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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