WORKING DRAFT authorea.com/10482

# Introduction

Business site selection has always been high-stakes: the opening of a new business location has extremely large monetary implications. Location can impact margins, response to competition, and effective exploitation of possible market segments (Clarke 2013)(Cliquet 2013)(Ghosh 1983). It is also well-established that convenience is a significant factor in consumer decisions, especially those regarding food (Bonke 1996). In a university setting, decisions such as food vendor placement become particularly important, as daily food is the second highest consumer expenditure for college students (Adams 1997). In the present study, these understandings were incorporated into a decision procedure regarding the position of a hypothetical hot dog vendor on a college campus, in which convenience for students was evaluated using spatial information.

## Assigned problem

A map was given of a college campus showing the walking paths and dormitories and approximate distances between the intersections (Figure 1). We were asked to answer questions about the location of a hot dog vender:

1. Where on campus should you set up your stand?

2. How does your location change if you set up two stands?

3. Suppose A and C are female dorms and D, E, and F are male dorms. How would your location change if 30 percent of females and 80 percent of males are likely to eat at your stand?

4. Suppose the path between B and C and the path between E and D go uphill and that it is twice as hard to walk uphill as downhill. How would your choice change?

## Proposed solution

We propose an algorithm that determines the most convenient location as the position that minimizes the distance between the dormitories and the hot dog vendor location.

Map representing the college campus, where A, C, D, E, and F correspond to a dormitory. A and C are female dorms, and D, E, and F are male dorms.

# Assumptions

The proposed model assumes that:

1. The closer the hot dog stand is to the student’s dorm, the more convenient the hot dog stand is.

2. The more traffic encountered by the hot dog stand, the more business it will receive.

3. Each dorm has the same number of students.

4. Every student wants to go to each dorm equally.

5. Students will tend to choose the shortest path to their desired dorm.

6. Students are always hungry.

7. The number of students in each dorm is the same.

8. The same number of students from each dorm will go out.

9. The most traffic will be at the intersections rather than along a path.

# Model

To find the point with the greatest convenience for students, a factor $$c$$ was calculated, called the “convenience factor.” This convenience factor was defined as the overlaps of paths divided by the average distance between the dormitories, as given by the equation: $$c=\frac{t}{a}$$. Greater intersection traffic is directly proportional and greater average distance indirectly proportional to the convenience factor. This equation controls for variations in modes of transportations and walking speeds: it determines the ease of traveling to vendor position in an absolute sense.

### Defining variables

$$t$$ was defined as intersection traffic, or the overlaps of the paths between the dorms, calculated as the number of times in which a point coincided with a path ( $$\overline{AB}$$, \(\overline{CD