Recent Mathematical Approaches to Service Territory Design

Abstract

Many companies and institutions operate a field service workforce to provide services at their customers' sites. Examples include the sales force of consumer goods manufacturers, the field service technicians of engineering companies, and the nurses of home-health care providers. To obtain clearly defined areas of responsibility, the geographical region under study is in many cases subdivided into service territories, each of which is served by a single field worker or a team of field workers. The design of service territories is subject to various planning criteria. The most common ones are geographical compactness, contiguity, and balance in terms of workload or income potential, but there can be several additional criteria and requirements depending on the specific application. In this thesis, we deal with the development of mathematical models and methods for service territory design problems. Our focus is on planning requirements that are relevant for practice, but have received little attention in the existing literature on territory design so far. We address the question how these requirements can be incorporated into mathematical models and mathematical programming based solution methods. We first present requirements that restrict the feasible assignments of customers to field workers and provide components for their integration into mathematical models. We further consider the requirement that customers must be served multiple times during a given planning horizon. We introduce the resulting problem, which we call the multi-period service territory design problem (MPSTDP). It has not yet been studied in the literature. The emphasis is put on the scheduling task of the MPSTDP, which deals with the assignment of service visits to the days of the planning horizon. We formally define this task and devise a heuristic solution method. Our heuristic produces high-quality solutions and clearly outperforms the existing software product of our industry partner. Moreover, we present the first specially-tailored exact solution method for this task: a branch-and-price algorithm that incorporates specialized acceleration techniques, such as a fast pricing heuristic and symmetry reduction techniques. Ultimately, we study the design of territories for parcel delivery companies. We address the tactical design of the territories and their daily adjustment in order to cope with demand fluctuations. The problem involves determining the number of territories and assigning heterogeneous resources to the territories, a combination not yet addressed in literature. We propose different models as well as a heuristic solution approach, and we perform an extensive case study on real-world problem data.