic Keywords in the Prior Keywords after LDA

Freshness

Apple*, Areas, Avocado, Bad, Bak-ing, Black, Blue, Bread, Breast, Brown,Browning, Caramel, Carmel, Cheese,Chewy, Chicken, Package Item Y, Col-lapse, Cookies, Crunchy, Cucumbers,Dark, Decay, Degrees, Diet, Discol-ored, Do not like, Dots, Dough, Exp,Expired, Fatty, Flavor, Frozen, Gray,Green, Grey, Gristle, Hard, Hour*,Lettuce, Life, Like, Looks, Mold*,Mushy, Onion*, Overripe, Patties, Pep-pers, Pink, Plain, Proofing, Red*, Ripe,Rise, Rotten, Salty, Shelf, Shelf life,Shiny, Shrink, Sliced, Slimy, Smell, Soft,Soggy, Sour, Spoiled, Spotted, Spread-ing, Stale, Sticky, Stored, Taste, Tem-perature, Thermometer, Tomato*, TooDark, Transparent, Tuna, Underripe*,Watery, Wet, White, Wrinkled*, Yellow

Apples, Avocado, Black, Breast, Brown,Cheese, Chicken, Cookies, Crunchy,Cucumbers, Dark, Degrees, Discolored,Dots, Frozen, Green, Hour, Hours,Lettuce, Looks, Mold, Moldy, Mushy,Onions, Overripe, Patties, Peppers,Pink, Red, Ripe, Rotten, Slimy, Smell,Soft, Soggy, Spotted, Sticky, Stored,Temperature, Thermometer, Tomato*,Tuna, Underripe*, Watery, Wet, White,Yellow

Packaging

Bag*, Bloated*, Box*, Busted, Case,Casebags, Cases, Chips, Package ItemY, Cookies, Cooler, Crushed, Cut, Dam-age*, Degrees, Package Item X*, Edges,Empty, Filled, Fold, Frame, Full, Handle,Holes, Inconsistent, Ink, Large, Leak-ing, Length, Lids, Missing, Only , Open,Overfill, Package, Seal, Seam, Short,Small, Smashed, Storage, Tabs, Tape-flaps, Tear, Temperature, Thermome-ter, Thick, Thin, Torn, Underfill, Under-weight, Weight

Bag*, Bloated*, Box*, Busted, Case*,Chips, Cookies, Cooler, Cut, Dam-aged, Degrees, Package Item X*, Filled,Frame, Large, Leaking, Missing, Open,Seal, Seam, Short, Small, Smashed,Storage, Tapeflaps, Temperature, Ther-mometer, Thick, Thin, Torn

DeliveryCar, Date, Degrees, Deliver*, Driver,Exp, Hour, Late, Outside, Present, Sat-urday, Thermometer, Time, Truck

Car, Date, Degrees, Deliver*, Driver,Hour, Late, Outside, Present, Saturday,Thermometer, Time, Truck,

Table 7: Keywords in the prior (second column) and after the LDA application (third column) fortopic modeling that identify main supply chain quality issues. Notes: * implies different forms of the word,e.g., Spot* includes the words “spot,” “spotty,” “spots,” “spotted,” and so forth. Meanwhile, to protect confidentiality of thedata provider, we are not listing any trademarked terms and have replaced two such terms with “Package Item A” and “PackageItem B”, respectively.

Appendix B: Proofs

Before we begin the proofs for the lemmas in the paper, we would like to provide a few useful formulas for

all the proofs below.

• Recall that we have λ∼Gamma(aλ, bλ) where aλ and bλ are the shape and rate parameter, respectively.

Thus, the pdf of λ, denoted as fλ(λ|aλ, bλ), is given as follows:

43

fλ(λ|aλ, bλ) =baλλ

Γ(aλ)λaλ−1 exp(−λbλ) (11)

• Meanwhile, we have θ∼Gamma(aθ, bθ) where aθ and bθ are the shape and rate parameter, respectively.

Thus, the pdf of θ, denoted as fθ(θ|aθ, bθ), is given as follows:

fθ(θ|aθ, bθ) =baθθ

Γ(aθ)θaθ−1 exp(−θbθ) (12)

• Using the moment generating function of a gamma distributed random variable, we have

Eλ[ecλ] =baλλ

(bλ− c)aλand Eθ[ecθ] =

baθθ(bθ − c)aθ

(13)

• Gamma function Γ(k) and lower incomplete gamma function are defined as follows:

Γ(k) =

∫ ∞0

tk−1e−tdt and γ(k,x) =

∫ x

0

tk−1e−tdt (14)

Note that all of proofs below are inspired by Braun et al. (2015) or a special case of the proofs there.

Proof of Lemma 1 in Section 4.2.2.

Consider a customer i whose transaction pattern during the observation period [0, T ] is characterized

by Ωij = (Kij , tij ,δdij,qij , q

dj,Zipj , T ). Recall that we have pijk = 1− exp(−θyijk). Thus, we can simplify the

likelihood function (4) by replacing pijk with 1− exp(−θyijk). We get

Lij(Ωij |λ, θ, ·) = λKij−1 exp(−λ(tijKij − tij1

)− θYijKij−1

)−λKij−1 exp

(−λ(tijKij − tij1)− θYijKij

)+λKij−1 exp

(−λ(T − tij1)− θYijKij

),

where Yijk =∑m=k

m=1 yijm. Note that λ and θ are independent. By taking the expectation over the random

variables λ and θ, we have

Eλ,θ[Lij ] = Eλ[λKij−1e

−λ(tijKij−tij1)]Eθ[e−θYi,j,Kij−1

]−Eλ

[λKij−1e

−λ(tijKij−tij1)]Eθ[e−θYijKij

]+Eλ

[λKij−1e−λ(T−tij1)

]Eθ[e−θYijKij

]. (15)

In particular, we have

Eλ[λKij−1e

−λ(tijKij−tij1)]

=

∫ ∞0

λKij−1e−λ(tijKij−tij1)

fλ(λ|aλ, bλ)dλ

=baλλ

Γ(aλ)

∫ ∞0

λaλ+Kij−2e−λ(bλ+tijKij−tij1)

dλ

=baλλ

Γ(aλ)(bλ + tijKij − tij1)aλ+Kij−1

∫ ∞0

Λaλ+Kij−2e−ΛdΛ

=Γ(aλ +Kij − 1)baλλ

Γ(aλ)(bλ + tijKij − tij1)aλ+Kij−1.

(16)

Note that we obtain the third equality in (16) by transforming variables with Λ = λ(bλ + tijKij − tij1) , and

we obtain the last equality based on the definition of the Γ(k) function given in (14). Following the same

logic, we get

Eλ[λKij−1e−λ(T−tij1)

]=

Γ(aλ +Kij − 1)baλλΓ(aλ)(bλ +T − tij1)aλ+Kij−1

. (17)

44

Based on the results on the generating function of a gamma distributed random variable given in (13), we

have

Eθ[e−θYi,j,Kij−1 ] =baθθ

(bθ +Yi,j,Kij−1)aθEθ[e−θYijKij ] =

baθθ(bθ +YijKij )

aθ. (18)

Combining (15), (16), (17) and (18), we have

Eλ,θ[Lij(Ωij |αFQ, αNQ, αd, αint,αZIP , λ, θ)]

=Γ(aλ+Kij−1)

Γ(aλ)

baλλ

(bλ+tijKij−tij1)aλ+Kij−1

(bθ

bθ+Yi,j,Kij−1

)aθ(

1−(bθ+Yi,j,Kij−1

bθ+YijKij

)aθ (1−

(bλ+tijKij−tij1bλ+T−tij1

)aλ+Kij−1))

. (19)

Q.E.D.

Proof of Lemma 2 in Section 7.2.

Consider a customer i whose transaction pattern during the observation period [0, T ] is characterized

by Ωij = (Kij , tij ,δdij,qij , q

dj,Zipj , T ). We next derive the probability that such customer is still active at

restaurant j at the end of time period T , which is denoted as PAijT . To do so, we first characterize such

probability conditional on a given λ and θ, which we denote as P (A|λ, θ,Ωij).

Note that after the last transaction, customer i either churns with probability pijKij or is still active but

has not visited the focal restaurant j since the last transaction with probability (1− pijKij )e−λ(T−tijKij )

. To

this end, we have

P (A|λ, θ,Ωij) =(1− pijKij )e

−λ(T−tijKij )

pijKij + (1− pijKij )e−λ(T−tijKij )

. (20)

To get PAijT , we need to take expectation of P (A|λ, θ,Ωij) over the joint posterior distribution of λ and θ.

We denote the joint posterior pdf of λ and θ as fposλ,θ (λ, θ|aλ, bλ, aθ, bθ). Based on Bayes’ rule, we have

fposλ,θ (λ, θ|aλ, bλ, aθ, bθ) = P (λ, θ|Ωij) =Lij(Ωij |λ, θ, ·)fλ(λ|aλ, bλ)fθ(θ|aθ, bθ)

Eλ,θ[Lij(Ωij |λ, θ, ·)]. (21)

We now have

PAijT = P (A|Ωij) =

∫ ∞0

∫ ∞0

P (A|λ, θ,Ωij)fposλ,θ (λ, θ|aλ, bλ, aθ, bθ)dλdθ.

Combining (20), (21), (11), (12) and (15), we get

PAijT =

(1−

(bλ +T − tij1

bλ + tijKij − tij1

)aλ+Kij−1(

1−

(bθ +YijKijbθ+Yi,j,Kij−1

)aθ))−1

.

The detailed algebra technique to get the equality above is similar to the proof of Lemma 1. Q.E.D.

Proof of Lemma 3 in Section 7.1.

Consider a customer i whose transaction pattern during the observation period [0, T ] is characterized

by Ωij = (Kij , tij ,δdij,qij , q

dj,Zipj , T ). We next derive her expected number of transactions in the future

t† period (after the end of observation horizon T ) conditional on her transaction pattern Ωij for given

45

parameters λ and θ. Let X(t†) be the number of transactions in the future t† periods. As one can see, we

shall have

E[X(t†)|λ, θ,Ωij ] = P (A|λ, θ,Ωij) ·E[X(t†)|λ, θ,Ωij ,A],

where A represents the event that customer i stays active at restaurant j by time T . Recall that the first term

P (A|λ, θ,Ωij) is given by (20). The second term E[X(t†)|λ, θ,Ωij ,A] is the expected number of transactions

in the future t† period conditional on λ, θ, Ωij and event A.

To derive the second term, we let τ + T be the time when customer i becomes inactive at restaurant j.

We next derive the pdf of tau, which will be useful later. We let X(t) be the number of transactions during

the time periods from T to T + t. Note we have

P (τ > t) =

∞∑k=1

P (τ > t|X(t) = k)P (X(t) = k),

where P (τ > t|X(t) = k) is equivalent to the probability that customer survived all the k transactions. Thus,

we have P (τ > t|X(t) = k) = e−θY†ijk , where Y †ijk =

∑k

0 y†ijm. Recall that y†ijm is identical to yijm given in (3)

with the modification that the subscription m in y†ijm refers to the mth transaction after time period T rather

than during the observation period [0, T ]. Meanwhile, given that X(t) follows a shifted Poisson process, we

have P (X(t) = k) = (λt)k−1e−λt

(k−1)!. Thus, we have

P (τ > t) =

∞∑k=1

(λt)k−1e−λt

(k− 1)!e−θY

†ijk .

We denote the pdf of τ as fτ (τ), which can be derived by differentiating the equation above over t. It is

given by

fτ (τ) = e−λτ∞∑k=1

(λτ)k−1e−θY†ijk

(k− 1)!(λ− k− 1

τ).

We next derive E[X(t†)|λ, θ,Ωij ,A]. In particular, we have

E[X(t†)|λ, θ,Ωij ,A] = E[X(t†)|λ, θ,Ωij ,A, τ > t†]P (τ > t†) +

∫ t†

0

E[X(t†)|λ, θ,Ωij ,A, τ ≤ t†]fτ (τ)dτ

= λt†

(∞∑k=1

(λt†)k−1e−λt†

(k− 1)!e−θY

†ijk

)+

∫ t†

0

λτfτ (τ)dτ

=

(∞∑k=1

(λt†)ke−λt†

(k− 1)!e−θY

†ijk

)+

∞∑k=1

e−θY†ijk

(k− 1)!

∫ t†

0

(λτ)k(λ− k− 1

τ

)e−λτdτ

=

∞∑k=1

γ(k,λt†)

Γ(k)e−θY

†ijk .

To this end, we have

E[X(t†)|λ, θ,Ωij ] =(1− pijKij )e

−λ(T−tijKij )

pijKij + (1− pijKij )e−λ(T−tijKij )

·∞∑k=1

γ(k,λt†)

Γ(k)e−θY

†ijk .

Thus, we have

46

E[X(t†)|Ωij ] =

∫ ∞0

∫ ∞0

E[X(t†)|λ, θ,Ωij ]fposλ,θ (λ, θ|aλ, bλ, aθ, bθ)dλdθ

= PAijT

∞∑x=1

(YijKij + bθ

YijKij +Y †ijx + bθ

)aθB

(t†

t†+ bλ +T − tij1;x,aλ +Kij − 1

),

(22)

where B(

t†

t†+bλ+T−tij1;x,aλ +Kij − 1

)is the cumulative distribution function of the beta distribution with

parameter x and aλ +Kij − 1 evaluated at t†

t†+bλ+T−tij1. We refer the readers to equation (23) in Appendix

A of Braun et al. (2015) for the detailed algebra to obtain the second equality above. Q.E.D.

Derivation of the posterior probability of a given customer making 0 transaction in the future

t† period P (0|t†, ·) defined in Section 5.2.

Consider a customer i whose transaction pattern during the observation period [0, T ] is characterized by

Ωij = (Kij , tij ,δdij,qij , q

dj,Zipj , T ). Let the number of transactions in the future t† be X(t†). Note that the

probability that customer i makes 0 transaction in the future t† period equals to the sum of the probability

that customer i becomes inactive at the end of observation period T and the probability that customer i is

still active but has not made any transaction yet within the next t† period after the observation period T .

To this end, we have

P (Xij(t†) = 0|λ, θ,Ωij) = 1−P (A|λ, θ,Ωij) +P (A|λ, θ,Ω)e−λt

†,

where P (A|λ, θ,Ωij) is given in (20) above.

The posterior expected probability of making 0 transaction in the future t† period P (Xij(t†) = 0|Ωij) is

then given by

P (Xij(t†) = 0|Ωij) =

∫ ∞0

∫ ∞0

P (Xij(t†) = 0|λ, θ,Ωij)f

posλ,θ (λ, θ|aλ, bλ, aθ, bθ)dλdθ

=C0(G1 +G2).

(23)

where fposλ,θ (λ, θ|aλ, bλ, aθ, bθ) is the joint posterior distribution of λ and θ given in (21). The algebra for the

second equality is similar to that in the Proof of Lemma 1. Moreover, C0, G1 and G2 are given by

C0 =

(bλ + tijKij − tij1

)aλ+Kij−1 (bθ +Yi,j,Kij−1

)aθΓ(aλ+Kij−1)Γ(aθ)

·

(1−

(bθ +Yi,j,Kij−1

bθ +YijKij

)aθ·

(1−

(bλ + tijKij − tij1

bλ+T−tij1

)aλ+Kij−1))−1

,

G1 =

(Γ(aθ)

(Yi,j,Kij−1 + bθ)aθ− Γ(aθ)

(YijKij + bθ)aθ

)Γ(aλ +Kij − 1)

(bλ + tijKij − tij1)aλ+Kij−1,

G2 =Γ(aθ)

(YijKij + bθ)aθ· Γ(aλ +Kij − 1)

(T − tij1 + t∗+ bλ)aλ+Kij−1.

47

Appendix C: Validation of Text Analysis Approach.

To validate the seeded LDA results, we calculate three quality metrics of the estimated topic-keyword prob-

ability distribution.

The first quality metric is the average topic coherence, defined by Mimno et al. (2011), as

Coherence=1

Oκ

Oκ∑κ=1

p∑u=2

u−1∑v=1

logD(wκu,w

κv ) + 1

D(wκv ), (24)

where (wκ1 , . . . ,wκp ) is the list of p most probable words in topic κ, Oκ is the number of topics, D(w) is the

number of complaints containing the word w, and D(w,w′) is the number of complaints containing both

w and w′. The general idea behind this measure is to gauge the interpretability of each topic based on

co-occurences of its keywords. Topics with larger topic coherence have been shown to be more interpretable

by human judges (Mimno et al. 2011).

The second quality metric, Hellinger Distance, is the average distance between topics in the topic-keyword

probability distribution (Blei and Lafferty 2009). The idea here is that topics that are further apart contain

keywords that are more distinct and having less overlap, which tends to result in better interpretability.

Hence, the methods with higher Hellinger Distance are preferred.

Finally, the third quality metric is the entropy of the topic-keyword probability distribution, defined as

Entropy=− 1

Oκ

Ok∑κ=1

∑w

P(w|Topic κ) log(P(w|Topic κ)), (25)

where κ indexes the topic and w words (Hall et al. 2008). Higher entropy values indicate that the topic

distributions are more evenly spread over the topics. Thus, lower entropy values are desired for more distinct

topics and greater interpretability.

Table 1 shows that the seeded LDA method is preferred to the standard LDA topic model with uninformed

prior according to all three quality metrics.

Appendix D: Validity of Instrumental Variables

Here we provide detailed estimation results to show that our instruments are valid and satisfy the two

necessary and sufficient conditions of relevance and exclusion (Wooldridge 2001).

We begin by assessing the relevance condition, which states that the instruments must be correlated with

the endogenous variables (complaint counts in our case). In the first stage of the 2SLS model, we use linear

regression to explain the endogenous variables COMPLcat

jl for cat ∈ Fresh,Package,Delivery using the

instruments (DIST,POS,STORENUM) and controls Cj as independent variables. Estimation results from

these regressions are shown in Table 8. It is important to note that at least one of the instruments is statis-

tically significant when explaining each endogenous variable. To rigorously check the relevance condition, we

perform the so-called weak instruments test, a partial F-test with the null hypothesis that, given the control

variables, the instrument effects are all equal to zero. Table 9 shows that we reject the null hypothesis in

each case, providing statistical evidence that the relevance condition is satisfied.

The exclusion condition states that instruments should not be correlated with the error term from the

second stage of the 2SLS model. As such, we use linear regression to explain the residuals from the second

48

stage of the 2SLS model using the instruments as independent variables. Table 10 shows the full estima-

tion results and that the instruments are not correlated with the residuals, since none of the instruments

are statistically significant individually or collectively through the F-test, thus providing evidence that the

exclusion condition is not violated.

Dependent variable:

COMPLFresh COMPLDelivery COMPLPackaging

(1) (2) (3)

Zip 1 −0.008∗∗∗ −0.001∗∗∗ −0.002

(0.002) (0.0005) (0.001)

Zip 2 0.006∗∗∗ −0.0004 0.001

(0.002) (0.0004) (0.001)

Zip 3 −0.007∗∗∗ −0.001 0.002

(0.002) (0.0005) (0.001)

Restaurant age 0.002∗∗∗ 0.0003∗∗∗ 0.0004∗

(0.0004) (0.0001) (0.0003)

Manager ability 0.003∗∗∗ 0.0003 0.002∗∗

(0.001) (0.0002) (0.001)

Distance 0.0001∗∗∗ 0.00001∗ 0.00004∗

(0.00003) (0.00001) (0.00002)

POS implementation flag 0.010∗∗∗ 0.001 0.001

(0.002) (0.0005) (0.002)

Number of stores per distributor 0.0002∗∗∗ −0.00000 0.0001∗∗

(0.00004) (0.00001) (0.00003)

Constant −0.091∗∗∗ −0.004 −0.037∗∗∗

(0.018) (0.004) (0.012)

Observations 20,233 20,233 20,233

R2 0.004 0.001 0.001

Adjusted R2 0.004 0.001 0.001

F Statistic (df = 8; 20224) 10.053∗∗∗ 3.146∗∗∗ 2.450∗∗

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Table 8: Estimation results from the first stage of the 2SLS model.

statistic p-value

COMPLFresh 9.738 < 0.01

COMPLPackaging 3.330 0.0187

COMPLDelivery 3.760 0.0103

Table 9: Results from the weak instruments test results establishing that the proposed instrumentssatisify the relevance condition.

49

Dependent variable:

Residual

Distance 0.000

(0.0005)

POS implementation flag 0.000

(0.036)

Number of stores per distributor −0.000

(0.001)

Constant −0.000

(0.201)

Observations 20,233

R2 0.000

Adjusted R2 −0.0001

Residual Std. Error 1.671 (df = 20229)

F Statistic 0.000 (df = 3; 20229)

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Table 10: Estimation results from the regression to check the exclusion condition of the 2SLS model.