Recent Mathematical Approaches to Service Territory Design

Many companies and institutions operate a field service workforce to provide services at their customers\u27 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

A concise guide to existing and emerging vehicle routing problem variants

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges

A concise guide to existing and emerging vehicle routing problem variants

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges.</p

Tactical Problems in Vehicle Routing Applications

The class of Vehicle Routing Problems (VRPs) is one the most studied topics in the Operations Research community. The vast majority of the published papers focus on single-period problems, with a few branches of the literature considering multiperiod generalisations. All of these problems though, consider a short horizon and aim at optimising the decisions at an operational level, i.e. that will have to be taken in the near future. One step above are tactical problems, i.e. problems concerning a longer time horizon. Tactical problems are of a fundamental importance as they directly influence the daily operations, and therefore a part of the incurred costs, for a long time. The main focus of this thesis is to study tactical problems arising in routing applications. The first problem considered concerns the design of a fleet of vehicles. Transportation providers often have to design a fleet that will be used for daily operations across a long-time span. Trucks used for transportation are very expensive to purchase, maintain or hire. On the other side, the composition of the fleet strongly influences the daily plans, and therefore costs such as fuel or drivers’ wages. Balancing these two components is challenging, and optimisation models can lead to substantial savings or provide a useful basis for informed decisions. The second problem presented focuses on the use of a split deliveries policy in multi-period routing problems. It is known that the combined optimisation of delivery scheduling and routing can be very beneficial, and lead to significant reductions in costs. However, it also adds complexity to the model. The same is true when split deliveries are introduced. The problem studied considers the possibility of splitting the deliveries over different days. An analysis, both theoretical and numerical, of the impact of this approach on the overall cost is provided. Finally, a districting problem for routing applications is considered. These types of problems typically arise when transportation providers wish to increase their service consistency. There are several reasons a company may wish to do so: to strengthen the customer-driver relationship, to increase drivers’ familiarity with their service area, or, to simplify the management of the service area. A typical approach, considered here, is to divide the area under consideration in sectors that will be subsequently assigned to specific drivers. This type of problem is inherently of a multi-period and tactical nature. A new formulation is proposed, integrating standard routing models into the design of territories. This makes it possible to investigate how operational constraints and other requirements, such as having a fair workload division amongst drivers, influence the effectiveness of the approach. An analysis of the cost of districting, in terms of increased routing cost and decreased routing flexibility, and of several operational constraints, is presented

Service Consistency in Vehicle Routing

This thesis studies service consistency in the context of multi-period vehicle routing problems (VRP) in which customers require repeatable services over a planning horizon of multiple days. Two types of service consistency are considered, namely, driver consistency and time consistency. Driver consistency refers to using the fewest number of different drivers to perform all of the visits required by a customer over a planning horizon and time consistency refers to visiting a customer at roughly the same time on each day he/she needs service. First, the multi-objective consistent VRP is defined to explore the trade-offs between the objectives of travel cost minimization and service consistency maximization. An improved multi-objective optimization algorithm is proposed and the impact of improving service consistency on travel cost is evaluated on various benchmark instances taken from the literature to facilitate managerial decision making. Second, service consistency is introduced for the first time in the literature to the periodic vehicle routing problem (PVRP). In the PVRP, customers may require multiple visits over a planning horizon, and these visits must occur according to an allowable service pattern. A service pattern specifies the days on which the visits required by a customer are allowed to occur. A feasible service pattern must be determined for each customer before vehicle routes can be optimized on each day. Various multi-objective optimization approaches are implemented to evaluate their comparative competitiveness in solving this problem and to evaluate the impact of improving service consistency on the total travel cost. Third, a branch-and-price algorithm is developed to solve the consistent vehicle routing problem in which service consistency is enforced as a hard constraint. In this problem, the objective is to minimize the total travel cost. New constraints are devised to enhance the original mixed integer formulation of the problem. The improved formulation outperforms the original formulation regarding CPLEX solution times on all benchmark instances taken from the literature. The proposed branch-and-price algorithm is shown to be able to solve instances with more than fourteen customers more efficiently than either the existing mixed integer formulation or the one we propose in this paper

Planning the delivery of home-based long-term care: A mathematical programming-based tool to support routes' planning

The adequate planning of home-based long-term care (HBLTC) is essential in the current European setting where long-term care (LTC) demand is increasing rapidly, and where home-based care represents a potential cost-saving alternative from traditional inpatient care. Particularly, this planning should involve proper route planning to ensure visits of health professionals to patients’ homes. Nevertheless, literature in the specific area of HBLTC planning is still scarce. Accordingly, this paper proposes a tool based on a mathematical programming model – the LTCroutes – for supporting the daily planning of routes to visit LTC patients’ homes in National Health Service-based countries. The model allows exploring the impact of considering different objectives relevant in this sector, including the minimization of costs and the maximization of service level. Patients’ preferences, traffic conditions and budget constraints are also considered in the proposed model. To illustrate the applicability of the model, a case study based on the National Network of LTC in Portugal (RNCCI) is analysed.O planeamento adequado de cuidados continuados ao domicílio é essencial na conjuntura atual Europeia em que a procura de cuidados continuados está a aumentar rapidamente, e em que os cuidados ao domicílio representam uma alternativa com potencial de poupança de custos relativamente ao tradicional internamento hospitalar. Particularmente, é necessário haver um planeamento adequado das rotas dos profissionais de saúde às casas dos pacientes. No entanto, a literatura na área específica de planeamento de cuidados continuados ao domicílio ainda é escassa. Nesse sentido, este artigo propõe uma ferramenta baseada num modelo de programação matemática - o LTCroutes - para apoiar o planeamento diário das rotas para visitar as casas dos pacientes com necessidade de cuidados continuados em países com Serviço Nacional de Saúde. O modelo desenvolvido permite explorar o impacto de considerar diferentes objetivos relevantes neste setor, incluindo a minimização de custos e a maximização do nível de serviço. As preferências dos pacientes, condições de trânsito e restrições de orçamento também são consideradas no modelo proposto. Para ilustrar a aplicabilidade do modelo, é analisado um caso de estudo baseado na Rede Nacional de Cuidados Continuados Integrados (RNCCI) em Portugal

Pattern-based decompositions for human resource planning in home health care services

Home health care services play acrucial role in reducing the hospitalization costs due to the increase of chronic diseases of elderly people. At the same time, they allow us to improve the quality of life for those patients that receive treatments at their home. Optimization tools are therefore necessary to plan service delivery at patients' homes. Recently, solution methods that jointly address the assignment of the patient to the caregiver (assignment), the definition of the days (pattern) in which caregivers visit the assigned patients (scheduling), and the sequence of visits for each caregiver (routing) have been proposed in the scientific literature. However, the joint consideration of these three level of decisions may be not affordable for large providers, due to the required computational time. In order to combine the strength and the flexibility guaranteed by a joint assignment, scheduling and routing solution approach with the computational efficiency required for large providers, in this study we propose a new family of two-phase methods that decompose the joint approach by incrementally incorporating some decisions into the first phase.The concept of pattern is crucial to perform such a decomposition in a clever way. Several scenarios are analyzed by changing the way in which resource skills are managed and the optimization criteria adopted to guide the provider decisions. The proposed methods are tested on realistic instances. The numerical experiments help us to identify the combinations of decomposition techniques, skill management policies and optimization criteria that best fit with problem instances of different size

Dynamically accepting and scheduling patients for home healthcare

Importance of home healthcare is growing rapidly since populations of developed and even developing countries are getting older quickly and the number of hospitals, retirement homes, and medical staff do not increase at the same rate. We present Scenario Based Approach (SBA) for the Home Healthcare Nurse Scheduling Problem. In this problem, arrivals of patients are dynamic and acceptance and appointment time decisions have to be made as soon as patients arrive. The primary objective is to maximise the average number of daily visits. For the sake of service continuity, patients have to be visited at the same days and times each week during their service horizon. SBA is basically a simulation procedure based on generating several scenarios and scheduling new customers with a simple but fast heuristic. Then results are analysed to decide whether to accept the new patient and at which appointment day/time. First, two different versions of SBA, Daily and Weekly SBA are developed and analysed for a single nurse. We compare Daily SBA to two greedy heuristics from the literature, distance and capacity based, and computational studies show that Daily SBA makes significant improvements compared to these other two methods for a single nurse. Next, we extend SBA for a multi-nurse case. SBA is compared to a greedy heuristic under different conditions such as same depot case where nurses start their visits from and return to same place, clustered service area, and nurses with different qualification level. SBA gives superior results under all experiment conditions compared to the greedy heuristic