**Author details**

Carlos Duran-Hernandez1 \*, Rene Ledesma-Alonso2 \*, Gibran Etcheverry1 \* and Rogelio Perez-Santiago2

1 Department of Computing, Electronics and Mechatronics, Universidad de las Américas Puebla, San Andrés Cholula, Puebla, Mexico

2 Department of Industrial and Mechanical Engineering, Universidad de las Américas Puebla, San Andrés Cholula, Puebla, Mexico

\*Address all correspondence to: jose.duranhz@udlap.mx; rene.ledesma@udlap.mx and gibran.etcheverry@udlap.mx

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Chapter

Abstract

integer programming

support this decision-making process.

ing the BUs in a territory as close together as possible.

1. Introduction

113

Problem

Comparison of Dispersion

María Gabriela Sandoval Esquivel,

Roger Z. Ríos-Mercado and Juan Díaz

Measures for a Territory Design

Territory design consists of dividing a geographic area into territories according

Territory design deals with the discrete assignment of basic units (BUs) (such as

Mathematical formulations of territory design problems have been developed since 1965. As noted in Kalcsics et al. [1], most of the research related to territory design problems is tied to specific applications and thus have specific planning criteria accordingly. However, three types of requirements can be identified in most territory design applications: balance, connectivity, and compactness. Balance refers to having territories of the same size, and a size is defined upon an activity measure related to the problem application. For example, the size of the territory may be defined as the number of inhabitants in an area or the amount of workload involved. Connectivity constraints require all the BUs of a territory to be connected. Compactness is another spatial characteristic that is rather vaguely defined as hav-

Compactness is crucial in most applications of territory design because this leads to shorter (more inexpensive) routes when distributing product or visiting the BUs

zip-code areas, blocks, etc.) into clusters with restrictions defined by planning criteria. The need for a territory design plan is present in several social planning contexts such as political districting and commercial territory design. The motivation to divide a geographical area is related to the fact that smaller areas are easier to manage. In practice, a territory design requires a lot of time and effort and, in most cases, needs to be performed recurrently as the environment evolves and new needs develop. Thus, it is desired to have an automatic or computational method to

to certain planning criteria. In most applications, it is desired that the resulting territories are balanced, connected, and compact. We analyze different ways of measuring dispersion, each cast in a particular mixed-integer linear programming model. One is based on p-centers and the other on p-medians. The experimental work includes a comparison between these two models in terms of robustness.

Keywords: territory design, p-center, p-median, dispersion measures,
