Incorporating Road Networks into Territory Design

TL;DR

This paper introduces graph theoretic models that incorporate road network data into territory design, improving the creation of balanced, contiguous, and efficient territories through adapted algorithms and optimization techniques.

Contribution

It develops novel graph models and modifies existing algorithms to integrate road network considerations into territory design problems.

Findings

Models effectively incorporate road network data.

Algorithms outperform traditional methods on real-world instances.

Enhanced territories show improved compactness and efficiency.

Abstract

Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized. Desired properties of territories often include a reasonable balance, compact form, contiguity and small average journey times which are usually encoded in the objective function or formulated as constraints. We address the territory design problem by developing graph theoretic models that also consider the underlying road network. The derived graph models enable us to tackle the territory design problem by modifying graph partitioning algorithms and mixed integer programming formulations so that the objective of the planning problem is taken into account. We test and compare the algorithms on several real world instances.