Creating the Optimal Wedding Seating Chart

University of Nebraska at Omaha University of Nebraska at Omaha

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Theses/Capstones/Creative Projects University Honors Program

5-2023

Creating the Optimal Wedding Seating Chart Creating the Optimal Wedding Seating Chart

Madison Lane

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Creating the Optimal Wedding Seating Chart

Thesis by

Madison Lane

In Fulﬁllment of the Requirements for the

University Honors Program

Thesis/Capstone/Creative Project

DEPARTMENT OF MATHEMATICAL AND STATISTICAL SCIENCES

UNIVERSITY OF NEBRASKA AT OMAHA

ADVISOR: DR. FABIO VITOR

©May, 2023

Madison Lane

ABSTRACT

The purpose of this project is to develop an eﬀective seating arrangement for a wedding

reception that enhances the comfort of guests. The ultimate aim is to create a harmonious and

enjoyable atmosphere for all attendees. To achieve this, an integer program was designed to

optimize the seating arrangement for the author’s upcoming wedding on May 27th, 2023. To

ensure accuracy and feasibility, actual feedback was gathered from the guests to evaluate their

compatibility and preferences. The proposed seating chart optimization not only addresses

the placement of guests but also determines the number of tables required for the reception.

The integer program’s decision variables were deﬁned based on the table assignment for each

guest, which are used to generate an optimal seating plan. This approach helps to ensure

that each guest is seated at a table with people they get along with, fostering a welcoming

and cohesive environment. By creating a well-organized seating plan, this project aims to

provide a positive and comfortable experience for all guests attending the author’s wedding

reception. Furthermore, this project’s results may be applicable to other events, providing

valuable insights into seating arrangement optimization for future occasions.

TABLE OF CONTENTS

Abstract 2

List of Figures 3

List of Tables 5

1 Intro duction 6

1.1 Description of Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2 Organization of Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Literature Review 8

2.1 Current Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Non-Wedding Seating Problems . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Other Seating Chart Optimization . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Data Collection 11

3.1 Survey Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Handling Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Mathematical Model 15

4.1 Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Decision Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.4 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.5 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5 Results 20

5.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6 Conclusion 23

6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

References 25

Appendices 26

LIST OF FIGURES

2.1 Guest Positioning at a Table. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Example of the Survey Sent to Guests . . . . . . . . . . . . . . . . . . . . . . 12

4.1 Ranges Implementation in Python . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Parameters Implementation in Python. . . . . . . . . . . . . . . . . . . . . . 17

4.3 Parameter Connections on Python. . . . . . . . . . . . . . . . . . . . . . . . 17

4.4 Decision Variable Implementation in Python. . . . . . . . . . . . . . . . . . . 18

4.5 Objective Function Implementation in Python. . . . . . . . . . . . . . . . . . 18

4.6 Constraint Implementation in Python. . . . . . . . . . . . . . . . . . . . . . 19

5.1 Optimal Seating Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

LIST OF TABLES

3.1 Data Collected from Guests . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Positive Connections after Standardization . . . . . . . . . . . . . . . . . . . 14

4.1 Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Decision Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.4 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.1 Guest Relationship to the Couple. . . . . . . . . . . . . . . . . . . . . . . . . 22

A.1 Microsoft Excel Positive Connections Data Part 1. . . . . . . . . . . . . . . . 26

A.2 Microsoft Excel Positive Connections Data Part 2. . . . . . . . . . . . . . . . 27

A.3 Microsoft Excel Negative Connections Data Part 1. . . . . . . . . . . . . . . 28

A.4 Microsoft Excel Negative Connections Data Part 2. . . . . . . . . . . . . . . 29

Chapter 1

Introduction

In March of 2021, the author’s ﬁanc´e Luis proposed to them, and they were ecstatic to

begin planning their dream wedding. However, as they delved deeper into the process, they

quickly realized how overwhelming it could be. After they had selected a venue for their

reception, they began to focus on the ﬁner details of the event, including determining where

each guest would sit. They recognized that creating an optimal seating chart was essential to

ensure that all of the guests felt comfortable and enjoyed themselves. They spent countless

hours discussing the best way to seat their guests, considering the guests’ personalities,

relationships, and preferences. They realized that seating guests with people they knew and

felt comfortable with would create a relaxed and enjoyable atmosphere. However, they also

had to consider any potential tensions between guests, as seating people who did not get

along could lead to discomfort and tension.

1.1 Description of Problem

Creating a seating chart for a wedding reception can be a daunting task, as it involves

accommodating a large number of guests and ensuring that everyone has a comfortable and

enjoyable experience. This report delves into the process of creating an optimal wedding

seating chart, exploring the various factors that should be taken into consideration and

outlining strategies to ensure that all guests are happy with their seating arrangements.

One of the most critical factors to consider when creating a seating chart is the relation-

ships between guests. To ensure that each guest feels at ease and can enjoy the reception,

it is essential to seat them with people they know and are comfortable with. This helps

to create a relaxed atmosphere, where guests can socialize freely and enjoy the company of

those around them. However, it is also important to consider the dynamics between guests,

as seating individuals who do not get along well together can lead to tension and discomfort.

Other factors to consider when creating a seating chart include the size and layout of the

venue, the number of tables required, and any special accommodations that need to be made

for guests with speciﬁc needs or preferences. Eﬀective seating chart planning can also help

to promote a smooth ﬂow of the reception, ensuring that guests can easily access food and

beverages, and allowing for eﬃcient service from the catering staﬀ.

Creating an optimal seating chart for a wedding reception requires careful planning and

attention to detail. By taking into account the various factors that contribute to a positive

guest experience, such as relationships between guests and venue layout, planners can ensure

that everyone has a memorable and enjoyable time at the wedding reception.

1.2 Organization of Paper

Chapter 2 presents a brief review of existing research on seating arrangements. Chapter

3 details the methods used to collect and standardize data for this project. Chapter 4

introduces the mathematical model that was developed, including explanations of its ranges,

parameters, decision variables, objective function, and constraints. Chapter 5 then outlines

the results of the project. Finally, Chapter 6 provides a conclusion to the project and outlines

areas for future research.

Chapter 2

Literature Review

The purpose of this brief literature review is to examine existing research on seating chart

optimization for events. The review will delve into the challenges faced when constructing a

seating plan that satisﬁes a range of constraints such as group aﬃliations, potential tensions

or bonds between guests, seating requirements or restrictions, and arranging guests around

tables of appropriate sizes and shapes. The review will examine notable studies that have

tackled this issue. Additionally, the review will highlight the diﬀerent approaches taken by

these studies in terms of their objective functions.

2.1 Current Tools

Creating seating charts for a wedding is not a new concept, and brides and grooms are

always looking for ways to create their seating charts. According to Mattia (2022), there

are many websites, such as WeddingWire and Zola, that provide templates to guide couples

through the process of designing their seating chart. These websites ask for information such

as the shape and size of tables, the number of tables, and the names of guests. Once the

couple inputs this information, WeddingWire gives them a drag-and-drop template to lay

out their seating chart, while Zola provides more of a spreadsheet form for arranging guests.

These websites oﬀer more direction when it comes to layout.

Waida (2020) provided an in-depth list of things that couples should consider when

designing their seating chart. They emphasized that before designing a seating chart, couples

should ﬁrst ﬁnd what questions and concerns they may have. Some of the ideas they listed

when considering a seating chart includes how guests know each other and how the couple

would like families to be seated together. In addition, they also stressed that children and

people who may require a wheelchair should be speciﬁcally considered when planning a

seating chart. Waida also listed the size and shape of the tables and the number of tables

as some of the most important things to know when designing a seating chart. Overall, this

article provides an important list of considerations when designing a wedding seating chart.

2.2 Non-Wedding Seating Problems

Weddings and other events are not the only instances where seating arrangements play

a crucial role in achieving a goal. Seating charts have been used in various research papers

to examine concepts such as classroom social dynamics. In a study by Braun, van den Berg,

and Cillessen (2020), teachers were shown to use seating arrangements to manage classroom

social dynamics, leading to positive eﬀects on students’ social relationships. The study

investigated the impact of a shortened seating chart intervention on both target and nontarget

students and whether the teachers’ eﬀectiveness in managing social dynamics moderated the

intervention’s eﬀects. Similarly, Ptak (1988) discussed his own use of a computer program to

randomly assign seats to students every six weeks in his classroom. The random arrangement

allows for students of varying abilities and problem-solving styles to work together during

group activities. Students are given a worksheet to indicate their preferred seating location

and partner, and they also complete graph paper grids for problem-solving activities.

2.3 Other Seating Chart Optimization

Lewis & Carroll (2016) conducted a study on wedding seating charts, focusing on the

challenges of ﬁnding a suitable seating plan that satisﬁes a range of constraints. These con-

straints can include guests belonging to certain groups, potential tensions or bonds between

guests, seating requirements or restrictions, and arranging guests around tables of appropri-

ate sizes and shapes. To tackle these challenges, the researchers meticulously examined the

layout of tables and determined the optimal seating arrangement for each guest, as shown

in Figure 2.1. They designed an algorithm to achieve this seating chart and implemented

it using ActionScript 3.0. However, the number of possible seating plans can quickly be-

come overwhelming for larger groups, rendering a naive approach impractical. In response,

commercial software solutions now exist that leverage advanced algorithms, such as genetic

algorithms, to help construct seating plans.

Bellows & Peterson (2012) proposed a mathematical model for seating chart opti-

mization at events. Their model seeks to maximize the number of connections a particular

guest has at their table, meaning that the model will aim to seat guests who know each

other at the same table. They used a connection matrix to describe which guests know each

other. The study describes the sets, variables, and parameters used in the model and ex-

plains the linearization of the model to facilitate its solution. The model can be solved using

mixed-integer linear optimization techniques to ﬁnd the global optimal solution. The GAMS

software with the CPLEX solver was used to solve the model.

Source: Lewis & Carroll (2016)

Figure 2.1: Guest Positioning at a Table.

However, it’s worth noting that Bellows & Peterson ﬁlled out the connection matrix

themselves rather than asking the guests directly. As a result, it may not have accurately

reﬂected the guests’ opinions. Additionally, the researchers focused heavily on optimizing

positive relationships at the tables, rather than minimizing negative ones. In contrast, the

author of this project took both factors into consideration by asking for feedback from the

guests and looking at the invited parties as a whole, rather than just the individual guests.

The author also wanted to ﬁnd a way to maximize positive relationships while also minimizing

negative relationships and a speciﬁc table.

2.4 Goals

The two reports mentioned earlier took diﬀerent approaches in their objective functions.

Bellows & Peterson’s (2012) model aimed to maximize connections at each table. In contrast,

Lewis & Carroll (2016) aimed to minimize costs at each table. These diﬀerent approaches

provide valuable insights into appropriate objectives for optimizing a seating arrangement.

While there are examples of models that focus on either minimizing costs or maximizing

connections, there is limited information on models that combine the two objectives.

To build on the research discussed in the literature review, the author sought to

develop a mathematical model that could optimize a wedding seating chart by maximizing

positive connections and minimizing negative ones among guests at each table. Furthermore,

the author aimed to ﬁnd an unbiased method of gathering feedback from the guests attending

the wedding. The following chapter outlines how data was collected and managed for this

project.

Chapter 3

Data Collection

To collect meaningful data about wedding guests’ seating preferences, each guest was

contacted and asked to ﬁll out a survey. Madison and Luis sent a link to the survey, which

instructed guests to rate other invited parties on how much they would like to sit by them.

Guests were given no guidance from Madison and Luis and were required to interpret the

survey according to their own preferences. Each invited party was asked to designate one

representative to complete the survey.

3.1 Survey Set Up

The survey was sent to members of a party. The survey consisted of two questions:

“What is your name?” and “Please rate other invited parties on how much you would like to

sit by them.” The ﬁrst question was used to identify the response to the speciﬁc party. The

second question was about how much the guests would like to sit by other invited parties.

The guests were given a list of all invited parties and asked to rate them on a scale from -3

to 3, with -3 meaning “I would strongly prefer to NOT be seated by them” and 3 meaning “I

would strongly prefer to be seated by them.” This range was selected to allow a neutral value

of 0 to ideally be recognized by guests. By setting this range, the goal was to have guests

rank people they do not want to sit by a value less than zero and rate people they do want

to sit by a value greater than zero. Since some guests may have avoided negative numbers

for fear of “being too mean,” having the positive range go from 0 to 3 allowed for enough

space that they could have a distinguished diﬀerence between those they would prefer to sit

by and those they would prefer to not sit by. See Figure 3.1 for an example of the survey.

3.2 Handling Data

To minimize bias in the results, the survey responses were standardized. Each guest’s

responses were translated into preferred guests, not preferred guests, and indiﬀerent guests.

To do this, the median score for each guest was calculated, and guests who ranked above the

median were classiﬁed as preferred guests, those who ranked below the median were classiﬁed

as not preferred guests, and those who ranked at the median were classiﬁed as indiﬀerent

guests.

Figure 3.1: Example of the Survey Sent to Guests

To account for cases where the median score was the same as the maximum or mini-

mum score, alternative standardization methods were used. When the maximum score was

the same as the median score, guests who ranked at the median were classiﬁed as preferred

guests, and those ranked below the median were classiﬁed as not preferred guests. When the

minimum score was the same as the median score, guests who ranked above the median were

classiﬁed as preferred guests, and those ranked at the median were classiﬁed as not preferred

guests. If the minimum and maximum scores were the same as the median score, all guests

were classiﬁed as indiﬀerent.

This process allowed for the collection of meaningful data about wedding guests’

seating preferences, and alternative standardization methods were developed to handle any

potential inconsistencies in responses. Once the data was standardized, the values were

translated to a 1 when a party preferred sitting by another party, and translated to a -1

when a party did not prefer sitting by another party. These values are referred to as utilities

and costs throughout the paper and have been converted to a dollar value equal to them.

To illustrate how the data was collected and standardized, Table 3.1 presents the responses

from ten parties (a through j), each assigned a letter for consistency throughout the project.

It should be noted that this sample only includes a portion of the responses collected from

the 32 parties considered in this study. Nonetheless, it provides a clear example of how the

data was standardized. Subsequently, Table 3.2 displays the positive connections after the

data was standardized. The following chapter outlines the model used to optimize the seating

chart using the data collected from the guests.

Table 3.1: Data Collected from Guests

Guest a b c d e f g h i j

a 3 3 3 -1 3 -3 -3 0 -3 0

b 3 3 3 -1 3 -3 -3 0 -3 -1

c 2 3 3 -2 3 -3 -3 0 -3 -1

d 2 3 3 -1 3 -3 -3 0 -3 -1

e 2 3 3 -1 3 -3 -3 0 -3 -1

f -1 -3 -3 -1 0 3 3 3 -1 3

g -1 -3 -3 -2 0 3 3 3 0 2

h -1 -3 -3 -2 0 3 3 3 0 1

i -1 -3 -3 -2 0 3 3 3 0 1

j 0 -3 -3 -2 0 3 2 0 -2 0

k 1 1 -3 -2 0 3 1 0 -1 2

l 0 -3 -3 -2 0 3 0 0 -1 3

m 0 -2 -3 -2 0 3 2 0 -3 1

n -3 -3 -3 -2 0 -3 0 2 -3 3

o 0 -2 -3 -2 -2 -3 -3 2 -3 -3

p -1 -3 -3 -2 -2 -3 -3 2 -3 -3

r -1 -3 -3 -2 -2 -3 -3 2 -3 -3

t 1 -3 -3 -2 -2 -3 -3 2 -2 -3

u 2 -3 -3 -2 -2 -3 -3 2 -2 -3

v 2 -3 -3 -2 -2 -3 -3 2 -2 -3

w 2 -3 -3 -2 -2 -3 -2 2 -2 -3

x 1 -3 -3 -2 -2 -3 -3 2 -2 -3

y 1 -3 -3 -2 -2 -3 -3 2 -2 -3

z 2 -3 -3 -2 -2 -3 -3 2 -2 -3

aa 2 -3 -3 -2 3 -3 -3 2 -2 -3

ab -1 -3 -3 -2 0 -3 -3 2 -2 -3

ac -1 -3 -3 -2 0 -3 -3 2 -2 -3

ad -1 -3 -3 -2 0 -3 -3 2 -2 -3

ae -2 -3 -3 -2 0 -3 -3 2 -3 -3

af -2 -3 -3 -2 0 -3 -3 2 -3 -3

ah 0 -3 -3 -2 0 -3 -3 2 -2 -3

ai -1 -3 -3 -2 0 3 -3 2 -2 -3

aj -1 -3 -3 -2 0 -3 2 2 0 1

ak -2 -3 -3 -2 0 3 -3 2 -2 -3

al 2 -3 -3 -2 0 3 2 2 -1 1

Table 3.2: Positive Connections after Standardization

Guest a b c d e f g h i j

a 0 1 1 1 1 0 0 0 0 1

b 1 0 1 1 1 0 0 0 0 1

c 1 1 0 0 1 0 0 0 0 1

d 1 1 1 0 1 0 0 0 0 1

e 1 1 1 1 0 0 0 0 0 1

f 0 0 0 1 0 0 1 1 1 1

g 0 0 0 0 0 1 0 1 1 1

h 0 0 0 0 0 1 1 0 1 1

i 0 0 0 0 0 1 1 1 0 1

j 0 0 0 0 0 1 1 0 0 0

k 1 1 0 0 0 1 1 0 1 1

l 0 0 0 0 0 1 1 0 1 1

m 0 1 0 0 0 1 1 0 0 1

n 0 0 0 0 0 0 1 0 0 1

o 0 1 0 0 0 0 0 0 0 0

p 0 0 0 0 0 0 0 0 0 0

r 0 0 0 0 0 0 0 0 0 0

t 1 0 0 0 0 0 0 0 0 0

u 1 0 0 0 0 0 0 0 0 0

v 1 0 0 0 0 0 0 0 0 0

w 1 0 0 0 0 0 1 0 0 0

x 1 0 0 0 0 0 0 0 0 0

y 1 0 0 0 0 0 0 0 0 0

z 1 0 0 0 0 0 0 0 0 0

aa 1 0 0 0 1 0 0 0 0 0

ab 0 0 0 0 0 0 0 0 0 0

ac 0 0 0 0 0 0 0 0 0 0

ad 0 0 0 0 0 0 0 0 0 0

ae 0 0 0 0 0 0 0 0 0 0

af 0 0 0 0 0 0 0 0 0 0

ah 0 0 0 0 0 0 0 0 0 0

ai 0 0 0 0 0 1 0 0 0 0

aj 0 0 0 0 0 0 1 0 1 1

ak 0 0 0 0 0 1 0 0 0 0

al 1 0 0 0 0 1 1 0 1 1

Chapter 4

Mathematical Model

This project uses an integer program, which is a mathematical optimization problem that

seeks to maximize a linear function subject to constraints where the decision variables must

be integers.

In this case, the objective function is represented by the equation z = c

x, where c is

a vector of objective coeﬃcient and x is a vector of decision variables. The constraints are

represented by the matrix equation Ax ≤ b, where A is a matrix, and b is a vector. Also

where c ∈ R

, x ∈ Z

, A ∈ R

m×n

, and b ∈ R

The solution to the problem results in values for the decision variables that satisfy all

constraints and provide the optimal value for the objective function. The input data for the

model is represented by the parameters c, b, and A.

Sections 4.1 through 4.4 provide an overview of the speciﬁed ranges, parameters, decision

variables, objective function, and constraints for the problem.

The model implementation utilized the PuLP library version 2.7.0 in Python version

3.11.2 and the COIN-OR Branch and Cut Solver (CBC). PuLP is a tool that helps solve

optimization problems in Python and CBC is an open-source solver for mixed-integer linear

programming (MILP) problems. This combination of tools enabled the eﬃcient generation of

an optimal seating arrangement that maximized utility while satisfying problem constraints.

The full implementation of the code on Python, using the PuLP language, can be found in

the Appendix, speciﬁcally in Figure A.1, Figure A.2, Figure A.3, and Figure A.4.

4.1 Ranges

To generalize a model, it is often necessary to deﬁne countable sets using ranges. In

the context of this particular model, two distinct ranges have been employed to create these

countable sets. The ranges used in this project are listed in Table 4.1 and the implementation

of the ranges in PuLP is shown in Figure 4.1.

Table 4.1: Ranges

Variable Meaning

G = {1, 2, ..., 35} Denote each invited party

T = {1, 2, ..., 12} Denote all tables for guests to be sat at

Figure 4.1: Ranges Implementation in Python

4.2 Parameters

Parameters are the known data inputted into the model. This project contains six pa-

rameters. The parameters used in this project are listed in Table 4.2 and the implementation

of the parameters in PuLP is shown in Figure 4.2. As previously mentioned, the positive

and negative relationships in the seating chart reﬂect how the invited parties feel toward one

another. Moreover, weights are assigned to indicate how much the couple values positive and

negative relationships. In the present study, the author assigned a weight of ﬁve to negative

relationships, meaning that they considered a negative relationship to be ﬁve times as costly

as a positive relationship.

Table 4.2: Parameters

Variable Meaning

i,j

The positive relationship value between party i ∈ G and party j ∈ G

i,j

The negative relationship value between party i ∈ G and party j ∈ G

The number of guests in party i ∈ G

m The maximum number of guests that can sit at each table

The weight of utilities

The weight of costs

Figure 4.2: Parameters Implementation in Python.

The parameters needed for this problem were stored in a Microsoft Excel Spreadsheet

and read into Python using the code shown in Figure 4.3. Tables A.1-A.5 show the full

Microsoft Excel Spreadsheet used.

Figure 4.3: Parameter Connections on Python.

4.3 Decision Variables

In this problem, the model’s decision-making process involves selecting unknown values

known as decision variables. These variables are of two types: binary and integer. Binary

variables are either 0 or 1, representing the presence or absence of something. On the other

hand, integer variables are whole numbers that often indicate a quantity of something. In this

project, the model incorporates two integer and three binary decision variables to achieve

the desired outcome. These variables serve as critical inputs to the model, helping it to

generate precise solutions that meet the speciﬁed constraints. The decision variables used in

this project are listed in Table 4.3 and the implementation of the decision variables in PuLP

is shown in Figure 4.4.

Table 4.3: Decision Variables

Variable Meaning

i,k



1, if party i ∈ G sits at table k ∈ T

0, otherwise

i,k



1, if party i ∈ G sits at table k ∈ T

0, otherwise

i,j,k



1, if party i ∈ G and party j ∈ G sits at table k ∈ T

0, otherwise

The total utility at table k ∈ T

The total cost at table k ∈ T

Figure 4.4: Decision Variable Implementation in Python.

4.4 Objective Function

This project aims to maximize the number of positive connections among guests while

minimizing the number of negative connections among guests. This is achieved by maximizing

the total number of positive connections minus the total number of negative connections. The

implementation of the decision variables in PuLP is shown in Figure 4.5.

max z = w

k∈T

− w

k∈T

Figure 4.5: Objective Function Implementation in Python.

4.5 Constraints

A constraint in an integer program is a mathematical expression that limits the feasible

values of the decision variables to a speciﬁc set of integers or a range of values. This project

contains six constraints. The constraints used in this project are listed in Table 4.4.

Table 4.4: Constraints

Constraint Purpose

k∈T

i,k

= 1 ∀i ∈ G Ensures that each guest is only sat once

i,k

= c

i,k

∀i ∈ G, k ∈ T Ensures that the two decision variables that seat a party are equal.

i∈G

i,k

) ≤ m ∀k ∈ T Ensures that the number of guests at the table ﬁt

i∈G

i,k

) ≥ m ·

∀k ∈ T Ensures that each table is at least halfway full

i∈G

j∈G

i,j,k

i,j

) = tp

∀k ∈ T Find the total positive connections

i∈G

j∈G

i,j,k

i,j

) = tp

∀k ∈ T Find the total positive connections

Figure 4.6: Constraint Implementation in Python.

With the mathematical model and data collection procedures in place, the next step

was to apply the model to generate a seating chart and evaluate its eﬀectiveness. The results

of this analysis are presented in the following chapter.

Chapter 5

Results

The ﬁnal solution was found by implementing the model introduced in Chapter 4 using

Python version 3.11.2. Python is a programming language that is freely available to everyone

as open-source software. This means that not only is it free to use, but it also comes with

access to the source code, allowing developers to modify and enhance the language to better

suit their needs. Being open-source has helped make Python one of the most widely used

programming languages in the world, as it enables anyone to contribute to its development

and improvement. Within Python, the PuLP language was used for optimization. Within

PuLP, the COIN-OR Branch and Cut Solver (CBC) was used to solve the integer program.

The optimal solution found once the model was implemented suggests that the seating

arrangement in Table 5.1 would be the optimal seating chart for the speciﬁed wedding. This

optimal seating chart would result in $2,880 of utility. Table 5.1 shows how each letter on

the seating chart corresponds to an invited party.

5.1 Sensitivity Analysis

To ensure that proper weights were assigned to the cost and utility portions of the

objective function, a sensitivity analysis was performed. A sensitivity analysis is a technique

used to determine how sensitive the output of a system or model is to changes in its inputs

or parameters. It involves testing the eﬀects of varying one or more input factors on the

output or outcome of a model and helps to identify which input factors have the greatest

impact on the model’s output. In a sensitivity analysis, diﬀerent values or ranges of values

are assigned to the input factors, and the resulting changes in the output are observed and

analyzed. This helps to determine how much the output changes in response to changes in

the input factors, and to identify which input factors are most important in determining the

output.

In conducting the sensitivity analysis, the weights assigned to costs and utility were

varied to assess their impact on the ﬁnal solution. It was found that when the weight assigned

to the utility increased, the total objective value also increased, whereas a decrease in the

utility weight resulted in a lower objective value. Intriguingly, it was observed that changes

in the weight assigned to costs did not aﬀect the total objective value. This implies that the

program was able to seat guests without any negative connections adjacent to each other, as

evidenced by the consistent objective value across diﬀerent cost weights.

It can be noted that the model presented in Figure 5.1 contains 22 empty seats. In

this speciﬁc case, the couple wanted to utilize all the tables available at their venue since they

were not charged per table. Instead, 12 tables were included in the rental of the venue. In

other cases where a couple may have to pay per table used, they could specify the minimum

number of tables they would need to seat everyone. In the case shown in Figure 5.1, the

couple would have needed only 10 tables to seat all the guests.

Figure 5.1: Optimal Seating Chart.

Table 5.1: Guest Relationship to the Couple.

Code Primary Relationship to the Couple

a Bride’s Father, Step-Mother, and Siblings

b Bride’s Grandparents

c Bride’s Uncle & Cousins

d Bride’s Uncle

e Bride’s Aunt

f Bride’s Mother, Step-Father, and Siblings

g Bride’s Step-Sister & Nephew

h Bride’s Step-Brother

i Bride’s Step-Brother

j Bride’s Aunt & Cousins

k Bride’s Aunt & Cousin

l Bride’s Uncle & Cousins

m Bride’s Grandparents

n Bride’s Grandmother

o Groom’s Parents

p Groom’s Sister & Niece

r Groom’s Brother & Nieces

t Friend of the Couple

u Friend of the Couple

v Friend of the Couple

w Friend of the Couple

x Friend of the Couple

y Friend of the Couple

z Friend of the Couple

aa Friend of the Couple

ab Friend of the Couple

ac Friend of the Couple

ad Friend of the Couple

ae Professor of the Couple

af Professor of the Couple

ah Family Friend

ai Professor of the Couple

aj Family Friend

ak Family Friend

al Family Friend

Chapter 6

Conclusion

In conclusion, this project aimed to create an optimal seating arrangement for wed-

ding guests that would enhance their overall experience and satisfaction by placing them

alongside like-minded individuals. The proposed seating chart was developed using a math-

ematical model and data collection procedures that considered various constraints and pref-

erences, such as group aﬃliations, guest relationships, seating requirements, and table sizes

and shapes. The model was designed to both maximize positive connections among guests

and minimize negative ones, resulting in a seating arrangement that promoted a positive and

enjoyable atmosphere for all attendees.

After a thorough analysis of the results obtained from the seating arrangement, the

couple has decided to adopt the proposed seating chart. The seating chart not only satisﬁes all

the constraints and preferences set forth by the couple but also ensures guest satisfaction. By

incorporating feedback from guests and considering the relationships between invited parties,

the proposed seating chart maximized positive connections while minimizing negative ones,

resulting in a seating arrangement that was both functional and enjoyable.

Overall, the proposed seating chart provides a novel approach to seating guests at

weddings and other events, which can lead to a more enjoyable experience for all attendees.

This project demonstrates the power of mathematical modeling and optimization techniques

in solving real-world problems and highlights the potential for their application in event

planning and management.

6.1 Future Work

Future work for this project can take various directions. Firstly, the optimized seating

arrangement proposed in this project can be further analyzed to evaluate its success in terms

of guest satisfaction and overall event success. This analysis can include surveying guests

post-event to gather feedback on their experience and assessing any changes in the event’s

atmosphere or engagement levels. Additionally, alternative seating chart optimization models

can be explored to compare their eﬀectiveness with the proposed model.

In terms of applying the model to other events, future research can explore how

seating arrangements can impact various types of events, such as conferences, workshops,

and business meetings. These events often have diﬀerent requirements and objectives, and

therefore, diﬀerent seating arrangements may be necessary. Furthermore, exploring how the

seating arrangement impacts attendee engagement and interaction in these events could lead

to more eﬀective event planning strategies.

Another potential area of research is the data collection process. This project used a

rating system to gather data on relationships between guests, but alternative data collection

methods could be explored to increase the accuracy and comprehensiveness of the data. This

could include utilizing social network analysis tools to map out the relationships between

guests or implementing surveys that ask guests to rate their comfort level with sitting next

to certain individuals.

Overall, this project lays the groundwork for further research on seating chart opti-

mization and its impact on event success. By continuing to explore and develop this area

of research, we can improve the guest experience at events and increase the success of these

events.

REFERENCES

[1] Bellows, Meghan L, and J.D. Luc Peterson. “Finding an Optimal Seating Chart.” Annals

of Improbable Research, 12 Feb. 2012, https://improbable.com/2012/02/12/ﬁnding-an-

optimal-seating-chart-for-a-wedding/.

[2] Braun, Summer S., et al. “Eﬀects of a Seating Chart Intervention for Target and Non-

target Students.” Journal of Experimental Child Psychology, vol. 191, 2020, p. 104742,

https://doi.org/10.1016/j.jecp.2019.104742.

[3] Lewis, Rhyd, and Fiona Carroll. “Creating Seating Plans: a

Practical Application.” Taylor & Francis Online, 21 Dec. 2017,

https://www.tandfonline.com/doi/full/10.1057/jors.2016.34.

[4] Mattia, Nancy. “5 Digital Wedding Seating Chart Tools to Simplify Planning.”

Brides, Brides, 4 Jan. 2022, https://www.brides.com/story/digital-seating-charts-

wedding-planning.

[5] Ptak, Dave. “Probability and the Seating Chart.” The Mathematics Teacher, vol. 81, no.

5, 1988, pp. 393–397, https://doi.org/10.5951/mt.81.5.0393.

[6] Waida, Maria. “How to Create a Wedding Seating Chart in 15 Simple Steps.” Social

Tables, 10 Aug. 2020, https://www.socialtables.com/blog/event-planning/how-to-create-

seating-chart-wedding/.

APPENDICES

A Appendix A

Table A.1: Microsoft Excel Positive Connections Data Part 1.

Table A.2: Microsoft Excel Positive Connections Data Part 2.

Table A.3: Microsoft Excel Negative Connections Data Part 1.

Table A.4: Microsoft Excel Negative Connections Data Part 2.

Table A.5: Microsoft Excel Party Size Data.