Predicting NoShows to Create an Effective Overbooking ...€¦ · unprofitable one. Various...

Predicting NoShows to Create an Effective

Overbooking Policy for Restaurants

Madeleine Shannon

Advisor: Professor Ivan Canay

Northwestern University Mathematical Methods in the Social Sciences

2015

Table of Contents

I. Abstract…………………………………………………………………….3

II. Acknowledgments………………………………………………………….4

III. Introduction………………………………………………………………...58

IV. Literature Review…………………………………………………………..814

V. Data Description…………………………………………………………...1417

VI. Model....……………………………………………………………………1820

VII. Results……………………………………………………………………...2124

VIII. Overbooking Policy and Implications……….……………………………..2530

IX. Conclusion………….………………………………………………………3032

X. Tables and Figures………………………………………………………….3338

XI. References………………………………………………………………….3940

XII. Appendix A...………………………………………………………………4146

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http://www.completeseating.com/


I. Abstract

Customers who do not show up for their reservations are extremely costly for

restaurants—an unfilled table may be the difference between a profitable night and an

unprofitable one. Various strategies employed to reduce noshow rates are only slightly effective.

However, other industries have used overbooking to substantially mitigate the cost of a given

noshow rate. Despite the risk of jeopardizing customer satisfaction, a moderated overbooking

policy can be effective for restaurants. I estimate the probability that restaurant customers will be

noshows using a large data set of reservation and restaurantspecific variables. I use this

logistic model to inform an overbooking policy for restaurants, emulating the overbooking

strategy of airlines and healthcare clinics. Restaurant overbooking has not been extensively

studied, and to my knowledge, no suggested policy has been developed by incorporating the

predicted probability of noshows. The data I use include 74,926 observations from fifteen

restaurants over four years. I find that a customer’s previous reservationkeeping behavior at the

restaurant in question has the largest marginal effect on whether he or she will be a noshow. I

recommend an overbooking policy that uses this variable to stratify customers and find that a

sample restaurant could save over $220,000 per year.

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II. Acknowledgments

First and foremost, I would like to thank my advisor, Professor Ivan Canay, for all of his

advice and guidance throughout this entire process. He was instrumental to the completion and

success of this thesis. I would also like to thank Chris Butler for generously providing me with

the data and helping to develop my ideas early on. Thank you to Professor Rogerson for so

enthusiastically brainstorming my topic with me and for encouraging me to tackle this empirical

project. Germán Bet was extremely helpful in answering my questions during office hours and

engaging with my results. I’d like to thank all of my family and friends who helped edit my work

and for their support in general, which is always invaluable. Finally, I’d like to thank Marc Vetri

for stimulating my interest in the world of food and for the best meal I’ve ever eaten.

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III. Introduction

Noshows—customers who fail to show up for their reservation—are a persistent and

costly problem for restaurants. So costly, in fact, that some restaurants have resorted to

personally outing noshows on Twitter, by name (Forbes 2013). Restaurateurs know that making

money means turning tables. A night in a restaurant is a delicate dance: one must rotate the

customers in and out as quickly as possible while still giving them a personal, enjoyable

experience. Since every empty table in a restaurant is lost revenue, and restaurants operate with

slim margins (typically around 3% 5%), noshows can be the difference between a profitable

night and a costly one. The noshow problem affects almost every restaurant—some cities, such

as New York, report restaurant noshow rates of up to 20% (Reddy 2012). This means that a

restaurant with a capacity of 50 people and an average check size of $100 for a table of two,

could be losing up to $500 in revenue each hour due to noshows. Restaurants are confronted 1

with an interesting problem: customers face no cost for not showing up for their reservation, and

yet, restaurants suffer when they hold an empty table.

Due to this costly predicament, restaurants have employed various strategies to combat

noshows. First, the optimality of taking reservations has been called into question. Despite the

fact that customers value the guaranteed seating that comes with a reservation, restaurants give

them away for free. Customers make reservations in advance, without knowing how much they

will value that reservation when it comes. The customers only fix their valuation at the time they

decide whether or not to show up; thus, there is no incentive for them to honor their reservation

if they find that their current valuation is not as high as it was when they made the reservation.

1 Assuming a table turn time of one hour and a 20% noshow rate, without accounting for differences in check size or turn time due to party size.

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Reservations are useful, however, because they allow restaurants to shift their customers

into offpeak times by informing them that onpeak times are filled. So, reservations allow

restaurants to collect more money on slow days at the risk of losing money on fast days due to

noshows. Reservations also lead to more efficient table assignments since variations in arriving

party sizes are known ahead of time. That said, as demand increases, offering reservations

becomes less and less optimal because seats can be filled with walkins (Alexandrov and

Lariviere 2007). But not every restaurant has ample demand. Three Michelin star restaurants, for

example, are typically reserved for special occasions and therefore generally do not generate

enough foot traffic to fill tables on the spot. Restaurants that do offer reservations have found

some success combating noshows in other ways: confirming reservations via text or by phone,

requiring a credit card to hold the reservation and threatening a noshow fee, or refusing to serve

customers who did not show up for their last reservation at that restaurant (McKeever 2013).

While these strategies slightly reduce the noshow rate, none are universally successful and some

are unnecessarily harsh.

Clearly, it is hard to force people to honor reservations. The next best option, then, is for

restaurants to find a way to mitigate the costs associated with noshows. One such strategy,

overbooking, has been successfully applied in other industries. Airlines, hotels, and clinical care

settings use overbooking policies to offset the cost of noshows. Airlines have profitably applied

overbooking to the extent that it is now common practice. Some airlines will overbook up to

50% of their seats (Massey n.d.). By giving vouchers to people who volunteer to take another

flight and refunding those who are bumped involuntarily, airlines employ a compensation

scheme that allows them to oversell quite frequently, potentially without damaging customer

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loyalty (although this is debated by Wangenheim and Bayón 2007, see section IV of this paper).

Both hotels and airlines use priority stratification of customers to determine who will be

overbooked or bumped, giving loyal customers some security.

Clinical care settings have also benefitted from overbooking. Unlike airlines, however,

noshows in doctors offices are distributed throughout the day; they do not occur at one moment.

Appointment overbooking in this setting is more nuanced, yet still has been shown to be

beneficial (LaGanga and Lawrence 2007, discussed in section IV of this paper). The downside to

appointment overbooking is that customers may face increased waiting times and service

providers may work overtime, although customers are not typically “bumped” out of their

appointments.

Overbooking in restaurants has not been extensively studied. Restaurant reservation

overbooking mirrors clinical appointment overbooking because just as appointments are spread

out over the day, reservations are spread throughout the restaurant’s open hours. However, this is

an imperfect analogy. There are many important aspects of reservations that increase the

complexity of a restaurant overbooking policy, such as varying party size and the vast

importance of customer satisfaction. Customer satisfaction is more important for restaurants than

healthcare clinics because doctors are selling a necessary service, while restaurants are selling an

optional experience. Creating a restaurant overbooking policy is also difficult because of a lack

of publicly available data—especially for small, independent restaurants. These restaurants

themselves may not know the extent of their noshow problem.

In order to create an effective overbooking policy for restaurants, it is necessary first to

obtain and use this private data to understand the noshow problem. Why are customers not

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showing up? What makes one customer more likely to be a noshow than another? To answer

these questions, I use a large data set to create a model that predicts the probability of a customer

being a noshow and then use this model to inform an overbooking policy—allowing restaurants

to decide whether or not to use reservation overbooking on a given night, and if so, by how

much. To my knowledge, this is the first time that a large data set of individual reservations and

restaurant characteristics has been used to estimate a binary choice model. In turn, the estimated

choice model provides a framework to develop an effective overbooking policy that incorporates

the predicted probability of being a noshow given observed characteristics of the customers and

restaurant.

IV. Literature Review

The existing literature mainly focuses on four topics related to restaurant overbooking:

noshows in general, restaurant reservations, overbooking in other industries, and the behavioral

consequences of overbooking. Restaurant overbooking itself is only briefly mentioned in a few

studies in these areas.

NoShows in General

Much of the previous work around noshows has been anecdotal. An article in The

Washington Post (2003) asserted that noshows not only cause restaurants to lose money on

unfilled tables, but also lead to additional costs due to wasted food. According to this article, in

order to combat noshows some restaurants only take reservations on weeknights, when they

benefit most from guaranteeing seats, and operate as walkin only restaurants on the weekends

when demand is higher. In Remarkable Service (2014), The Culinary Institute of America

offered a grim outlook for dealing with noshows; it suggests that even reconfirmed reservations

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often lead to noshows. And, despite the fact that reservations help restaurants shift demand to

offpeak times, they warn that offering reservation times an hour or more outside of the

originally requested time will dramatically increase the chance of a noshow. The tradeoff

between filling tables effectively via overbooking and customer service is troublesome as

well—“it might be preferable to lose a table for a night rather than risk losing a valuable

customer” (Remarkable Service, page 124). Oh and Su (2012) proposed a pricing policy and

noshow penalty to deal with noshows. Their results showed that restaurants should charge a

noshow penalty as high as the price of the meal while providing a discount to customers for

their meal if they show up.

Restaurant Reservations

As mentioned earlier, the optimality of taking reservations has been addressed in

previous studies. For example, Alexandrov and Lariviere (2007) assume a single evening, with a

priori homogenous customers who all consume the same capacity, and find that reservations can

be profitable under any of the following circumstances: uncertain market size, when the evening

is divided into peak and offpeak periods, or under strong competition. Reservations are not

recommended when customers are likely to favor just one firm in the market or in a large market

where sales will be lost to noshows. Bertsimas and Shioda (2003) used a stochastic gradient

algorithm to create a model that determines how many reservations to accept for a particular day

given information on reservation requests, walkins, and noshow rates. This study differs from

the current study because it assumes a constant noshow probability of 10%, which I will show is

a limiting assumption.

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Overbooking in Airlines

There has been a considerable amount of past research that focuses on overbooking in the

airline industry—with somewhat mixed results. Rothstein (1985) and Arenberg (1991) view

airline overbooking as an economic necessity. With reported noshow rates of 10% to 20%,

airlines allegedly must resort to overbooking to offset losses from unfilled aircrafts. Since the

writing of those articles, airline overbooking has become more prevalent and

nuanced—Coughlan (1999) proposed an improved airline overbooking model by addressing the

multiclass system that most airlines use. Suzuki (2002) took into account the negative effect of

overbooking on customer behavior and showed that despite the significant size of this effect,

airlines should not reduce overbooking because the positive gain far outweighs the negative

consequences. In a later work (Suzuki 2004), she addressed the net benefit of airline overbooking

and found it to be positive under all conditions, but far less than the reported gross benefit that

most airlines focus on.

Overbooking in Healthcare

In the healthcare world, the practice of patient overbooking has become more widespread

as well. LaGanga and Lawrence (2007) found that overbooking allows healthcare clinics to serve

more patients and improve provider productivity, but it can also lead to increased patient wait

times and provider overtime. In another study, increased provider overtime was taken into

account and overbooking was still shown to be beneficial. East Carolina University’s Student

Health Services Clinic, which had a 10.8% patient noshow rate prior to the study, employed an

overbooking model that included the effects of employee burnout and saved around $95,000 per

semester while improving healthcare access for students. They found that overbooking by

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10%15% was the most effective. Zeng, Zhao, and Lawley (2010) showed that overbooking

positively affects showup rates by reducing appointment delay—the time between requesting an

appointment and being seen by a doctor—but negatively affects showup rates by increasing

office delay—the amount of time spent waiting in the office before being seen. Because of this,

they suggest using a selective dynamic overbooking strategy that takes into account their finding

that overbooking has different effects for patient populations with different characteristics. Both

Shonick and Klein (1977) and Dove and Schneider (1981) created models that use patient

characteristics to predict noshow rates and subsequently inform overbooking policy. Shonick

and Klein found age and sex within age to be significantly related to noshows and proposed

overbooking enough patients so that the expected number of arrivals based on the estimated

probabilities of arriving is equal to clinic capacity. Dove and Schneider found that the most

important predictor of appointment keeping is a patient’s previous appointmentkeeping pattern.

This study, too, suggested scheduling patients based on the expected number of patients who will

show up, but found that overbooking based on the average noshow rate is a simple and effective

method for clinics.

Behavioral Consequences of Overbooking

The behavioral consequences of overbooking were addressed by Wangenheim and Bayón

(2007), who found that customers who experience the negative effects of overbooking

significantly reduce their interactions with the firm, while customers who benefit from

overbooking only slightly increase their interactions, suggesting that firms who chose to

overbook should consider the longterm consequences of assuming a revenuecentric approach

over a customercentric one. In his article “The Customer is Not Always Right,” Sorrell responds

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to this claim by asserting that when deference to the customer leads to a significant loss of

revenue (as it often does), the customer should not come first. Suzuki (2002) accounted for the

behavioral consequences of overbooking gone awry, as discussed earlier, and found overbooking

to be beneficial despite these consequences.

Overbooking in Restaurants

An overbooking policy for restaurants is mentioned briefly in Oh and Su’s work (2012).

They incorporate overbooking into their model of noshow penalty fees and meal pricing and

find that as the market size increases with respect to restaurant capacity, the optimal meal price

with overbooking increases, the optimal noshow fee decreases, and profit with overbooking

increases. See their results reproduced in Appendix A, Figure A1. Overbooking for restaurants is

also addressed by Alexandrov and Lariviere (2011)—their model assumes customers are

atomistic and they suggest overbooking by giving out K/F(T) reservations, yielding K actual

patrons (where K is capacity and F(T) is the number of customers interested in dining out on a

slow night). The overbooking policy they propose seems to suggest that overbooking is the

definitive answer to noshows, but this is oversimplified due to assumptions made in the

theoretical setting.

Advancing Existing Literature

As discussed, the negative effects of restaurant noshows and the motivation behind

taking reservations have been addressed in previous work. Overbooking in the airline and

healthcare industries has been looked at fairly extensively from both economic and behavioral

viewpoints. Patron characteristics have been used successfully to inform overbooking policy in

the clinical care setting. However, despite the rampant problem of noshows in the restaurant

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industry, a comprehensive combination of these studies has not yet been tackled.

Perhaps overbooking in restaurants has not been extensively studied due to a lack of

sufficient data in the restaurant industry, especially relative to the wealth of available data from

airlines and healthcare clinics. Both the airline and healthcare industries heavily depend on data.

These industries consist of huge, publicly owned corporations that must use data to operate

efficiently. The restaurant industry, however, is mostly made up of many small, private, and

highly competitive singular units. Large restaurant groups and hotel restaurants are the

exception; they are financially supported by the overarching company and therefore have the

capacity to collect and analyze their data, although certainly not all of them do. Only 12% of

restaurants in the U.S. have over 50 employees, while 46% of restaurants in the U.S. have under

10 employees. These singular, oneoff restaurants are usually the ones who are hit hardest by 2

noshows. They typically do not even collect data, let alone use it to their advantage. OpenTable

has played a big role in giving restaurants the opportunity to own their data. Restaurants paying

for the OpenTable service can track their customers, view their noshow rates, and start

marketing campaigns. It certainly is important that restaurants know and keep track of these

statistics, but it is more important that this information is actually analyzed and used to make

changes.

Using customer data collected from many restaurants, I will advance the existing

literature by proposing an overbooking policy for restaurants that is informed by a predictive

noshow model based on customer and restaurant characteristics. I will also attend to restaurants’

unique need for superior customer service by suggesting compensation schemes in the event that

2 Business Data from the US Census Bureau http://censtats.census.gov/cgibin/cbpnaic/cbpcomp.pl

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overbooking goes awry. To my knowledge, this analysis has never been done.

V. Description of Data

I worked with three categories of variables: the first is restaurantspecific data that

include demographic information about the restaurants in my data set; the second is Yelp

information (price and rating) for each restaurant, which I manually collected from Yelp; and the

third is reservationspecific data that include information about each reservation in every

restaurant.

Manipulating the Data Set

I received the restaurantspecific and reservationspecific data from Chris Butler (see

acknowledgments), founder of Complete Seating, “a reservation, waitlist, and seating

management service,” similar to OpenTable. The data span from February 27, 2011 through the 3

end of 2014. My first challenge was converting this rich data into a workable form. I planned to

conduct my analysis in STATA, but the data set was in the form of a MySQL dump, which is

unreadable by STATA. To understand why, it is helpful to understand what MySQL and STATA

are. MySQL is a specialized database software that allows users to store and retrieve data

efficiently. SQL is a computer language used to access data from MySQL. STATA is a data

analysis program—not a database. In order to move the data from MySQL, where it was stored,

and into STATA, I first created a local SQL server and connected to it via Sequel Pro. Then, I

created a new database and imported the MySQL dump file. This allowed me to export the data

as a .csv file, thereby converting the MySQL dump into a file type readable by STATA.

3 www.completeseating.com

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In order to create my final data set, I manually appended the restaurant data set with the

Yelp information that I collected by searching for each restaurant on Yelp.com. Yelp information

is missing for three out of the fifteen restaurants. I merged the restaurant and Yelp information

data set onto the reservationlevel data set using the restaurant ID number that was included in

both data sets. The final reservationlevel data set includes 74,926 observations.

Category 1: Restaurantspecific Variables

The first category of variables comprises the restaurantlevel data set which has

information about the fifteen restaurants that used the Complete Seating service to collect

reservations and acquired enough reservations to be included in the final data set (at least 100).

Three restaurants were dropped under these conditions: two because they had gathered less than

ten reservations each and another because all 117 of its observations were generated by walkins.

The retained restaurants are located in the following cities in California: San Francisco (10

restaurants), Burlingame (1), Novato (1), Oakland (1), Sonoma (1), and Winnipeg in Canada (1).

The data include choices the restaurant has made about reservations and guest communication.

For instance, restaurants chose how far in advance reservations can be made (ten out of sixteen

restaurants allow reservations 30 days in advance), the minimum and maximum party size for

reservations (minimum is one person for all but one restaurant, which has a two person

minimum, and the maximum varies between four and sixteen people), whether or not to restrict

large parties, and the number of people that constitutes a large party. Regarding guest

communication, the restaurant may or may not have allowed automated communication with the

guest through text, email, and/or phone, and may or may not allow waitlist requests via text,

phone, and/or widget (via the Complete Seating application). Finally, the restaurant chose how

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many days in advance it would confirm the reservation with the guest: 1 day in advance (for

thirteen of the restaurants), 2 days (for one restaurant), or 7 days (for one restaurant).

Category 2: ManuallyInputted Variables

To this data, I appended the second category of variables: Yelp rating and Yelp price. It

should be noted that the Yelp information was collected in 2015 and therefore may not match the

Yelp ratings or prices at the time of many reservations in the data set—it is treated as a proxy.

Yelp information is missing for three restaurants, as mentioned, which were not listed on Yelp.

This is likely due to restaurant closure or name change. These three restaurants account for 1,176

observations. The Yelp rating is 3.5 out of five stars for eight of the restaurants. The Yelp price

is two out of four (with four being the most expensive) for seven restaurants.

Category 3: Reservationspecific Variables

The third category of variables is reservationspecific. This data set initially included

information about seatings that originated from walkins via the waitlist, cancellations, and from

reservations that were made in advance. For my purpose of predicting noshows, only

reservations that were made in advance and cancellations within one hour of the reservation time

were kept. An unidentifiable guest id, which is missing for 4,384 reservations, is used to note if

the guest is a repeat customer or a firsttime guest, and if that guest has been a noshow in the

past at this restaurant. Additionally, a “guest record” can be gleaned from this by tracking the

ratio of the number of noshows to the number of total reservations throughout the guest’s

history with the restaurant. Variables related to guest ID have 70,542 observations. Also included

in this data set are: the time of the requested reservation, the party size, the origin of the

reservation (whether it was made over the phone or from the restaurant website), the guest’s area

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code, and guest notes. Party size is one or two people almost half the time. Guest notes include

birthday and anniversary notes, requests for special tables, and notifications about allergies or

vegetarian diets—28% of the reservations have guest notes of some kind. The guest’s area code

was matched to the restaurant’s area code to create an approximate indicator for whether or not

the guest is located nearby the restaurant. After the reservation has been made, it is noted

whether or not the guest was contacted to confirm their reservation (80% were) and if so, how

this was done (via email, phone, or text). Finally, cancellations and noshows are recorded at the

time they occur. Summary statistics for the variables included in my data can be found in Table

1, section X.

The Dependent Variable

The response variable of interest is a noshow indicator. I defined noshows as those

customers who either did not show up or cancelled within an hour of the reservation time, under

the assumption that it would not be reasonable for the restaurant to acquire a new reservation to

replace the canceled reservation within an hour. Of course, walkins may act as a replacement in

these cases, but having enough walkins to make up for noshows is not certain, and walkins are

not included in the data set. Restaurant hosts can indicate noshows either by recording a

noshow datetime or marking the “state” of the party as a noshow. With variation in the use of

the application, some hosts did one or the other and perhaps some noshows went unrecorded

entirely. Labeling cancellations within an hour of the reservation time as “noshows” will also

act as a buffer for these cases. The final noshow rate in the data is 10.9%.

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VI. Model

Let Y denote the noshow indicator and (X, Z) be a vector of reservationspecific and

restaurantspecific covariates. The following model is used to estimate the effects of different

restaurantspecific and reservationspecific characteristics on the probability of a reserver being a

noshow:

(1) Pr( = 1 | ) = ,Y jit , ZX jit jit [βX γZ ]Λ ′ jit + ′ jit + δj

where j indexes restaurants, i indexes reservations, and t indexes time. takes three forms in [∙]Λ

this analysis: a linear function for OLS, a logistic function for Logit, or a cdf normal function for

Probit. I split the covariates into two groups. The vector includes six coreX jit

reservationspecific variables. The vector includes restaurantspecific variables, which areZ jit

only used in some specifications as controls. Finally, denotes restaurant fixed effects. δj

The six core variables are: Party Size, Same Area Code Indicator, Repeat Guest

Indicator, Confirmation Indicator, Previous NoShow Indicator, and Guest Note Indicator. Same

Area Code Indicator is used as a proxy for whether or not the customer lives nearby the

restaurant and is 1 when the restaurant and customer share the same area code. Repeat Guest

Indicator is based on an unidentifiable guest ID and is 1 when that customer has previously made

a reservation at that restaurant. Confirmation Indicator is 1 when the customer was either called

or texted to confirm the reservation sometime before the reservation time, and 0 otherwise.

Previous NoShow Indicator is 1 when the customer did not show up to a previous reservation at

that restaurant—by definition, Repeat Guest is 1 whenever Previous NoShow is 1. Guest Note

Indicator is 1 if the customer included any kind of special instructions with his/her requested

reservation, and 0 if not. These core variables are all reservationspecific and therefore are easy

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for the restaurant to track and respond to. Additionally, they all provide potential reasons for a

guest to be more or less likely to show up. For example, if someone takes the time to enter a

guest note about a special occasion, it is reasonable to believe that that person will be more

inclined to show up for their reservation. If a customer lives in the same area code as the

restaurant he or she reserved with, that customer has a lower cost of getting to his or her

reservation and therefore may be more likely to show up. Similar lines of reasoning can be

applied to the other variables.

There are five total specifications for each form of Each specification addresses a [∙].Λ

potential problem with the estimations obtained from the simple model (specification 1), which

includes only Specification 2 includes control variables that are restaurantspecific, in.X jit ,Z jit

order to draw out bias captured in the six core reservationspecific variables. Specification 3

includes restaurant fixed effects, in order to control for heterogeneity caused by consistent,δj

unobserved differences between restaurants that affect the observed variables. For example, if

one restaurant has a host who is always rude when calling to confirm a reservation, we might

expect this to lead to an increase in noshows. This effect would not be captured by the six core

variables, but would be potentially correlated with them. Specification 4 relaxes the assumption

that are iid by using clustered standard errors at the restaurant level, therefore, X , Z ) (Y jit jit jit

allowing for arbitrary correlation between the observations corresponding to the same restaurant.

A potential problem with this specification, however, is that there are only fifteen restaurants,

which leads to a small number of clusters and may cast doubt on the asymptotic arguments

behind inference with clustered standard errors. Specification 5 includes interactions between the

most predictive variable, Previous NoShow Indicator, and some of the other core variables. It is

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worth noting that the interpretation of the coefficients reported for specification 5 differs from

that of specifications 14.

First, let be a linear function. This gives us OLS regressions with the previous five [∙] Λ

different specifications, see Table 2. I ran OLS regressions first in order to get rough baseline

estimates of these six variables’ effects. The effects are consistent across every specification,

suggesting that the six variables chosen lead to predictable changes in the dependent variable.

However, in order to estimate probability, a linear regression is not wellsuited because it does

not account for the fact that Y is binary, and therefore may lead to predicted probabilities that are

outside (0,1).

A more suitable choice is a logistic regression which treats the dependent variable as

discrete—taking either 0 or 1—by using a function whose range lies in [0,1]. Let be a [∙]Λ [∙]Λ

logistic function to produce Logit regressions, once again with five different specifications, see

Table 3. The marginal effects in this table were estimated with all other core variables set to their

average values. Marginal effects estimated with Party Size at it’s mean and all other core

variables at 0 or at 1 can be found in Appendix A, Tables A1 and A2 respectively.

As a final robustness check, I ran a Probit model, which represents an alternative popular

parameterization of the conditional probability of noshows. The signs and magnitude of the six

core variables are consistent with Logit findings and therefore both models seem to provide a

similar approximation, see Appendix A, Table A3. Thus, the results will be based on the Logit

model for the remainder of this paper.

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VII. Results

Estimates of equation (1) show that customer characteristics are predictive of the

probability of being a noshow. The relevant estimates can be seen in Table 3, which reports

Logit regressions with all variables at their average value, for all five specifications discussed

earlier. Estimates of all six core variables are significant in every specification (except

Confirmation Indicator in Specification 4). Since the effects are consistent across all

specifications, for the purposes of discussion, I will henceforth focus on specification 2, which

includes restaurantspecific controls. For reference, some results from specification 2 are

compared to those from specification 5 as a robustness check and are found to be consistent, see

Appendix A, Figure A3.

An increase in the following variables, or a change from 0 to 1, results in a decrease in

the probability of being a noshow: Party Size, Same Area Code Indicator, Repeat Guest

Indicator, Guest Note Indicator. Changing the following variables from 0 to 1, however, leads to

an increase in the probability of being a noshow: Confirmation Indicator and Previous NoShow

Indicator. Previous NoShow Indicator has the largest marginal effect on the probability of being

a noshow. This finding is consistent with that of Dove and Schneider (1981) in the context of

healthcare. A customer who was previously a noshow at that particular restaurant is 41% more

likely to be a noshow than a customer who was not, all else equal.

According to the model, customers who were called or texted to confirm their reservation

are also more likely to be a noshow. This is a surprising result and deserves a brief discussion. It

is a considered common knowledge in the restaurant industry that confirming reservations helps

to reduce noshows, but this finding suggests the opposite. There are two potential reasons for

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this contradiction. First, restaurants recognize that confirming reservations with customers

reduces noshows because it allows customers who are not planning to show up to cancel their

reservation immediately, giving the restaurant a chance to rereserve that table. The customers

who cancel during the confirmation may well have been noshows if they were not contacted to

confirm their reservation. Confirmation, therefore, is effective for customers who forgot about

their reservation or who cannot show up but did not plan to call the restaurant to cancel. In this

sense, confirming does reduce noshows, but this benefit is not captured in my model since my

data only focus on customers who either did not cancel or cancelled within an hour of their

reservation time. Second, there could be measurement error in this variable that is introducing

bias. The source of the error is unknown, but summary statistics shown in Table 4 provide some

insight. Customers without guest IDs show the biggest negative effect of being contacted—their

noshow percentage is 17% when contacted and only 11% when not contacted. That said, they

are only contacted 2% of the time. Based on the guest notes, it seems that many reservations

without guest IDs are created by the restaurant staff for friends, family, or special guests

(investors, etc.). It is still hard to draw conclusions about these reservations, however, and

therefore I leave this variable noted as an inconsistency.

To fully explain the meaning of each variable's effects, it is best to consider two sample

customers—the “best case” customer and the “worst case” customer. Let the best case customer

have the lowest chance of being a noshow. In order to do this, I set each of the six core variables

to their most beneficial value (except for Party Size, which, for simplicity, is set to its average

value, 4, in both cases). For example, since changing Same Area Code Indicator from 0 to 1

decreases the probability of being a noshow, the best case customer will have Same Area Code

22



Indicator set to 1. The baseline probability of being a noshow for the best case customer is

3.4%. The worst case customer has each of the core indicator variables set to the least beneficial

value—the opposite of the best case settings. For example, Same Area Code Indicator for the

worst case customer is set to 0. The baseline probability of being a noshow for the worst case

customer is 44.3%.

Once we have the baseline settings for each indicator variable in both cases, it is

interesting to see what happens to the predicted noshow probability when one indicator variable

is switched from its base value while the others remain. This is depicted in Figure 1 (an

alternative depiction with precise probabilities can be found in the Appendix A, Figure A2) .

Switching Same Area Code Indicator from its best case baseline value of 1, depicted by , to 0,

depicted by , while leaving all other variables at their best case values, changes the probability

of noshow from 3.4% to 5.0%, an increase of 1.6 percentage points. Switching Same Area Code

Indicator from its worst case baseline value of 0, depicted by , to 1, depicted by , while

leaving all other variables at their worst case values, changes the probability of noshow from

44.3% to 35.1%, a decrease of 9.2 percentage points. From this, we can conclude that having the

same area code as the restaurant has a minimal effect on the probability of being a noshow if the

customer closely resembles a best case customer, but it has a much larger effect when he or she

closely resembles a worst case customer. A similar line of interpretation applies to all other core

variables shown in Figure 1.

Repeat Guest and Previous NoShow, however, deserve additional explanation. The best

case customer is a repeat guest who is not a previous noshow: Repeat Guest = 1, depicted by ,

23



and Previous NoShow = 0, depicted by . Switching Repeat Guest to 0, then, represents a new

customer in the best case. As seen in Figure 1, a new customer who otherwise resembles a best

case customer has a noshow probability of 7.7%. The worst case customer is a previous

noshow, and by definition, also a repeat guest: Repeat Guest = 1, Previous NoShow = 1.

However, it is not accurate to say that the worst case customer is a repeat guest, because that is

reserved for the case where Repeat Guest = 1 and Previous NoShow = 0. So, in Figure 1 there is

no worst case baseline value for Repeat Guest. When Repeat Guest = 1, depicted by , this

refers to a repeat guest who is not a previous noshow but otherwise resembles a worst case

customer. When Repeat Guest = 0, depicted by , this refers to a new customer, and is also the

value shown for Previous NoShow = 0 (even though Previous NoShow also takes 0 when

Repeat Guest = 1).

The most important takeaway from Figure 1 is that in some cases a deviation from the

worst case customer leads to a lower probability of being a noshow than a deviation from the

best case customer for the same variable. For example, if the customer resembles a best case

customer except he or she is a previous noshow, the probability of being a noshow is 27.4%. If

the customer resembles a worst case customer, but is a new customer instead of a previous

noshow, the probability of being a noshow is just 13.8%. It seems that Previous NoShow

trumps the effect of the other variables. Even if the customer has entirely beneficial

characteristics, if he or she was a previous noshow, it would be preferable to have a customer

with all the “wrong” characteristics who is not a previous noshow.

A similar phenomenon is seen with Repeat Guest—a worst case repeat guest is preferable

to a bestcase new customer. Figure 2 explains this finding further. It shows the best case and

24



worst case predicted probabilities of noshow for three categories of customers: repeat guests

who are not previous noshows, new customers, and previous noshows. Here it is evident that a

best case previous noshow is far more likely to be a noshow than a worst case new customer

and a best case new customer is more likely to be a noshow than a worst case repeat guest. Due

to these findings, this customer stratification will be used to create an overbooking policy for

restaurants.

VIII. Overbooking Policy and Implications

In order to design an overbooking policy, it is useful to quantify the results above using a

sample restaurant. Of the fifteen restaurants, Restaurant 8 is the most representative—it has

13,797 observations, a noshow rate of 11.5%, a Yelp rating of 3.5, a Yelp price of 3 dollar

signs, and a confirmation percentage of 73.2%. Restaurant 8’s best case customer has a predicted

noshow probability of 3.6%, and its worst case customer has a predicted noshow probability of

52.6%. Figure 3 shows the distribution of Restaurant 8’s customers as they are divided into the

three categories discussed earlier (Category 1: repeat guests who are not previous noshows,

Category 2: new customers, and Category 3: previous noshows). It also shows the maximum,

average, and minimum noshow probabilities for each of these customer segments. Repeat guests

make up 27% of Restaurant 8’s customers and have an average predicted probability of noshow

of 7%. New customers make up 68% of Restaurant 8’s customers and have an average predicted

probability of noshow of 11%. Previous NoShows make up just 5% of Restaurant 8’s

customers, but have an average predicted probability of noshow of 47%.

Based on these findings, there are two ways to solve for the expected percent of

customers who will show up to Restaurant 8. Equation (2) uses the customer stratification

25



discussed above and equation (3) uses the predicted probability of noshow for every reservation

at Restaurant 8,

(2) E(Percent Show Up | Restaurant 8) =

[Percent Customers in Category i (1 Average NoShow Probability for Category i)]∑3

i=1×

= (27 0.93) + (68 0.89) + (5 0.53) = 88.28%× × ×

(3) E(Percent Show Up | Restaurant 8) =

[Party Size for Reservation j (1 Predicted NoShow Probability for Reservation j)] /∑13,797

j=1×

(Party Size for Reservation j) 100% = 81.86%.∑13,797

j=1×

According to equation (2), Restaurant 8 can expect 88% of its customers to show up on a

given night (note that this prediction is consistent with Restaurant 8’s average noshow rate).

What does this prediction mean for Restaurant 8’s bottom line? The following calculations will

assume Restaurant 8 only takes reservations and cannot fill the table after a noshow. In October

of 2012, Restaurant 8 was open 25 days of the month. It had 37 reservations on average per

night. The average party size per reservation is 3 customers. So Restaurant 8 was serving 111

customers on average per night. Based on the expected percent of customers who will show up,

only 98 of those customers would arrive (111 0.88 = 98). Thus 13 people would be noshows.×

Restaurant 8 has a fixed price menu that costs $65 and an optional wine pairing that costs $49.

Assuming 50% of customers opt for the wine pairing, and everyone tips 18%, Restaurant 8’s

average check size is $105 per person. When 13 people do not show up, Restaurant 8 loses

$1,365 per night. That is a loss of $409,500 in revenue per year! But what if Restaurant 8

overbooked?

26



In order to create an efficient overbooking policy, the following variables need to be

considered:

C Restaurant capacity

N Number of customers booked

E Expected number of customers who will arrive, from equation (2) or (3)

A Number of customers who actually arrive

W Number of customers who arrive without overbooking

The goal of an overbooking policy is to find the optimal N for each night the restaurant is open.

An ideal overbooking policy would have N such that: N > A = C > W. The risk with any

overbooking policy is that too many customers show up as a result of overbooking and there is

not enough room in the restaurant to accommodate them: N > A > C > W. The practical

implications of taking this risk are costly—a bad Yelp review or an angry customer can damage

a restaurant’s reputation. With this in mind, my goal is not to find an optimal booking policy,

necessarily, but instead an efficient one, so that: N > C ≥ A > W. This overbooking policy must

be clearly communicated to busy restaurant owners and therefore should also be simple.

Restaurant 8 could overbook based on expected value, so that: N > E = C > W. This is

suggested by Dove and Schneider (1981) and Shonick and Klein (1977) for overbooking patients

in healthcare settings. There are two ways to implement overbooking using expected value. The

first, based on equation (2) above, involves dividing customers into three categories and using

the average predicted probability of each category to find the expected number of customers who

will show up. The second way, based on equation (3) above, involves calculating the expected

number of people who will show up based on the noshow probability for each reservation.

27



Due to the high risk of overbooking, mentioned earlier, it is important to know the

accuracy of the predicted expected values produced by my model before using those predictions

to overbook. In order to do this, I randomly divided the data into two groups. First, I ran the

logistic model on group 1. Then I divided the customers in group 2 into three categories, repeat

guests, new customers, and previous noshows, and used the estimates generated from the model

to find the average predicted probability of noshow for each category. Using equation (2), I

calculated the total expected number of arrivals, E, for group 2. I compared this value to the

actual number of customers who arrived from group 2, A, and found that my model predicts A

with 95% accuracy,

(4) = 0.95.AE

I used the same method to find the accuracy of the expected value predictions based on equation

(3), and found that predictions from that model are 94% accurate. Therefore, I will focus on

equation (2) since it is slightly more accurate. Overbooking based on expected value is ideal

when arrivals are predicted with 100% accuracy. Since this is nearly impossible due to

unobservable random variation in human behavior, I suggest restaurants employ an overbooking

policy based on modified expected values. Instead of overbooking so that the number of

expected arrivals equals restaurant capacity: N > E = C > W, restaurants should overbook with a

buffer so that the number of expected arrivals equals 95% of restaurant capacity: N > E =

(0.95)C > W.

Let Restaurant 8’s capacity be its average number of reservations per night, 37,

multiplied by its average party size per reservation, 3: (37 3 = 111). As shown previously,×

28



equation (2) predicts that 88.28% of reservations will show up on a given night. This means 98

seats are expected to be filled out of the 111 available. Using the suggested policy, Restaurant 8

should overbook until 95% of its capacity is expected to be filled, or until 105 seats are filled.

This means Restaurant 8 should book enough customers, N, so that 88.28% of N equals 105.

Restaurant 8 must solve for N in the following equation:

(5) (N = Number of booked customers) (Percent of customers expected to show up)× = (0.95) (C = Capacity)×

N(0.8828) = (0.95)(111)

N = 119

(N C) = (119 111) = 8.

Restaurant 8 should book 8 customers over capacity. In doing so, Restaurant 8 can expect

E = 105 customers to show up. Without overbooking, Restaurant 8 was expected to fill only W =

98 seats. The additional 7 seats that could be filled by implementing an overbooking policy could

save Restaurant 8 $220,500 per year. 4

Alternative overbooking policies suggested by previously mentioned studies are more

complex. Bertsimas and Shioda (2003) and Oh and Su (2012) incorporate additional factors into

their models such as walkin demand or the effect of noshow penalties. However, neither study

incorporates the distribution of noshow probabilities based on a customer stratification. In fact,

Bertsimas and Shioda (2003), assume that the probability of noshows is independent and

identically distributed across parties of the same size, which I have shown is not the case.

Therefore, the findings of the current study can help advance the work of nonempirical previous

studies that have depended on simplifying assumptions. To create a more thorough overbooking

4 7 additional customers/night x $105/customer x 25 nights open/month x 12 months/year = $220,500 saved/year

29



policy, one would need to employ a structural model that describes the behavior of consumers

and restaurants, and how the market operates. This would likely be more accurate than the

reduced form model suggested here and future work could address this.

An effective overbooking policy must also take into account the potential downside of

overbooking discussed by The Culinary Institute of America (2014), Wangenheim and Bayón

(2007), and Hirschman (1970). As noted earlier, the risk with overbooking lies in the nonzero

probability that the number of customers who arrive will exceed restaurant capacity: N > A > C >

W. The restaurant has two choices in this case: increase the wait time of every customer in order

to accommodate additional arrivals or refuse service to a few customers with reservations. There

are costs associated with either choice. Let’s assume the restaurant chooses to turn some

customers away. In this case the restaurant would have to provide enough compensation to avoid

a damaging loss in customer loyalty or restaurant reputation. I suggest a voucher equal to the

price of a meal—for Restaurant 8 this would be a $65 voucher per person. An analogous strategy

is successfully employed by airlines, however there are many important market differences

between airlines and restaurants that must be addressed.

First, unlike airlines, restaurants do not typically overbook and they certainly do not often

bump customers. Therefore the public response to a restaurant’s compensation scheme is

untested. Second, the airline industry is an oligopoly—there are huge barriers to entry and few

dominant firms. Customers therefore do not have much choice between firms nor the power to

significantly damage a firm’s reputation. This is contrasted with the nearly perfect competition of

the restaurant market. Here, customers can easily switch between firms and in doing so they have

the power to affect a firm’s profits. That said, the offer of a free meal is likely ample

30



compensation for the cost of a lost reservation. If this is the case, then the benefits of

overbooking will outweigh the costs of compensation doled out in the infrequent event of

overbooking gone awry. Further research should address optimal compensation schemes for

restaurants.

IX. Conclusion

Using a large data set of restaurant and reservationspecific variables, I predicted the

probability of a restaurant customer being a noshow and found that whether a customer showed

up for his or her previous reservation is the most important predictor of future behavior. Using

this variable, I divided customers into three categories: repeat guests who are not previous

noshows, new customers, and previous noshows. I suggested an overbooking policy for

restaurants by calculating the expected number of customers who will arrive based on the

distribution of customers in this stratification and the average predicted probability of noshow

for each category. Due to the 95% accuracy of my model, I recommended overbooking until the

expected number of arrivals equals 95% of the restaurant’s capacity. Despite the risks associated

with overbooking in the case where it goes awry, the benefits of decreasing the high costs

associated with noshows very likely outweigh the necessary increase in costs of compensation.

Therefore, overbooking may help lead to a long overdue power shift in the restaurant industry

from customers to restaurants themselves. Further studies could be done to increase the

complexity of the suggested overbooking policy by addressing complications such as: customer

response to increased wait times or compensation, the effect of an overbooking policy on the

noshow rate itself, and importantly, further empirical experiments could be done using

31



overbooking in some restaurants and comparing the effects to similar counterpart restaurants

without overbooking policies.

32



X. Tables and Figures

Table 1: Descriptive Statistics

Variables

Total Show Noshow Difference

Mean SD Mean SD Mean SD mshowmnoshow

Category 1: Restaurantspecific

Booking days in advance 29.89 6.84 29.94 6.92 29.47 6.18 0.47

Minimum Party Size 1.02 0.13 1.02 0.13 1.02 0.14 0.00

Maximum Party Size 6.81 2.93 6.78 2.90 7.09 3.11 0.30

Restricts Large Parties 0.08 0.27 0.08 0.27 0.04 0.20 0.04

Large Party Threshold 5.85 0.53 5.84 0.55 5.92 0.39 0.08

First Confirmation Days in Advance 1.65 1.60 1.67 1.64 1.43 1.20 0.24

Automated Communication via Text 0.94 0.25 0.94 0.24 0.92 0.27 0.02

Automated Communication via Email 0.93 0.26 0.93 0.25 0.92 0.27 0.01

Automated Communication via Phone 0.02 0.13 0.02 0.13 0.02 0.14 0.00

Allows Waitlist Requests Via Text 0.34 0.47 0.35 0.48 0.20 0.40 0.16

Allows Waitlist Requests Via Phone 0.02 0.13 0.02 0.13 0.02 0.14 0.00

Allows Waitlist Requests Via Widget 0.10 0.30 0.11 0.31 0.06 0.23 0.05

Category 3: Reservationspecific

Party Size 3.93 3.62 4.01 3.74 3.26 2.36 0.75

Same Area Code Indicator 0.50 0.50 0.51 0.50 0.42 0.49 0.10

Guest Note Indicator 0.28 0.45 0.29 0.45 0.21 0.41 0.08

Reservation Made via Phone 0.58 0.49 0.59 0.49 0.49 0.50 0.10

Reservation Made via Website 0.42 0.49 0.41 0.49 0.51 0.50 0.10

Confirmation Indicator 0.76 0.43 0.76 0.43 0.77 0.42 0.01

Confirmation via Phone Indicator 0.45 0.50 0.46 0.50 0.42 0.49 0.04

Confirmation via Text Indicator 0.30 0.46 0.30 0.46 0.35 0.48 0.05

Number of observations for variables above 74,926 66,759 8,167 —

Repeat Guest Indicator 0.33 0.47 0.33 0.47 0.31 0.46 0.03

Previous NoShow Indicator 0.05 0.22 0.04 0.19 0.18 0.38 0.14

Number of observations for variables above 70,542 62,864 7,678 —

Category 2: Manually Inputted

Yelp Rating 3.32 0.50 3.31 0.51 3.41 0.41 0.10

Yelp Price 2.73 0.44 2.74 0.44 2.68 0.47 0.06

Number of Observations for Category 2 73,750 65,654 8,096 —

33



Table 2: Estimates from OLS Regressions

OLS Regressions Specification

Variables 1 2 3 4 5

Party Size 0.004 (0.000)

0.004 (0.000)

0.004 (0.000)

0.004 (0.001)

0.004 (0.000)

Same Area Code Indicator 0.037 (0.002)

0.030 (0.003)

0.031 (0.003)

0.037 (0.010)

0.034 (0.002)

Repeat Guest Indicator 0.055 (0.002)

0.047 (0.002)

0.046 (0.002)

0.055 (0.008)

0.056 (0.002)

Confirmation Indicator 0.007 (0.003)

0.010 (0.003)

0.009 (0.003)

0.007 (0.007)

0.007 (0.003)

Previous NoShow Indicator 0.317 (0.008)

0.318 (0.008)

0.311 (0.008)

0.317 (0.018)

0.394 (0.024)

Guest Note Indicator 0.022 (0.003)

0.013 (0.003)

0.014 (0.003)

0.022 (0.010)

0.020 (0.002)

Other Controls No Yes No No No

Restaurant Fixed Effects No No Yes No No

Cluster s.e. No No No Yes No

Interactions No No No No Yes

Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses.

34



Table 3: Estimates from Logit Regressions

All variables evaluated at avg.

Specification

Variables 1 2 3 4 5

Party Size Marginal Effect (Marginal s.e.)

[Beta from Logit]

0.007 (0.001) [0.083]

0.006 (0.001) [0.077]

0.007 (0.001) [0.081]

0.007 (0.001) [0.083]

0.008 (0.001) [0.090]

Same Area Code Indicator 0.035 (0.002) [0.407]

0.025 (0.002) [0.297]

0.025 (0.002) [0.300]

0.035 (0.009) [0.407]

0.034 (0.002) [0.402]

Repeat Guest Indicator 0.061 (0.002) [0.780]

0.054 (0.002) [0.709]

0.052 (0.002) [0.696]

0.061 (0.009) [0.800]

0.061 (0.002) [0.801]

Confirmation Indicator 0.007 (0.003) [0.088]

0.009 (0.003) [0.117]

0.009 (0.003) [0.114]

0.007ª (0.006) [0.088]

0.007 (0.003) [0.082]

Previous NoShow Indicator 0.415 (0.011) [2.396]

0.406 (0.011) [2.368]

0.398 (0.011) [2.351]

0.415 (0.031) [2.396]

0.358 (0.022) [2.160]

Guest Note Indicator 0.020 (0.002) [0.245]

0.012 (0.003) [0.153]

0.014 (0.002) [0.173]

0.020 (0.009) [0.245]

0.020 (0.003) [0.251]



Cluster No No No Yes No


Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses. ªInsignificant results.

35



Table 4: Summary Statistics Related to Confirmation Indicator

Percent Show

Percent NoShow

Number of Observations

Confirmation | Total 89% 11% 56,839

Confirmation | Repeat Guest who is not a Previous NoShow 95% 5% 15,192

Confirmation | New Customer 89% 11% 37,818

Confirmation | Previous NoShow 63% 37% 3,032

Confirmation | No Guest ID = unknown customer category 83% 17% 77

No Confirmation | Total 90% 10% 18,087

No Confirmation | Repeat Guest who is not a Previous NoShow 95% 5% 3,704

No Confirmation | New Customer 90% 10% 9,444

No Confirmation | Previous NoShow 62% 38% 632

No Confirmation | No Guest ID = unknown customer category 89% 11% 4,307

36



Figure 1: Probability of NoShow When Indicators are Switched— Deviations from Best and Worst Case Baselines Specification 2

37



Figure 2: The Best Case and Worst Case Predicted NoShow Probabilities for Three Categories of Customers

Figure 3: Distribution of Restaurant 8’s Customers by Probability of NoShow as Compared to Distribution by Customer Type

38



References

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JSTOR. Web. 02 Apr. 2015. Bertsimas, D., and Romy S. "Restaurant Revenue Management."Operations Research 51.3

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Research Society 50.11, Yield Management (1999): 1098103.JSTOR. Web. 08 Apr. 2015.

Dove, H.G., and Schneider, K.C. "The Usefulness of Patients' Individual Characteristics in

Predicting NoShows in Outpatient Clinics." Medical Care 19.7 (1981): 73440. JSTOR. Web. 08 Apr. 2015.

Kros, J., Dellana, S., and West, D.. "Overbooking Increases Patient Access at East Carolina

University's Student Health Services Clinic." Interfaces 39.3, Applications of Management Science and Operations Research Models and Methods to Problems in Health Care (2009): 27187. JSTOR. Web. 08 Apr. 2015.

Forbes, P., "LA Restaurant Outs NoShows on Twitter." Eater. N.p., 25 Mar. 2013. Web. 04 Apr.

2015. Hirschman, Albert O. Exit, Voice, and Loyalty; Responses to Decline in Firms, Organizations,

and States. Cambridge, MA: Harvard UP, 1970. Print. LaGanga, L. R., and Lawrence, S.R. "Clinic Overbooking to Improve Patient Access and

Increase Provider Productivity." Decision Sciences 38.2 (2007): 25176. Web. Massey, R., "Scandal of Overbooked Holiday Flights." Mail Online. Associated Newspapers,

n.d. Web. 08 Apr. 2015. McKeever, A. "How Restaurants Can Deal With NoShow Diners." Eater. N.p., 22 Apr. 2013.

Web. 20 Apr. 2015. Oh, J., and Su, X. Pricing Restaurant Reservations: Dealing with NoShows (October 31, 2012). Reddy, S., "Knives Are Out for NoShow Diners." WSJ. N.p., 14 Mar. 2012. Web. 04 Apr. 2015. Rothstein, M., "OR Forum—OR and the Airline Overbooking Problem."Operations

Research 33.2 (1985): 23748. Web.

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Shonick, W., and Klein, B.W. "An Approach to Reducing the Adverse Effects of Broken

Appointments in Primary Care Systems." Medical Care 15.5 (1977): 41929. Web. Sorell, T., "The Customer Is Not Always Right." Journal of Business Ethics 13.11 (1994):

91318. JSTOR. Web. 08 Apr. 2015. Suzuki, Y. "An Empirical Analysis of the Optimal Overbooking Policies for US Major Airlines."

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Transportation Review 42.1 (2006): 119. Web. The Culinary Institute of America. "Reservations and Waiting Lists." Remarkable Service: A

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Wangenheim, F.V., and Bayón, T. (2007), Behavioral Consequences of Overbooking Service

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40



XII. Appendix A Figure A1: Reallocation Price and Profit from Oh and Su (2012) Overbooking Analysis

Note: Λ = Market size, µ = Restaurant capacity

41



Table A1: Estimates from Logit Regressions

Party size evaluated at avg. Other variables at 0

Specification

Variables 1 2 3 4 5


[Beta from Logit]

0.009 (0.001) [0.083]

0.008 (0.001) [0.077]

0.008 (0.001) [0.081]

0.009 (0.001) [0.083]

0.010 (0.001) [0.090]


0.026 (0.003) [0.297]

0.027 (0.003) [0.300]

0.039 (0.009) [0.407]

0.039 (0.003) [0.402]


0.054 (0.003) [0.709]

0.053 (0.003) [0.696]

0.065 (0.012) [0.800]

0.066 (0.003) [0.801]


0.012 (0.003) [0.117]

0.012 (0.003) [0.114]

0.010 (0.008) [0.088]

0.009 (0.004) [0.082]


0.456 (0.013) [2.368]

0.450 (0.013) [2.351]

0.487 (0.043) [2.396]

0.432 (0.022) [2.160]


0.014 (0.003) [0.153]

0.016 (0.003) [0.173]

0.025 (0.010) [0.245]

0.026 (0.003) [0.251]



Cluster s.e. No No No Yes No


Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses.

42



Table A2: Estimates from Logit Regressions

Party size evaluated at avg. Other variables at 1

Specification

Variables 1 2 3 4 5


[Beta from Logit]

0.017 (0.001) [0.083]

0.017 (0.001) [0.077]

0.017 (0.001) [0.081]

0.017 (0.003) [0.083]

0.017 (0.001) [0.090]


0.067 (0.007) [0.297]

0.067 (0.007) [0.300]

0.090 (0.029) [0.407]

0.081 (0.006) [0.402]


0.166 (0.009) [0.709]

0.161 (0.009) [0.696]

0.186 (0.035) [0.800]

0.174 (0.011) [0.801]


0.025 (0.007) [0.117]

0.024 (0.007) [0.114]

0.018ª (0.014) [0.088]

0.015 (0.006) [0.082]


0.278 (0.009) [2.368]

0.272 (0.009) [2.351]

0.254 (0.022) [2.396]

0.208 (0.016) [2.160]


0.034 (0.007) [0.153]

0.038 (0.007) [0.173]

0.053 (0.023) [0.245]

0.049 (0.007) [0.251]






43



Figure A2: Probability of NoShow When Indicators are Switched—Deviations from Best and Worst Case Baselines with Probability Values and Magnitude of Deviation Specified

Same Area Code

Repeat Guest Confirmation Previous

NoShow Guest Note Probability of NoShow

Magnitude of Deviation

Best Case: 1 1 0 0 1 3% ∅

Deviations from Best Case

0 1 0 0 1 5% 2

1 0 0 0 1 8% 5

1 1 1 0 1 4% 1

1 1 0 1 1 27% 24

1 1 0 0 0 4% 1

Same Area Code

Repeat Guest Confirmation Previous

NoShow Guest Note Probability of NoShow

Magnitude of Deviation

Worst Case: 0 1 1 1 0 44% ∅

Deviations from Worst Case

1 1 1 1 0 35% 9

0 1 1 0 0 7% 37

0 1 0 1 0 44% 0

0 0 1 0 0 14% 30

0 1 1 0 1 35% 9

44



Figure A3: Absolute Difference in Probability—Switching Indicators—Specification 2 vs. 5

45



Table A3: Estimates from Probit Regressions

All variables evaluated at avg.

Specification

Variables 1 2 3 4 5


[Beta from Logit]

0.007 (0.001) [0.040]

0.006 (0.001) [0.037]

0.006 (0.001) [0.039]

0.007 (0.001) [0.040]

0.007 (0.001) [0.042]


0.026 (0.003) [0.155]

0.026 (0.003) [0.157]

0.036 (0.010) [0.212]

0.035 (0.002) [0.207]


0.055 (0.002) [0.351]

0.053 (0.002) [0.346]

0.061 (0.008) [0394]

0.062 (0.002) [0.395]


0.010 (0.003) [0.061]

0.010 (0.003) [0.059]

0.008ª (0.006) [0.046]

0.007 (0.003) [0.043]


0.384 (0.010) [1.302]

0.378 (0.010) [1.293]

0.389 (0.025) [1.309]

0.361 (0.020) [1.238]


0.013 (0.003) [0.078]

0.014 (0.003) [0.087]

0.021 (0.009) [0.127]

0.021 (0.003) [0.127]






46



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