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Journal ArticleDOI

Static pickup and delivery problems: a classification scheme and survey

18 Apr 2007-Top (Springer-Verlag)-Vol. 15, Iss: 1, pp 1-31
TL;DR: A general framework to model a large collection of pickup and delivery problems, as well as a three-field classification scheme for these problems, is introduced.
Abstract: Pickup and delivery problems constitute an important class of vehicle routing problems in which objects or people have to be collected and distributed. This paper introduces a general framework to model a large collection of pickup and delivery problems, as well as a three-field classification scheme for these problems. It surveys the methods used for solving them.
Citations
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Journal ArticleDOI
TL;DR: A more general mathematical model for real-time high-capacity ride-sharing that scales to large numbers of passengers and trips and dynamically generates optimal routes with respect to online demand and vehicle locations is presented.
Abstract: Ride-sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere, and anytime. These services present enormous potential for positive societal impacts with respect to pollution, energy consumption, congestion, etc. Current mathematical models, however, do not fully address the potential of ride-sharing. Recently, a large-scale study highlighted some of the benefits of car pooling but was limited to static routes with two riders per vehicle (optimally) or three (with heuristics). We present a more general mathematical model for real-time high-capacity ride-sharing that (i) scales to large numbers of passengers and trips and (ii) dynamically generates optimal routes with respect to online demand and vehicle locations. The algorithm starts from a greedy assignment and improves it through a constrained optimization, quickly returning solutions of good quality and converging to the optimal assignment over time. We quantify experimentally the tradeoff between fleet size, capacity, waiting time, travel delay, and operational costs for low- to medium-capacity vehicles, such as taxis and van shuttles. The algorithm is validated with ∼3 million rides extracted from the New York City taxicab public dataset. Our experimental study considers ride-sharing with rider capacity of up to 10 simultaneous passengers per vehicle. The algorithm applies to fleets of autonomous vehicles and also incorporates rebalancing of idling vehicles to areas of high demand. This framework is general and can be used for many real-time multivehicle, multitask assignment problems.

920 citations

Journal ArticleDOI
TL;DR: This paper systematically outline the optimization challenges that arise when developing technology to support ride-sharing and survey the related operations research models in the academic literature.

858 citations


Cites background from "Static pickup and delivery problems..."

  • ...For excellent recent reviews on dynamic pick-up-and-delivery problems see Berbeglia et al. (2010) and Cordeau et al. (2007). A transportation request for an urban taxi typically arrives only a short time before the desired departure (Lee et al., 2004) and vehicle routes and schedules are updated each time a new transportation request arrives. The dynamic ride-sharing environment resembles an urban taxi environment in terms of the arrival process of transportation requests, i.e., rides, but also has the added complexity of an arrival process of transportation resources, i.e., drivers. That is, a urban taxi system tends to have better information about where and when individual resources will become available. Note that it is often passenger convenience rather than physical capacity that keeps taxis from serving multiple passengers simultaneously. Horn (2002) demonstrate that allowing multiple passenger parties together in a single taxi trip may decrease system-wide vehicle miles but increase the individual travel times of the passengers. They present a dispatching software to manage a fleet of demand-responsive taxis taking into account both passenger service quality considerations and fleet efficiency considerations. The system assigns new travel requests to vehicles based on minimum cost criteria and then periodically applies improvement procedures. The author conducts a number of simulation studies based on data from a real-life taxi operator in Australia. The tests show that the software tool operates effectively in a fairly dynamic environment and realistic problems sizes. Dial (1995) proposes an autonomous dial-a-ride taxi service that shares many similarities with dynamic ride-sharing. The fully automated system lets passengers reserve trips by phone or computer on short-notice. For routing and dispatching, the author suggests the use of a dynamic programming approach of Psaraftis (1980). The dynamic algorithm reoptimizes the not yet executed part of the tentative optimal route each time a new request appears. Since the algorithm can only solve very small instances the system only includes passenger requests that want to be served in the near future and runs the algorithm for each vehicle individually. In the area of freight transportation, full truckload carriers have to manage fleets of vehicles (e.g. containers, trailers, boxcars) that serve one load at a time, with orders continuously arriving over time (for a review see Powell et al. (2007)). The problem of sequentially assigning transportation requests to vehicles is typically referred to as the dynamic assignment problem (Spivey and Powell, 2004) or the dynamic stacker crane problem (Berbeglia et al., 2010). Yang et al. (2004) consider the real-time multi-vehicle truckload pickup and delivery problem....

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  • ...For excellent recent reviews on dynamic pick-up-and-delivery problems see Berbeglia et al. (2010) and Cordeau et al. (2007). A transportation request for an urban taxi typically arrives only a short time before the desired departure (Lee et al., 2004) and vehicle routes and schedules are updated each time a new transportation request arrives. The dynamic ride-sharing environment resembles an urban taxi environment in terms of the arrival process of transportation requests, i.e., rides, but also has the added complexity of an arrival process of transportation resources, i.e., drivers. That is, a urban taxi system tends to have better information about where and when individual resources will become available. Note that it is often passenger convenience rather than physical capacity that keeps taxis from serving multiple passengers simultaneously. Horn (2002) demonstrate that allowing multiple passenger parties together in a single taxi trip may decrease system-wide vehicle miles but increase the individual travel times of the passengers. They present a dispatching software to manage a fleet of demand-responsive taxis taking into account both passenger service quality considerations and fleet efficiency considerations. The system assigns new travel requests to vehicles based on minimum cost criteria and then periodically applies improvement procedures. The author conducts a number of simulation studies based on data from a real-life taxi operator in Australia. The tests show that the software tool operates effectively in a fairly dynamic environment and realistic problems sizes. Dial (1995) proposes an autonomous dial-a-ride taxi service that shares many similarities with dynamic ride-sharing. The fully automated system lets passengers reserve trips by phone or computer on short-notice. For routing and dispatching, the author suggests the use of a dynamic programming approach of Psaraftis (1980). The dynamic algorithm reoptimizes the not yet executed part of the tentative optimal route each time a new request appears....

    [...]

  • ...For excellent recent reviews on dynamic pick-up-and-delivery problems see Berbeglia et al. (2010) and Cordeau et al. (2007). A transportation request for an urban taxi typically arrives only a short time before the desired departure (Lee et al....

    [...]

  • ...For excellent recent reviews on dynamic pick-up-and-delivery problems see Berbeglia et al. (2010) and Cordeau et al. (2007). A transportation request for an urban taxi typically arrives only a short time before the desired departure (Lee et al., 2004) and vehicle routes and schedules are updated each time a new transportation request arrives. The dynamic ride-sharing environment resembles an urban taxi environment in terms of the arrival process of transportation requests, i.e., rides, but also has the added complexity of an arrival process of transportation resources, i.e., drivers. That is, a urban taxi system tends to have better information about where and when individual resources will become available. Note that it is often passenger convenience rather than physical capacity that keeps taxis from serving multiple passengers simultaneously. Horn (2002) demonstrate that allowing multiple passenger parties together in a single taxi trip may decrease system-wide vehicle miles but increase the individual travel times of the passengers....

    [...]

  • ...For excellent recent reviews on dynamic pick-up-and-delivery problems see Berbeglia et al. (2010) and Cordeau et al. (2007). A transportation request for an urban taxi typically arrives only a short time before the desired departure (Lee et al., 2004) and vehicle routes and schedules are updated each time a new transportation request arrives. The dynamic ride-sharing environment resembles an urban taxi environment in terms of the arrival process of transportation requests, i.e., rides, but also has the added complexity of an arrival process of transportation resources, i.e., drivers. That is, a urban taxi system tends to have better information about where and when individual resources will become available. Note that it is often passenger convenience rather than physical capacity that keeps taxis from serving multiple passengers simultaneously. Horn (2002) demonstrate that allowing multiple passenger parties together in a single taxi trip may decrease system-wide vehicle miles but increase the individual travel times of the passengers. They present a dispatching software to manage a fleet of demand-responsive taxis taking into account both passenger service quality considerations and fleet efficiency considerations. The system assigns new travel requests to vehicles based on minimum cost criteria and then periodically applies improvement procedures. The author conducts a number of simulation studies based on data from a real-life taxi operator in Australia. The tests show that the software tool operates effectively in a fairly dynamic environment and realistic problems sizes. Dial (1995) proposes an autonomous dial-a-ride taxi service that shares many similarities with dynamic ride-sharing. The fully automated system lets passengers reserve trips by phone or computer on short-notice. For routing and dispatching, the author suggests the use of a dynamic programming approach of Psaraftis (1980). The dynamic algorithm reoptimizes the not yet executed part of the tentative optimal route each time a new request appears. Since the algorithm can only solve very small instances the system only includes passenger requests that want to be served in the near future and runs the algorithm for each vehicle individually. In the area of freight transportation, full truckload carriers have to manage fleets of vehicles (e.g. containers, trailers, boxcars) that serve one load at a time, with orders continuously arriving over time (for a review see Powell et al. (2007))....

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Journal ArticleDOI
TL;DR: This classification is the first to categorize the articles of the VRP literature to this level of detail and is based on an adapted version of an existing comprehensive taxonomy.

800 citations

Journal ArticleDOI
01 Jun 2008
TL;DR: Single as well as multi vehicle mathematical problem formulations for all three VRPPD types are given, and the respective exact, heuristic, and metaheuristic solution methods are discussed.
Abstract: This paper is the second part of a comprehensive survey on pickup and delivery models. Basically, two problem classes can be distinguished. The first part dealt with the transportation of goods from the depot to linehaul customers and from backhaul customers to the depot. In this class four subtypes were 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 part now considers all those problems where goods are transported between pickup and delivery locations, denoted as Vehicle Routing Problems with Pickups and Deliveries (VRPPD). These are the Pickup and Delivery VRP (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 paired pickup and delivery points and user inconvenience taken into consideration). A single as well as a multi vehicle mathematical problem formulation for all three VRPPD types is given, and the respective exact, heuristic, and metaheuristic solution methods are discussed.

703 citations


Cites background or methods from "Static pickup and delivery problems..."

  • ...A survey on different solution methods can be found in (Berbeglia et al., 2007)....

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  • ...Another survey on different solution methods can be found in Berbeglia et al. (2007)....

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Journal ArticleDOI
TL;DR: This article surveys the subclass of problems called dynamic pickup and delivery problems, in which objects or people have to be collected and delivered in real-time, and discusses some general issues as well as solution strategies.

638 citations


Cites background from "Static pickup and delivery problems..."

  • ...These problems are the dynamic counterparts of the one-to-one static PDPs surveyed in Berbeglia et al. (2007)....

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  • ...These problems are the dynamic counterparts of the one-to-one static PDPs surveyed in Berbeglia et al. (2007). Finally, some conclusions are provided in Section 7....

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References
More filters
Book
01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Abstract: This is the second edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’’ W. H. Freeman & Co., San Francisco, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed. Readers having results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.), or open problems they would like publicized, should send them to David S. Johnson, Room 2C355, Bell Laboratories, Murray Hill, NJ 07974, including details, or at least sketches, of any new proofs (full papers are preferred). In the case of unpublished results, please state explicitly that you would like the results mentioned in the column. Comments and corrections are also welcome. For more details on the nature of the column and the form of desired submissions, see the December 1981 issue of this journal.

40,020 citations

Journal ArticleDOI
TL;DR: In this paper, the authors describe a self-organizing system in which the signal representations are automatically mapped onto a set of output responses in such a way that the responses acquire the same topological order as that of the primary events.
Abstract: This work contains a theoretical study and computer simulations of a new self-organizing process. The principal discovery is that in a simple network of adaptive physical elements which receives signals from a primary event space, the signal representations are automatically mapped onto a set of output responses in such a way that the responses acquire the same topological order as that of the primary events. In other words, a principle has been discovered which facilitates the automatic formation of topologically correct maps of features of observable events. The basic self-organizing system is a one- or two-dimensional array of processing units resembling a network of threshold-logic units, and characterized by short-range lateral feedback between neighbouring units. Several types of computer simulations are used to demonstrate the ordering process as well as the conditions under which it fails.

8,247 citations

Book
01 Dec 1973

5,169 citations


"Static pickup and delivery problems..." refers methods in this paper

  • ...In the first phase clusters of customers are formed using the average linkage method ( Anderberg 1973 )....

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