This paper is the first part of a comprehensive survey on pickup and delivery problems. Basically, two problem classes can be distinguished. The first class, discussed in this paper, deals with the transportation of goods from the depot to linehaul customers and from backhaul customers to the depot. This class is denoted as Vehicle Routing Problems with Backhauls (VRPB). Four subtypes can be considered, namely the Vehicle Routing Problem with Clustered Backhauls (VRPCB -all linehauls before backhauls), the Vehicle Routing Problem with Mixed linehauls and Backhauls (VRPMB -any sequence of linehauls and backhauls permitted), the Vehicle Routing Problem with Divisible Delivery and Pickup (VRPDDP -customers demanding delivery and pickup service can be visited twice), and the Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP -customers demanding both services have to be visited exactly once). The second class, dealt with in the second part of this survey, refers to all those problems where goods are transported between pickup and delivery locations. These are the Pickup and Delivery Vehicle Routing Problem (PDVRP -unpaired pickup and delivery points), the classical Pickup and Delivery Problem (PDP -paired pickup and delivery points), and the Dial-A-Ride Problem (DARP -passenger transportation between paired pickup and delivery points and user inconvenience taken into consideration). Single as well as multi vehicle versions of the mathematical problem formulations are given for all four VRPB types, the corresponding exact, heuristic, and metaheuristic solution methods are discussed. Zusammenfassung Der vorliegende Artikel ist Teil I einer umfassendenÜberblicks-arbeit in zwei Teilenüber pickup and delivery Probleme. Grundsätzlich können zwei Problemklassen unterschieden werden. Die erste Problemklasse, mit der sich dieser Artikel befasst, beinhaltet all jene Probleme, die Auslieferungen von einem Depot zu Auslieferungs-Kunden (linehaul customers) und Abholungen von Rück-ladungs-Kunden (backhaul customers) zu einem Depot behandeln. Diese Problemklasse wird im Folgenden als Vehicle Routing Problems with Backhauls (VRPB) bezeichnet. Vier verschiedene Problemtypen können weiters unterschieden werden: das Vehicle Routing Problem with Clustered Backhauls (VRPCB), alle Auslieferungen müssen vor den Abholungen durchgeführt werden, das Vehicle Routing Problem with Mixed linehauls and Backhauls (VRPMB), gemischte Ausliefer-und Abholsequenzen sind gestattet, das Vehicle Routing Problem with Divisible Delivery and Pickup (VRPDDP), Kunden, die Ausliefer-und Abholservice verlangen, können zweimal besucht werden, und das Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP), Kunden, die beide Services verlangen, können nur genau einmal angefahren werden. Die zweite pickup and delivery Problemklasse wird in Teil II dieser Arbeit behandelt. Sie beinhaltet all jene Problemtypen, die sich mit Transporten zwischen Abhol-und Auslieferungsorten befassen: das Pickup and Delivery Vehicle Routing Problem (PD...

Highlights• First bi/multi-objective model for the home care routing and scheduling problem• Insight in and analysis of the trade-off between costs and client inconvenience • A metaheuristic algorithm based on Multi-Directional Local Search• Numerical experiments on new benchmark instances based on real-life data • The trade-off is substantial, indicating the need for well-considered decisions AbstractOrganizations providing home care services are inclined to optimize their activities in order to meet the constantly increasing demand for home care. In this context, home care providers are confronted with multiple, often conflicting, objectives such as minimizing their operating costs while maximizing the service level offered to their clients by taking into account their preferences. This paper is the first to shed some light on the trade-off relationship between these two objectives by modeling the home care routing and scheduling problem as a biobjective problem. The proposed model accounts for qualifications, working regulations and overtime costs of the nurses, travel costs depending on the mode of transportation, hard time windows, and client preferences on visit times and nurses. A distinguishing characteristic of the problem is that the scheduling problem for a single route is a bi-objective problem in itself, thereby complicating the problem considerably. A metaheuristic algorithm, embedding a large neighborhood search heuristic in a multi-directional local search framework, is proposed to the solve the problem. Computational experiments on a set of benchmark instances based on real-life data are presented. A comparison with exact solutions on small instances shows that the algorithm performs well. An analysis of the results reveals that service providers face a considerable trade-off between costs and client convenience. However, starting from a minimum cost solution, the average service level offered to the clients may already be improved drastically with limited additional costs.

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Dial-a-ride problems deal with the transportation of people between pickup and delivery locations. Given the fact that people are subject to transportation, constraints related to quality of service are usually present, such as time windows and maximum user ride time limits. In many real world applications, different types of users exist. In the field of patient and disabled people transportation, up to four different transportation modes can be distinguished. In this article we consider staff seats, patient seats, stretchers and wheelchair places. Furthermore, most companies involved in the transportation of the disabled or ill dispose of different types of vehicles. We introduce both aspects into state-of-the-art formulations and branch-and-cut algorithms for the standard dial-a-ride problem. Also a recent metaheuristic method is adapted to this new problem. In addition, a further service quality related issue is analyzed: vehicle waiting time with passengers aboard. Instances with up to 40 requests are solved to optimality. High quality solutions are obtained with the heuristic method.

Demographic change towards an ever aging population entails an increasing demand for specialized transportation systems to complement the traditional public means of transportation. Typically, users place transportation requests, specifying a pickup and a drop off location and a fleet of minibuses or taxis is used to serve these requests. The underlying optimization problem can be modeled as a dial-a-ride problem. In the dial-a-ride problem considered in this paper, total routing costs are minimized while respecting time window, maximum user ride time, maximum route duration, and vehicle capacity restrictions. We propose a hybrid column generation and large neighborhood search algorithm and compare different hybridization strategies on a set of benchmark instances from the literature.

T he consistent vehicle routing problem (ConVRP) takes customer satisfaction into account by assigning one driver to a customer and by bounding the variation in the arrival times over a given planning horizon. These requirements may be too restrictive in some applications. In the generalized ConVRP (GenConVRP), each customer is visited by a limited number of drivers and the variation in the arrival times is penalized in the objective function. The vehicle departure times may be adjusted to obtain stable arrival times. Additionally, customers are associated with AM/PM time windows. In contrast to previous work on the ConVRP, we do not use the template concept to generate routing plans. Our approach is based on a flexible large neighborhood search that is applied to the entire solution. Several destroy and repair heuristics have been designed to remove customers from the routes and to reinsert them at better positions. Arrival time consistency is improved by a simple 2-opt operator that reverses parts of particular routes.A computational study is performed on ConVRP benchmark instances and on new instances generated for the generalized problem. The proposed algorithm performs well on different variants of the ConVRP. It outperforms template-based approaches in terms of travel cost and time consistency. For the GenConVRP, we experiment with different input parameters and examine the trade-off between travel cost and customer satisfaction. Remarkable cost savings can be obtained by allowing more than one driver per customer.

The importance of customer satisfaction was identified by many industries as a key factor of competitive advantage. So, for companies in the small package shipping industry, it can be reasonable to increase the service quality even at the expense of transportation cost to gain customer loyalty. These companies noticed that customer satisfaction can be increased by providing consistent service in the form of visiting customers with the same driver at approximately the same time of the day over a certain time period. Motivated by this real-world problem, the consistent vehicle routing problem (ConVRP) combines traditional vehicle routing constraints with the requirements for service consistency. This article presents a fast solution method called template-based adaptive large neighborhood search for the described problem. Compared to state-of-the-art heuristics, the developed algorithm is highly competitive on the available benchmark instances. Additionally, new test instances are provided. These seem to be more challenging due to the variation of different model parameters and consequently help to identify interesting effects. Finally, a relaxed variant of the original ConVRP is presented. In this variant, the departure times from the depot can be delayed to adjust the service times of the customers. Experiments show that allowing later departure times considerably improves the solution quality under tight consistency requirements.